Incorporating Reliability Performance Measures into Operations and Planning Modeling Tools (2014)

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7RESEARCH BACKGROUND The chapters in this part of the report discuss the fundamental issues of incorporating travel time reliability into modeling tools, investigate the feasibility of incorporating such into plan- ning models, and identify the functional requirements for incorporating travel time reliability into simulation models. p A r t 1

8exacerbated recurrent congestion (if the baseline capacity is not adequate to accommodate even the average demand). • Network capacity model. This model should incorporate the average (baseline) capacity for the given season, day of week, and hour that is contrasted to the average demand to estimate a general inadequacy that leads to recurrent con- gestion. In addition to the baseline capacity, this model should include estimation of the impacts on capacity of lane/road closures for road maintenance/construction, as well as the impacts of extreme weather conditions (signifi- cantly different from the usual weather conditions for the given season and hour), both of which are major supply- side nonrecurrent congestion factors. • Network simulation model. This model should integrate the demand and network supply sides through route choice, traffic flow effects, and individual microsimulation of vehi- cles within the traffic flow. This model also provides a level- of-service-feedback to the demand model as part of a global demand-supply equilibration. This model should incorpo- rate the impacts of traffic control devices and the occur- rence of traffic incidents, factors that also generally lead to nonrecurrent congestion. However, when network capac- ity is generally inadequate and congestion levels are high, nonoptimal settings of traffic controls can result in (addi- tional) recurrent congestion effects. The incorporation of reliability factors into the models can be done in either of two principal ways: • Analytically. Travel time is implicitly treated as a random variable and its distribution, or some parameters of this dis- tribution (such as mean and variance) are described analyti- cally and used in the modeling process. • Empirically. The travel time distribution is not parameterized analytically but is simulated directly or explicitly through multiple model runs with different input variables (multiple scenarios). Fundamental Issues of Incorporating Travel Time Reliability into Modeling Tools C h A p t e r 2 Introduction The general methodology for the inclusion of reliability in planning and operational models formulated in this research is based on the basic notion that transportation reliability is essentially a state of variation in experienced (or repeated) travel times for a given facility or travel experience. The pro- posed approach is further grounded in a fundamental distinc- tion between (1) systematic variation in travel times resulting from predictable seasonal, day-specific, or hour-specific factors that affect either travel demand or network service rates and (2) random variation that stems from various sources of fluc- tuation that are largely unpredictable (to the user). A proposed general modeling framework for addressing both systematic and random variation is shown in Figure 2.1; the systematic sources of variation are addressed exogenously through model segmentation and demand-supply scenarios, creating the backdrop against which the random sources of variation are modeled. Depending on the intended application, these sources are modeled both in terms of their direct impact on network performance and the responses of travelers, which comprise resulting changes in travel demand. The general model framework includes three major com- ponents, each related to a certain subset of reliability factors associated with either recurrent or nonrecurrent congestion: • Demand model. This model should incorporate the average (baseline) demand for a specific season, day of week, and hour that can be compared with the corresponding average network capacity to estimate a general inadequacy of sup- ply that leads to recurrent congestion. In addition to the baseline demand, this model should include the generation of special events and a mechanism for accounting for other sources of day-to-day fluctuations in demand. A special event results in nonrecurrent congestion, while other day- to-day fluctuations can manifest themselves as either non- recurrent congestion (if the baseline capacity has enough reserves to accommodate most of the fluctuations) or

9 There are pros and cons associated with each method. The vision emerging from this research is that both methods are useful and could be hybridized to account for different sources of travel time variation in the most adequate and computa- tionally efficient way. In particular, the team considered ana- lytical methods whenever possible; they are generally preferable from both a theoretical point of view (particularly for network equilibrium formulations) and in terms of a more efficient use of computational resources in application. Generally, the factors that can be described by means of ana- lytical tools and probabilistic distributions relate to the baseline demand and capacity estimates, day-to-day variabil- ity in travel demand, impact of weather conditions, traffic control, route choice, meso effects associated with traffic flow physics, and individual driver behavior. Factors that can prob- ably be better modeled through explicit scenarios, rather than captured by probabilistic distributions, mostly relate to spe- cial events, road works, and occurrence of incidents. Some factors—like day-to-day fluctuations in demand, weather conditions, and traffic control—can be modeled in both ways. It should also be noted that an explicit simulation by scenarios is in itself based on a probabilistic distribution Demand model Network capacity Network simulation A Analytical methods S Multiple simulations Sources of unreliabilityRecurrent Non- recurrent Road works Weather Traffic control Special events Day-to-day fluctuation Incidents Inadequate base capacity Season Day of week Hour of day Systematic variation Average demand Average capacity A S S S A S A A A S S Route choice Flow meso effects & breakdowns Individual driver behavior A A A Figure 2.1. General methodology for incorporating reliability into traffic analysis models.

10 of input parameters (such as parameterized probability of occurrence of a certain event). However, the principal differ- ence is that the resulting variation in travel times is generated through multiple simulations, rather than derived analyti- cally from the distribution of input variables in a one-time network simulation. The following sections discuss each of the reliability factors in detail, survey existing approaches to their modeling, and propose specific approaches for the current project. Incorporating reliability into planning and operation Models Reliability as an Objective Network Performance Dimension Characterization of Reliability Through Variability of Travel Times In a very practical and constructive way, reliability is character- ized by the lack of variability of travel times. This approach is largely adopted for the current project, as well as for the entire set of SHRP 2 projects. It should be noted, however, that if a more general view of highway system performance is adopted that includes such additional dimensions as variable cost (e.g., as a result of real-time dynamic pricing) and safety, then the highway reliability definition should be extended accordingly. Another salient point specifically discussed in Institute for Transportation Studies (2008) is that reliability also can include the ideas of trustworthiness and reliance, which can be affected by information available to highway users. Travel time variability can be measured and analyzed in many different ways and at different levels of disaggregation; this is both important to and a complicating factor for this research. To constructively measure variability of travel times, a specific time unit must be chosen in terms of interval dur- ing the day (e.g., an hour between 7:00 a.m. and 8:00 a.m.), day of week (e.g., Monday), and season (e.g., fall). This is nec- essary to set aside differences in travel time that occur between hours of the day, between days of the week, and between sea- sons; such differences are considered systematic variations because they are predictable, at least for most highway users familiar with the travel conditions in the area. The remaining variability of travel times across different days for the same unit (hour, day of week, and season) can then be used as the basic measure of travel reliability. Many factors can produce different travel times for the same highway facility or route even if the same user drives through it on two or more consecutive workdays at the same time (see Figure 2.2). Also, because of differences in driving style, two different drivers may exhibit quite different patterns of travel behavior that result in significantly different travel times for exactly the same route even if they depart at the same time. Given all of these considerations, the team concludes that travel time variability should be measured by variation across individual trajectories for the given facility and time unit. This factor should be incorporated into network simulation tools (most naturally, through microsimulation). Thus, for reliability analysis purposes, the framework unifies all particle- based simulation approaches as long as they produce vehicle trajectories. This general modeling approach is based on two major principles: • Incorporate the causal or systematic determinants of vari- ability as much as possible (given the state of the art in traffic theories and behavioral models); and • Add the remaining inherent variation through suitably calibrated probabilistic mechanisms. However, from the perspective of evaluation of highway performance for planning purposes, it is not reasonable to include individual variation in travel times (and factors like Systematic variation Network reliability Individual variability Season of year Day of week Hour of day Main unit of operations analysis: Variability of average travel time for the same season, day of week, and hour of day across days Day-to-day variability in demand Alternative modes Traffic control Road works Weather conditions Special events Main unit of behavioral analysis: Variability of individual travel time for the same season, day of week, and hour of day across days Average demand Average network capacity Dynamic pricing Incidents Route choice Driving behavior Figure 2.2. Factors and dimensions of travel time variability.

11 driving style) as a reliability component. Thus, for measuring reliability from the operations perspective, travel time vari- ability should be averaged within the chosen time unit. For the current project, the team adopted the following definition for reliability as a highway performance measure: Reliability as a highway performance measure is characterized by variability of travel times for the same chosen time unit (hour, day of week, season) observed for different days and averaged across individual travel times observed within the unit for the same day. By virtue of this definition, the corresponding network simu- lations incorporating reliability should be implemented with the same level of temporal resolution in terms of demand and supply, that is, hour/day/season-specific trip tables and hourly static traffic assignments (STA) or dynamic traffic assignments (DTA) covering several successive hours. For individual behavioral analysis, additional sources of vari- ation, such as different routes and different driving styles across individuals, are important. Thus, the team arrived at a different definition for individual behavioral analysis and microscopic modeling: Reliability as a LOS measure for individual behavior is char- acterized by variability of travel time for the same chosen unit (hour, day of week, season) across individual travel times observed within the unit. This duality of reliability has a direct implication for the modeling approaches considered for the current project. Approaches that are based on macro modeling paradigms (i.e., operate with aggregate traffic flows) can only incorporate reli- ability in the aggregate sense (first definition). Approaches that are based on individual microsimulation (i.e., operate with individual particles like persons on the demand side and vehi- cles on the network supply side) can address both types of reli- ability. Because several meso modeling paradigms capture characteristics of individual particles, the lines are increasingly blurred between micro and meso approaches—thus the refer- ence to particle-based approaches as a basis for the approach developed in this study. Approaches to Quantification of Travel Time Variability Many quantitative measures have been proposed for travel time variability in different contexts, but most frequently for one of two distinct purposes: either for overall assessment of the highway facility performance, or for explaining individ- ual preferences for a route, trip departure time, or mode for a particular trip. All such measures can be derived from the travel time distribution and none of them can be claimed to be particularly right or exhaustive. Each of them makes sense in its particular context. From the perspective of highway operations, decisions about highway capacity expansion and traffic management reliability of travel times on a certain facility are naturally the focus of the analysis. Most of the actual data on travel time variability have been collected at the facility level. These data sources are valu- able for building analytical functions that relate reliability mea- sures to the traffic volume and facility characteristics (number of lanes, length, cross-sectional design, access, traffic signals). For example, robust statistical dependencies have been estab- lished between almost all reliability measures, including stan- dard deviation; 80th, 90th, and 95th percentile; buffer time and index; and average traffic volumes at the facility level. The SHRP 2 L03 project, Analytical Procedures for Determining the Impacts of Reliability Mitigation Strategies, specifically focused on this particular issue (Cambridge Systematics, Inc. et al. 2013). The specific measures of reliability that were proposed by the L03 team and which have largely been accepted in the majority of SHRP 2 projects are discussed in the next section. Having these functions in place, however, does not yet provide an immediate basis for network simulation and travel demand models. Highway facilities represent elemental links in the high- way network. The crux of the modeling challenge is that reli- ability measures have to be generated at the trip route level, since that is the unit for which travel choices are essentially modeled. Construction of route-level reliability measures from facility-level reliability measures is a nontrivial problem since almost all reasonable reliability measures (e.g., travel time stan- dard deviation) are not additive by links, and those that might be additive under certain conditions (e.g., travel time variances if assumed independent by links or buffer time) cannot be assumed independent in a general case. User’s Perspective Reliability as Travelers’ Subjective Perception and Determinant of Travel Behavior Travel demand models and network simulation tools are based on the mathematical representation of choices made by the travelers with respect to network routes, departure times, modes, destinations, and frequencies for each trip type. Specifi- cally, in the new generation travel demand models—called activity-based models (ABM)—and microscopic network sim- ulation tools, the individual nature of these choices has been made explicit. These models have been developed and esti- mated not only to replicate the observed aggregate traffic flows but also to replicate individual-level choices with the maximum degree of behavioral realism so as to provide reasonable predic- tions of responses to future scenarios and policies.

12 Obtaining behavioral realism in individual choices requires taking into account travelers’ subjective perceptions of reliabil- ity, as well as the entire set of highway LOS attributes. Subjective perceptions of travel attributes can be quite different from their objective measurements. This phenomenon is well known to transportation modelers and has been long taken into account in some manner within the framework of conventional models. For example, in transit assignment and mode choice, compo- nents of out-of-vehicle transit travel time such as wait and walk time are applied with perceived weights relative to in-vehicle time that are significant (in the range of 1.5 to 4.0). It is also not unusual for transit in-vehicle time to be differentiated by mode to reflect that rail modes are generally perceived as more conve- nient and comfortable than conventional bus. On the highway side, most of the travel models and network assignment procedures operate with a generic physical time variable regardless of the facility type, level of congestion, and associated reliability characteristics. There is compelling statis- tical evidence from behavioral studies that travelers place a very significant value on reliability and other highway time attri- butes, such as the level of congestion and driving conditions. Thus the concept of value of reliability (VOR) was introduced to complement value of time (VOT). See Concas and Kolpakov (2009) for a good survey of research and practical works in which VOT and VOR were estimated. The highway operations perspective primarily relates the quantification of reliability to the comprehensive monitoring and measurement of the actual physical traffic times and speeds observed in the traffic flow. In contrast, the user’s perspective cannot be directly measured with roadside observations; it can only be quantified by relating user choices with respect to net- work routes, trip departure times, modes, and so on to actual travel times and reliability measures. For each of these travel choices, the corresponding behavioral parameters like VOT and VOR are established by statistical estimation of the correspond- ing choice models. The SHRP 2 C04 project, Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand, is specifically devoted to this issue and provides behavioral models of route choice, trip departure time choice, and mode choice incorporating reliability measures for the L04 project (Parsons Brinckerhoff et al. 2013). In summary, the following two important aspects of the problem need to be taken into account when the user’s perspec- tive on reliability (and performance in general) is compared with the highway operations perspective: • The user perspective can include many perceived compo- nents and weights compared with the physical measures of average travel time and reliability in the highway operations perspective. The measure that looks the best and most sta- tistically significant from the highway operations perspec- tive might not be the best choice for modeling user responses. For example, the 95th percentile of travel time is favored in highway operations because it singles out the most critical cases of nonrecurrent congestion, mostly those associated with traffic incidents, road works, special events, and extreme weather (see Cambridge Systematics, Inc. 2005; Cambridge Systematics, Inc. et al. 2013). The current experience with models of individual behavior in the context of route choice, however, indicates that the decision-making point at which users evaluate reliability lies somewhere between the 80th and 90th percentile thus mixing recurrent and nonrecur- rent congestion (see Concas and Kolpakov 2009; Parsons Brinckerhoff et al. 2013). • The user perspective is inherently an entire-trip perspec- tive. Thus, the reliability measures for travel models and network simulation tools have to be synthesized at the O–D-route level, while the bulk of statistical evidence on highway operations is collected at the facility/link level. This synthesis is not a trivial task because practically all sensible reliability measures are inherently nonadditive (Institute for Transportation Studies 2008). Although reliability measures adopted for a travel model are different from reliability measures adopted for the analysis of highway operations, this fact does not mean that the opera- tional simulation tools cannot be used to generate the reliabil- ity measures needed for highway performance evaluation as an aggregate output. Eventually, the modeling tools designed in the current research will be able to generate the entire distribu- tion of travel times for each network link, which would suffice for constructing virtually any reliability measure. Reliability as a Decision-Making Factor in Transportation Operations and Scheduling In addition to the general highway systems performance per- spective and the individual driver’s perspective which consti- tute the focus for this research project, there are several other important highway users, each with its own perspective on reliability. The other types of highway users and their per- spectives include the following: • Freight companies and truck operators. In certain regions, trucks constitute a significant share of traffic, and it is a nor- mal practice to single them out as a separate vehicle class in traffic assignment (sometimes subdivided into heavy trucks, light trucks, and/or commercial vehicles), as well as have a separate demand model for them. Trucks are treated as a separate vehicle class because of their different speed and delay functions, possible network prohibitions, different toll rates, and VOT. With respect to reliability, trucks have an especially strong impact on traffic conditions and rep- resent a risk factor in traffic. In general, all else being equal,

13 the higher the share of trucks in the traffic, the higher the variability of travel times. A related issue that has not yet been fully explored is the associated willingness to pay for travel time savings and reliability improvements. The behavioral mechanism associated with freight movements under the condition of uncertain travel time is different from the con- sideration of reliability by private car drivers, although there may be some commonalities (such as the consideration of buffer times for on-time arrival at the destination). Some trucking companies, such as FedEx or UPS, might be signifi- cantly more willing to pay for improvement in travel time reliability than an average trucker because those companies specialize in real-time deliveries. It should be recognized, however, that modeling truckers’ responses to reliability improvements is fundamentally different from modeling private car users’ responses in that, frequently, the truckers are not the actual decision makers; thus the whole (compli- cated) aspect of dispatching and scheduling comes into play. • Logistics companies. This category is another (sometimes invisible) player on the field. Logistics companies essentially generate the demand for truck movements and affect all choices on the truckers’ side with respect to travel time and reliability improvements. Unfortunately, most transporta- tion models attempt to model truck movements directly and ignore the logistics component since it is very complicated. It is unrealistic to tackle this issue in the framework of the current project. • Bus companies. Transit service reliability is an issue that is equally as important as highway reliability for the improve- ment of modeling tools. Travelers perceive transit schedule adherence as one of the important attributes of a transit service (Institute for Transportation Studies 2008). Cars, trucks, and buses share the same road space in a mixed- traffic case, thus highway reliability directly affects bus ser- vices. It is generally agreed that due to their high occupancy levels, buses have very high underlying VOT and VOR per vehicle. This could be a very significant component in the evaluation of user benefits stemming from reliability improvements associated with special bus lanes as well as high-occupancy vehicle (HOV) and high-occupancy toll (HOT) lanes shared with buses. • Taxi cab companies. In some urban areas taxis constitute a significant share of the traffic. For example, the share of taxis in internal traffic in Manhattan is almost 40%. This is, however, a rare case; taxis represent a negligible compo- nent in traffic in most metropolitan regions in the United States. Consequently, for modeling purposes taxis are fre- quently mixed with high-occupancy vehicles in terms of VOT, VOR, and other behavioral attributes that govern their route choice, departure time choice, and other related choices. To be exact, the full-day movement of taxis is rarely modeled, and the modeling system includes only the portion of their itinerary associated with the passenger trips they serve. The validity of these modeling assump- tions has not been explored, and research relating to cab drivers’ behavior is practically nonexistent. These specific markets are not the focus of the current project and are left for future research. Reliability as a Result of Travel Decisions The inclusion of travel time reliability in operational models that are based on individual microsimulation implies a two- way linkage between the demand and network supply sides. In the direction from the network to the demand model, travel decisions (e.g., route choice) are obviously affected by reliabil- ity, with drivers strongly preferring routes that are more reli- able and predictable in terms of travel time. However, a model that includes only this linkage (i.e., feedback from the network supply model to the demand model that includes both average travel times and reliability measures) would not be complete without feedback to the network simulation. This aspect of modeling reliability is important and actually less explored: the generation of reliability measures as a result of travel decisions made by multiple participants in the traffic flow. The most common way to establish this linkage (with methods largely inherited from the equilibrium techniques developed for conventional network assignment tools) is to model link-level reliability measures as an aggregate statistical function of the average traffic volume (or average travel time), which is itself a function of average traffic volume (Watling 2006; Institute for Transportation Studies 2008). This is one possible approach, probably the most straightforward, and will be discussed in detail in the subsequent sections. A traffic microsimulation platform in combination with a microsimulation demand model offers additional ways to gen- erate travel time distributions for quantifying reliability, beyond the type of analytical functions of volume-delay-reliability that are built using aggregate statistical analysis (i.e., without explicit modeling of the particular mechanisms that lead to travel time variation). In particular, such phenomena as flow breakdown or the genesis of traffic collisions can be effectively and efficiently simulated explicitly at the micro- or meso-level. The same approach can be applied to special events on the demand side. This leads to the concept of an approach with multiple simulations (scenarios) that would produce travel time distributions (and any reliability measure derived from them) in a nonanalytically explicit way. This avenue of research is also discussed in detail in the subsequent sections. The ultimate outcome of the current project is a complete model that includes both analytical and empirical (multiple- simulation) features to produce a reasonable, stable demand- supply equilibrium solution accounting for travel time

14 reliability in both directions of the modeling: from supply to demand (impact of reliability on travel choices) and from demand to supply (generation of reliability measures as a result of travel decisions). Implication for Planning and Operation Models Improving Reliability as a Policy Objective Tackling traffic congestion and improving reliability has been recognized as one of the most important strategic goals of the highway transportation industry. Numerous technical mea- sures and policies related to these issues have been considered in the SHRP 2 program. However, the genesis of this research project is the recognition that it is essential to improve plan- ning models in parallel with these developments to have suit- able evaluation tools for projects and policies that improve reliability. From this perspective, when considering different possible approaches to the modeling of reliability, approaches that have the prospect of giving rise to a fully operational and com- plete regional travel model are taken the most seriously. For these, the following modeling principles should be met: • Measures of reliability should be incorporated into travel demand models, specifically in mode choice and time-of- day choice, and (through these choices or in a different way) incorporated into the other travel choices, such as destina- tion choice and trip frequency choice. This research direc- tion is characterized by the largest body of work and proposed approaches. However, most of the results reported so far have been based on stated preference (SP) exercises; only a few based on revealed preference (RP) cases have ever been published. • The reliability measures should be incorporated into net- work simulation models in such a way that they can be effec- tively generated within the network simulation procedure, as well as affect the route choice embedded in it. This research direction is characterized by a relatively scarce subset of pub- lished works and suggested approaches. Most of the attempts resulted in path-based route choice models with complicated path utilities that cannot be directly incorporated into real- world network simulations. • The travel demand models and network simulation models that incorporate reliability measures should be combined in a certain equilibrium framework. It is probably unrealis- tic to expect that a closed-form equilibrium formulation with reliability measures will ever be found. It is more real- istic to construct a so-called loosely coupled demand-supply model with at least some level of consistency between the reliability measures generated by the network simulation and those used in the route choice and demand models. The existence and uniqueness of the equilibrium (stationary) solution in this case becomes largely an empirical issue. This area has been demonstrated as part of the SHRP 2 C04 project with a restricted set of travel decisions in the equilibration loop (Jiang et al. 2011). • The travel demand models and network simulation mod- els that incorporate reliability measures must be opera- tional in large networks. This is especially challenging for the network supply side, since most of the proposed for- mulations inherently require path-based assignment. Incorporating Reliability as a Way of Improving Modeling Tools The incorporation of travel time reliability is generally recog- nized as one of the main strategic directions for improving modeling tools on both the demand and the network-supply sides. It relates equally to the reliability of highway and transit times, although only highway reliability is the subject of the current research. Current practice and the existing culture of travel modeling are almost exclusively based on modeling with average travel times, ignoring actual travel time variability. There is generally no difference in this regard between 4-step and advanced activity-based models on the demand side, or between static and dynamic traffic assignments on the network simulation side, in current practice. As the result of excluding reliability, many of the travel phenomena associated with reli- ability cannot be modeled properly; consequently, the models are required to incorporate a large number of nonbehavioral and nonparameterized constants that are calibrated to repli- cate the base year data. The following common examples can be specifically mentioned in this respect: • Large mode-specific biases in mode choice, specifically for rail transit services to areas associated with a high level of congestion (e.g., metropolitan cores). • Positive toll road biases that capture all factors beyond average travel time and cost trade-offs, but primarily reli- ability (though there are some other factors that can con- tribute to this bias such as toll-averse behavior in a region where toll roads have not been used before). These nonbehavioral and nonparametric components, how- ever, can only help to shape the model to look good for the base year. They are not helpful for modeling new projects and policies that are intended to change reliability. For example, modeling a dynamic real time pricing facility that is designed to maintain a guaranteed LOS on the managed lanes repre- sents a new challenge to travel modeling that cannot be fully addressed with existing models even excluding an explicit modeling of reliability.

15 Respective Roles of Planning and Operation Models in Addressing Reliability It is unrealistic to expect that it will be possible to establish one particular set of reliability measures associated with one par- ticular method of incorporating reliability into demand and network simulation tools—that is, “one size fits all.” First, as existing practice shows, there are different modeling tasks asso- ciated with highway planning and operations analysis that lead to different modeling frameworks and scales. Second, the team has distinguished between state-of-the-art, which reflects the best and theoretically consistent solutions available regardless of their complexity, and state-of-the-practice, which reflects numerous current constraints associated with the network size, reasonable runtime, data availability, and complexity for model use and analysis of results in a practical setting. The cur- rent research project aims to cover and provide guidance for all four possible combinations of the following modeling tasks and frameworks: • Complete regional-scale model for planning applications (e.g., traffic impacts of a new or significantly improved highway facility), including demand side and network simulation with consideration of equilibrium—a state-of-the-art ver- sion based on an advanced activity-based microsimulation demand model that provides a way to link the demand and supply sides at the individual level. • Complete regional-scale model for planning applications, including demand side and network simulation with con- sideration of equilibrium—a state-of-the-practice version based on an aggregate demand model. • Corridor-specific model for highway operations analysis, including demand side and network simulation—a state-of- the-art version based on microsimulation of demand with a mode choice component. • Corridor-specific model for highway operations analysis, including demand side and network simulation—a state-of- the-practice version based on aggregate demand without a mode choice component. The Crux of Reliability Modeling Significant progress has been made in recent years in research on reliability, in a number of different directions that include qualitative characterization of reliability and congestion [see Cambridge Systematics, Inc. (2005) for a good overview], quan- titative methods to measure reliability and VOR [see Concas and Kolpakov (2009) for a good synthesis], and mathematical models of reliability [see Institute for Transportation Studies (2008) for an extensive survey]. These research streams, however, have not yet been constructively combined into a single theoretical framework that would produce a complete operational travel model addressing reliability in both the demand and network simulation sides. The crux of the problem seems to be in the inevitable com- plexity that arises from any attempt to reconcile the following logical requirements for the model structure: 1. The model system should operate with some specific quan- titative measures of reliability—that is, travel time variabil- ity (standard deviation, buffer time, etc.)—in addition to average travel times and cost that are modeled in current practice. 2. The model system should integrate the demand and net- work simulation sides in a reasonable way. Ideally it should be an equilibrium formulation. In practical terms, some logical structure of feedback with an empirical proof of convergence obtained within a reasonable number of iter- ations would suffice. 3. The demand side of the model (specifically, mode choice and time-of-day choice, as well as other travel dimensions depending on the model structure) should be sensitive to the reliability measures. Since these models are inherently O–D-trip-level models, these reliability measures should be fed to them at the entire-route level. 4. The network side of the model (specifically, the functional or simulated dependences of link travel time distributions and derived reliability measures on link traffic volumes) should be based on the observed data from highway oper- ations. The physics of traffic flow occurs and is observed at the link level. From this point of view, the model should be well calibrated to replicate the observed link-time vari- ability patterns as functions of link (average) volumes. 5. The route choice model that is embedded in the network simulation model (assignment) should be sensitive to link reliability measures and also be able to produce O–D-level reliability skims for the demand model. So far, all attempts to formulate such a model have resulted in computationally overly demanding path-based constructs, because of the inherently non-additive-by-link structure of all conceivable reliability measures. These formulations also required some very specific and simplifying assumptions about the link-level distributions (e.g., independence) that fail to account for such essential features as the correlation between the adjacent links because of mutually shared traffic flow. For this reason, it is very difficult to reconcile requirements 2, 3, and 4 in a behaviorally reasonable and computationally effi- cient route-choice framework. In light of these considerations, the main objective of the current L04 research project is to find a solution to this prob- lem by means of certain empirically justified simplifications and arrive at a practical solution that can be applied at the regional scale.

16 Specific Impacts of Congestion and Travel Time Reliability on Individual Travel Behavior Travel time reliability has been generally recognized as an important missing component in the previous generation of travel demand models and network simulation tools. However, as important as it is, reliability is not the only additional issue or variable that needs to be incorporated into existing travel models to better address and account for congestion. To cap- ture the impact of reliability effectively and correctly in demand models, a behavioral framework that captures the various dimensions in which congestion and its manifestations affect travel choices is needed. The L04 team believes that a deeper understanding of congestion impacts on travel behavior should include several additional aspects that directly or indirectly interact with the perception and effect of reliability, as discussed in this section of the report. Unreliable Travel Times This is the most commonly recognized aspect of conges- tion that gives rise to the notion of reliability. As previously explained, the attempt to quantify this factor leads to dif- ferent measures of travel time variability. Perception of Highway Travel Time by Congestion Levels and Correlation with Reliability The practice of using differential weights for different travel time components was introduced long ago and has been uni- versally accepted for transit modeling. Transit in-vehicle time, walk time, and wait time are perceived differently by riders; the corresponding estimated utility function coefficients (weights) normally range between 1.0 and 4.0, with the highest weights associated with waiting time under uncertain conditions. There has not been, however, a parallel effort to estimate per- ceived highway time as a function of highway level of service. Perceived highway time has always been implicitly assumed to be a totally generic variable in both route choice and mode choice models, as well as in the use of mode choice “logsums” or “generalized cost” in the trip distribution and upper-level models (in a hierarchical choice structure). However, a behav- ioral analogue—between an uncertain waiting time for an unreliable transit service and an uncertain waiting time for being stuck in a car in a traffic jam—is appealing. The team believes that the idea of a perceived highway time structure (e.g., by travel speed categories) might be very beneficial from both a theoretical and a practical modeling perspective. Either as a simple operational proxy for reliability or as a complemen- tary model parameter, perceived highway travel time under different conditions might be useful, especially in the context of applied operational models. The reason that this is relevant for this project is because unreliability manifests itself and affects demand in several complementary ways that are weighted differently by travelers. Different Patterns of Highway User Behavior in Presence of Unpredictable Travel Times A major assumption underlying conventional modeling approaches that becomes unrealistic under congested condi- tions is that travelers (and specifically highway users) possess full information about all possible routes and modes and make rational decisions. In behavioral terms, congestion and associated unpredictability of travel times lead travelers to make seemingly irrational decisions based on intuition and past experience that may or may not be relevant for the cur- rent situation. In modeling terms, we might expect the associ- ated choice models to have relatively smaller coefficients for travel time and cost (more random behavior and regardless of VOT) compared with models estimated for uncongested areas where travel time is predictable. As a result, in a route choice framework we might expect large deviations from the calculated shortest path. This general pattern will be affected by the travel information system, and more so as congestion creates demand for real-time informa- tion. Travel information is especially essential for highway users who are not familiar with the area and do not implement trips along this route regularly; thus, this aspect requires some non- traditional segmentation of the driving population. Specific inclusion of reliability information in addition to prevailing travel times could significantly affect this behavior (Dong and Mahmassani 2009). Disequilibrium (Lagged Feedback) between Travel Demand and Network Performance Another interesting and less investigated aspect of modeling reliability relates to the equilibrium formulation. It is gener- ally recognized that travel models should reach a perfect (simultaneous) equilibrium between the demand and supply sides; a corresponding theory and effective algorithms are well established for aggregate 4-step models. While the con- cept of equilibration is more ad hoc with the new generation of activity-based microsimulation models, the intention is still to reach a perfect equilibrium. Equilibrating with reliability as a demand factor has only recently been reported in the con- text of a dynamic corridor analysis (Zhou et al. 2008). It is interesting to note that integrated land-use and transporta- tion models have never used the concept of static equilib- rium, since the land-use and transportation responses belong to different time scales. Most integrated land-use and trans- portation models incorporate the concept of lagged equilib- rium. In reality, there are also numerous and very different time scales within a travel demand model itself. In the

17 presence of congestion that makes travel time unstable, the process of traveler learning and adaptation associated with reaching equilibrium becomes longer and fuzzier. Integrating demand and supply models, with explicit consideration of reliability, has been addressed in the course of the current project, as well as part of the SHRP 2 C04 project. Different Time Scales for Traveler Responses Another important and related aspect is the identification of the time scales for each travel dimension and model compo- nent that are behaviorally appropriate and which can also result in operational model structures. This issue is also the focus of the SHRP 2 C04 project, Improving Our Understand- ing of How Highway Congestion and Pricing Affect Travel Demand (Parsons Brinckerhoff et al. 2013). The range of travel choices with very different time scales for traveler responses that are affected by travel time reliability is wide. Short-term responses include such travel dimensions as network route choice (including any portion of the route when new travelers’ information becomes available), route type choice (toll versus nontoll and/or managed lanes versus general-purpose lanes), trip departure times, and possibly mode choice (if a transit option is competitive). Since the perception of travel time reli- ability generally stems from observed variability over time, it requires a certain learning curve and experience from travelers to perceive it and respond to changes (though an advance information system that provides reliability estimates along with the shortest and/or average travel times can change this drastically). Models that are based on the distribution of travel times imply that the travelers have a good idea about this dis- tribution; in practical terms that probably means at least five to 10 recent trips along the route at the same time of day. Researchers have yet to explore how the modeling assump- tions about travelers’ knowledge and information match the reality, but this is largely the same problem with the conven- tional models that operate with average travel time. The assumptions about drivers’ perfect knowledge and immediate response to changes in average travel times are seen to be essen- tial for making the models analytically simple and operational, but they might be quite far from reality. Classification of Sources of Travel Time Variability Survey of the State of the Art and State of the Practice This is a well-explored area, at least on the qualitative side. There have been several comprehensive surveys reported in literature, reflecting some consensus regarding the major sources of travel time variability and corresponding mechanisms that affect travel time (Cambridge Systematics, Inc. 2005). Traffic delay factors. As stated in the request for proposal and according to previous research, seven major factors account for approximately half of all traffic delay and, there- fore, a great deal of the uncertainty associated with travel time: (1) traffic incidents, (2) work zones, (3) weather, (4) special events, (5) traffic control devices, (6) fluctuations in demand, and (7) inadequate base capacity. These factors are well described and analyzed in Anatomy of Congestion (Cambridge Systematics, Inc. 2005, Figure 2.3). They do not always affect travel time reliability separately. They often interact, which increases the challenge of reducing the uncertainty of travel time that drivers experience. While the L04 team accepts this classification as a very good and constructive starting point, this project incorpo- rates certain details in the research that are important for operationalizing the simulation models that would address these factors. In particular, this research distinguishes between the systematic and random variation factors (loosely corre- sponding to recurrent and nonrecurrent congestion) as well as between demand and supply (network) sides. Systematic and random fluctuations in demand and network supply. It is important to distinguish between systematic and random variations in both travel demand and network sup- ply. Speaking rigorously, reliability should only relate to the random variations (recurrent and nonrecurrent), while pre- dictable systematic variations should not be included. On the demand side, that means year-to-year trends (associated with population growth, land-use development, and transporta- tion network changes), seasonality, day-of-week fluctuations, and even certain large-scale one-time events planned in advance should not be considered as unreliability manifesta- tions, but rather modeled explicitly. For example, Olympic Games or large conventions should not be directly counted in the travel time variation measures. The systematic demand variations essentially affect the basic equilibrium point from which unreliability effects are measured. Factor 7, inadequate base capacity, also relates to the basic equilibrium point. In the same vein, systematic seasonal variations in the driv- ing conditions in certain regions due to extreme but predict- able weather (e.g., winter/icy periods in northern regions, rainy periods in tropical regions) should be included in the basic equilibrium conditions and not mixed together with the other seasons when the travel reliability measures are calculated. What follows is a suggested list of true random variation fac- tors that should be included in the reliability calculation. The factors are broken into demand-side and supply-side groups. On the demand side the following factors can be referred to as demand spikes: • Special events such as sport events, large conventions, exhi- bitions (Factor 4). This factor relates to nonrecurrent congestion.

18 • Day-to-day fluctuations due to an inherent randomness of individual behavior (people do not repeat the same trips exactly every day), as well as to variations on the activity supply side, for example, not the same business meeting in the office every day (Factor 6). This factor relates to recur- rent congestion since it is always present in the travel demand generation process. • Nonresident populations such as visitors staying in hotels and making trips in the area along with the modeled popu- lation of residents. If the number of visitors is significant and there is a clear seasonal pattern in their arrival, a spe- cial visitors’ model should be developed along with the core demand model. In any case, this demand component is normally characterized by a higher level of variation compared with the resident household behavior. This fac- tor relates to recurrent congestion since it is always present in the travel demand generation process. • Temporary closure or significant change in frequency of alternative modes (rail, bus, or other services). This factor relates to nonrecurrent congestion. On the supply side, the following factors can be referred to as drops in throughput: • Incidents (Factor 1). This factor relates to nonrecurrent congestion. • Work zones (Factor 2). Again, incidental traffic changes for road maintenance should be distinguished from planned large-scale road construction. This factor relates to non- recurrent congestion. • Weather/visibility beyond predictable seasonal fluctuations (Factor 3). This factor relates to nonrecurrent congestion. • Impact of traffic control devices (Factor 5). This factor generally relates to nonrecurrent congestion. • Randomness of individual driver behavior. For example, an HOV lane can be blocked by a single slow driver, just as one slow heavy truck can create a bottleneck on a two-lane road. This factor generally relates to recurrent congestion since it is always present in the traffic flow. Quantification of factors producing travel time variation. The team explored a method for modeling each type of factor of travel time variation. In general, a Monte Carlo variation of random numbers involved in the microsimulation process is only one of the approaches. Many of the seven factors fall into the area in which the randomness can be parameterized and probabilities can be assigned based on the known param- eters of the demand and/or supply. Quantification and integration of these factors in the demand-supply equilibrium is needed to produce the travel time distributions by link, segment, and trip (O–Ds) needed for modeling reliability. It is also necessary to produce the reliability performance measures for the entire system that will serve as the important output of the model for compari- son of different network alternatives, policy, and operation scenarios. The travel time distribution in general will reflect the combination of recurring and nonrecurring congestion as found in real networks. Systematic and random Fluctuations in travel demand and Network Supply: Impact on recurrent and Nonrecurrent Congestion The key question to address from a modeling standpoint, which goes to the heart of the functional requirements as reported in Chapter 4, has to do with the degree of determin- ism with which an inherently stochastic phenomenon can be represented. While this may seem like a contradiction in terms, it is not. The variability in system performance at the center of interest in this project has both systematic causes, which can be modeled and predicted, and causes that can only be modeled as random variables and which occur according to some probabilistic mechanism. There is, how- ever, a continuum between what may be captured as system- atic and what is viewed as a random process with partially or fully known characteristics. In particular, the following aspects have to be taken into account: • It is still necessary to model the physics of the vehicular traffic dynamics when such exogenous events occur. For example, if there is a lane blockage, or bad weather is simu- lated, we still need to be able to model how traffic reacts and maneuvers in this situation. In other words, we need the rules, or logic for vehicular flow under these events. • The statistical distributions need to be calibrated on a location-specific basis, and there is no guarantee that they would be stationary (time-invariant), resulting in considerable burden for practical application. • Because they are exogenously specified, the model would provide no sensitivity to factors that may affect these occur- rences and so would not be responsive to changes in supply and/or demand that are aimed at improving reliability. • Ideally, researchers should capture within the model itself the phenomena that cause the variability experienced in network travel times. It is at this level that differences will be manifested between different simulation approaches, includ- ing micro versus meso versus macro, as well as between the different behavioral rules that may be embedded in a given simulation model. As part of the conceptual framework developed in this study, several sources of variability need to be distinguished,

19 namely, demand- versus supply-side, exogenous versus endogenous, and systematic versus random. Examples in each cell of the resulting taxonomy are shown in Table 2.1. The focus in this research is primarily on modeling the variability in network performance experienced by a given demand pattern. In other words, exogenous variation in demand patterns is not of primary concern; the research does assume that the overall analysis framework recognizes exog- enous variation and allows for consideration of scenarios under different demand realizations, with both systematic and transient demand load variation. The core of the network/supply-side research lies in cap- turing the endogenous sources of variability. Historically, traffic operations (simulation) models have only dealt with supply-side sources of variation. Systematic endogenous sources have generally been at the core of what traffic simula- tion models seek to capture and reproduce. While most microsimulation models used in practice succeed only in capturing flow breakdown under certain situations, captur- ing congestion at junctions and delay at bottlenecks is one of the main capabilities of these models. In general, existing traffic simulation models used in practice tend to produce “sanitized” traffic behaviors without extreme driver maneu- vers. Random variation in various traffic phenomena has also been captured effectively in traffic microsimulation models. To the extent that these random variations are the result of fluctuations in individual vehicle responses, traffic micro- simulation tools (starting with the pioneering approach reflected in the NETSIM tool in the 1970s) sought to capture them through probabilistic quantities and events for virtually all represented driver behaviors. This has come to be viewed as inherent randomness in traffic performance, reflecting in part user heterogeneity and in part background variation that will be present in any microsimulation run. While the hetero- geneity of users is captured through exogenously specified distribution functions for certain key parameters, the inter- actions that determine the resulting performance and its variability are part of the model logic and phenomena explic- itly represented. Three main challenges must be addressed in dealing with these sources of variability: • Bifurcations and chaotic behavior. When do natural inherent fluctuations become more serious sources of disruption and/ or major delay? Some degree of variability is expected by users; purely random sources of randomness (i.e., white noise) tend to cancel out over long trajectories. However, in some cases, successive maneuvers amplify and lead to disrup- tions. Flow breakdown is one example in which time lags and sudden reactions may combine with traffic that is becoming unstable, and the throughput drops considerably. • Endogenizing collision occurrence. Existing models view collisions as exogenous random events that occur accord- ing to some probabilistic distribution input by the user. A recent review by Hamdar and Mahmassani (2008) showed how all existing car-following models used in traffic simu- lation tools effectively precluded the occurrence of colli- sions as a constraint. Alternative car-following models that explicitly produce collisions were proposed by Hamdar et al. (2008) and are currently under further development. • Behavioral parameters for both demand and supply phenom- ena. Included in the taxonomy (Table 2.1) are demand- side behaviors that deeply interact with the performance of the traffic system, namely, route choice and user responses to information and control measures. These remained out- side the realm of traditional microsimulation tools, in which route choice meant application of aggregate turning percentages at junctions as exogenous events. Meso models developed for operational planning applications and intel- ligent transportation system deployment evaluation intro- duced these behaviors explicitly into the realm of network traffic simulation models. They are now recognized as integral to any network-level simulation tool. The team’s approach views demand-side behavioral parameters (that govern phenomena such as route choice and user decisions Table 2.1. Taxonomy of Sources of Travel Time Variability Source of Variability type of Variability treatment in Modeling exogenous endogenous demand fluctuations Systematic Seasonality day of week Mode choice Time-of-day choice Route choice Random Special events weather conditions day-to-day variability in travel behavior Supply/network capacity fluctuations Systematic Road works lane closure Flow breakdown or capacity drop Random weather conditions collision occurrence Merge capacity

20 in response to information) as part of the range of behav- ioral parameters that determine supply-side relations (such as gap acceptance and lane changing in micro- simulation models). These parameters can be viewed as randomly distributed across the population of drivers in a given application that can be calibrated and specified externally, though they play a key role in determining var- ious aspects of network performance through the rules included in the simulation logic. The functional requirements presented in Chapter 4 are intended to identify phenomena and behaviors that account for the observed variability in network traffic performance and to determine the most effective approach for modeling these phenomena at both microscopic and mesoscopic levels. As noted, for reliability analysis purposes, the framework uni- fies all particle-based simulation approaches so long as they produce vehicle trajectories. The general approach to model- ing these phenomena is to incorporate as much as possible, and as may be supported by existing or in-progress theories and behavioral models, the causal or systematic determinants of variability; the remaining inherent variation is then added to the representation through suitably calibrated probabilistic mechanisms. To increase the framework’s usefulness and responsiveness to various reliability-improving measures, the team’s philosophy is to push as much as possible the portion of the total variation from the unexplained (noise) side of the equation to the systematic observable side. This approach can be implemented for both micro- and mesosimulation levels, both of which are addressed in this project. Notwithstanding the desire for explanation, the portion of variability that must be viewed as inherent, or random, is likely to remain substantial. This has important implications for how the models are used to produce reliability estimates, and how these measures are interpreted and in turn used operationally. Approaches to Incorporating travel time Variability into Network Simulation tools While significant progress has been made in understanding how different travel time reliability measures can affect such dimensions of travel demand as time-of-day (trip departure time) choice and route choice, the so-called supply-side of reliability that consists of network simulation of travel time variability measures remains largely an unexplored area. A significant breakthrough is needed to create a consistent methodology and computationally efficient network simula- tion tool that can incorporate distributed travel times. Several principally different ways can be outlined, and while it is too early to decide which of them is the most promising in all respects, some pros and cons are becoming clear. In particular, the following main dimensions and characteristics can be identified: • An analytical approach in which travel time is represented by a random variable (“implicit”) can be contrasted to an approach in which multiple simulation runs are imple- mented (“explicit”). An analytical approach has such advantages as closer relation to theoretical equilibrium formulations. It is tempting to tackle this issue as an exten- sion of the stochastic user equilibrium (SUE) model, though there is a principal difference between accounting for mean of the random travel time that is additive-by-link and any reliability measure. Additionally, a single simula- tion run (though with some implications for analytical complexity) seems more efficient computationally than a multiple-run strategy. Explicit multiple simulations do not directly correspond to any existing equilibrium theory. However, from a practical as well as behavioral perspective, this analytical approach is quite appealing. As shown below, this approach allows for a natural incorporation of such phenomena as special events (on the demand side) as well as flow breakdowns and incidents (on the supply side). An approach that assumes analytical integration with the demand model (assuming that some demand-supply equi- librium can be formulated, existence and uniqueness of the solution can be proved, and practical methods for finding this solution can be developed) can be contrasted to a loose coupling with the demand model by means of iterative application with feedback [referred to as a shell approach in Institute for Transportation Studies (2008)]. While the analytical integration approach has an obvious advantage, it currently looks unrealistic to achieve because of the complexity and frequent nonconvexity of both network- related cost and demand functions. Additional argument in favor of the loose coupling is that any individual micro- simulation, by introducing discreteness, inevitably devi- ates from the perfect analytical equilibrium that is based on continuous traffic flows and demand variables. • An approach in which the route choice is assumed to be affected by reliability (i.e., is inherently probabilistic) can be contrasted to a simpler approach in which route choice is assumed to be made deterministically based on the per- fect knowledge of the traffic conditions for each particular trip (by using advance information system, for example). In both cases, the route choice model can be either deter- ministic or probabilistic, reflecting the limited knowledge of the modeler. Accounting for reliability in the route choice, combined with a consistent generation of travel time reliability at the link and O–D-path levels, represents a complicated problem for which an effective and efficient solution has not yet been proposed. Route choice based on average travel times is a simpler solution that can be natu- rally combined with the explicit multiple-run approach

21 using conventional network simulation tools. It should be noted that a deterministic route choice does not mean deterministic travel times. Travel time variability can be simulated with fixed routes. • In network assignment techniques there is a principal dif- ference between link-based and path-based assignments. On the one hand, link-based assignments are much sim- pler and in general are more computationally efficient but they are limited to cost functions strictly additive by links. Path-based algorithms, on the other hand, require the gen- eration and explicit enumeration of the route sets for each O–D pair. They can, however, incorporate any form of cost function that is not necessarily additive by links. Most travel time variability measures such as standard deviation, any percentile (80th, 90th, or 95th) and associated buffer time, probability of a certain amount of delay, and so on are nonadditive by links. The only variability measure that is strictly additive by links is travel time variance but only if travel time distribution for different links are indepen- dent. Since independence is an unrealistic assumption, this approach has never been used and does not represent a solution. Some heuristic methods to scale link variability measures for each O–D path to make them additive are proposed in Table 2.2. Possible combinations of the four outlined aspects and perspectives to build an operational model are summarized in Table 2.2. Table 2.2. Approaches to Incorporating Travel Time Variability into Network Simulation Single or Multiple Simulation Integration with Demand Model Route Choice Made by Drivers Link-Based or path-Based perspective for Construction of operation tool Analytical model based on a single run Analytical integration with equilibrium solution Affected by reliability and uncertainty link-based Problematic in view of non-additive-by-link reliability measures; probably impossible Path-based Possible with different reliability measures in small networks depending on demand model structure Based on known or average travel time link-based Represents a surrogate with perceived high- way time by congestion levels; possible to implement in practice depending on demand model structure Path-based Not needed loose coupling with feedback Affected by reliability and uncertainty link-based Problematic in view of non-additive-by-link reliability measures; probably impossible Path-based Possible with different reliability measures in small networks Based on known or average travel time link-based Represents a surrogate with perceived high- way time by congestion levels; easy to implement in practice Path-based Not needed Multiple-run structure with explicit genera- tion of different travel times Analytical integration with equilibrium solution Affected by reliability and uncertainty link-based Problematic in view of non-additive-by-link reliability measures; has yet to be explored and will probably require reconsideration of demand-supply equilibrium Path-based has yet to be explored and will probably require reconsideration of demand-supply equilibrium Based on known or average travel time link-based Possible but requires reconsideration of demand-supply equilibrium Path-based Not needed loose coupling with feedback Affected by reliability and uncertainty link-based Problematic in view of non-additive-by-link reliability measures but can be implemented with some heuristics Path-based Possible with different reliability measures in small networks Based on known or average travel time link-based Straightforward Path-based Not needed

22 Specifics of ABM-dtA equilibration Versus Aggregate Models Two-Way Linkage Between Travel Demand and Network Supply The two-way linkage between travel demand and network supply has been described on the TF Resources website as follows: Since the technologies of microsimulation have been brought to a certain level of maturity on both the demand side (activity- based model, or ABM) and supply (network) side (dynamic traffic assignment, or DTA), the perspective of ABM-DTA inte- gration has become one of the most promising avenues in transportation modeling. Seemingly, the integration of the two models should have been as natural and straightforward as was the integration concept between a 4-step model and static traf- fic assignment (STA) [shown in Figure 3.1]. That relatively simple integration was based on the fact that both I/O entities involved in the process have the same matrix structure. The 4-step demand model produces trip tables needed for assign- ment, and the assignment procedures produce full level of ser- vice (LOS) skims in a matrix format that is needed for the 4-step model. Note that the LOS variables are provided for all possible trips (not only for the trips generated by the demand model at the current iteration). In this case we can say that the network model provides a full feedback to the demand model. The theory of global demand-network equilibrium is well developed for this case, and guarantees a unique solution for the problem, as well as a basis for effective practical algorithms. Both ABM and DTA operate with individual particles as modeled units (individual tours and trips) and have compat- ible levels of spatial and temporal resolution. It might seem that exactly the same integration concept as applied for 4-step models could just be adjusted to account for a list of indi- vidual trips instead of fractional-number trip tables. Moreover, the advanced individual ABM-DTA framework would provide an additional beneficial dimension for the inte- gration, in the form of consistent individual schedules (that can never be incorporated into an aggregate framework). Individual schedule consistency means that for each person, the daily schedule (i.e., a sequence of trips and activities) is formed without gaps or overlaps. However, a closer look at the ABM-DTA framework and consideration of the actual technical aspects of implementation reveals some nontrivial issues that need to be resolved before the advantages offered by an overall microsimulation frame- work can be realized. Specifically, the problem is that the feed- back provided by the DTA procedure does not cover all the needs of the ABM [as shown in Figure 3.2]. The crux of the problem is that, unlike in the 4-Step-STA integration, the microsimulation DTA usually produces an individual trajectory (path in time and space) for the list of actually simulated trips. It does not automatically produce trajectories for all (potential) trips to other destinations and at other departure times without additional computation. Thus, it would not provide the necessary level of service feedback to ABM at the disaggregate level for all modeled choices. Any attempt to resolve this issue by “brute force” would result in an impractical number of calculations, since all possible trips cannot be processed by DTA at the disag- gregate level. In fact, the list of trips for which the individual trajectories are normally produced is a very small share of all possible trips. [As shown in Figure 3.3,] one possible solution is to employ DTA to produce relatively coarse LOS matrices (the way they are produced by STA) and use these LOS variables to feed the demand model. This approach, in the aggregation of individual trajectories into coarse LOS skims, however, would lose much of the detail associated with DTA and the advantages of individual microsimulation (e.g., individual variation in VOTs or other person characteristics). Essen- tially with this approach, the individual schedule consistency concept would be of limited value because travel times would C h A p t e r 3 Integrating Travel Time Reliability into Planning Models

23 ABM-dtA Integration principles The emphasis in the L04 project is on truly integrating the demand and network models and not merely connecting them through aggregate measures in an iterative application. This approach is based on the following principles: • A fully disaggregate approach implemented at the indi- vidual level (travel tours by person). • Conceptual integration of the demand and network simula- tion procedures that ensures a fully consistent daily schedule for each individual. This approach is principally different from so-called iterative loose coupling of the demand and supply models. • The basic travel unit that is exchanged between ABM and DTA is a travel tour, rather than an elemental trip. Moreover, in many procedures, the basic unit would be an entire indi- vidual daily schedule (household-day or person-day, if there is no joint travel). Subsequent tours also put timing con- straints on the current tour that should be taken into account in any scheduling or rescheduling procedure. • Representation of user heterogeneity (individual travel varia- tions) in network-based choice processes, with implications for optimum path computations. • New algorithms that fully exploit the particle-based (individual) representation of vehicles flowing through the network in computing equilibria or other demand-supply consistent states. • Recognition that different policies call for different types of solutions, with varying degrees of user information and feedback—such as nonrecurrent congestion with limited or local information which calls for one-shot simulations ver- sus recurrent congestion which calls for a long-term dynamic equilibrium solution versus applications in which day-to- day learning and evolution may be more important than the final states. • Exploiting advanced concepts from agent-based modeling for integrating behavior processes in a network context, with special-purpose data structures geared to the physical and behavioral processes modeled. Consistency of Individual Daily Schedule The concept of a fully consistent individual daily schedule is illustrated in Table 3.1. The daily schedule of a person is mod- eled for 24 hours starting at 3:00 a.m. on the simulation day and ending at 3:00 a.m. next day (formally represented as 27:00). The integrated model operates with four schedule- related types of events: (1) in-home activities, (2) out-of-home activities, (3) trips, and (4) tours. Start and end times of activi- ties logically relate to the corresponding departure and arrival times of trips connecting these activities. Each tour spans Figure 3.1. Integration of 4-step model and static assignment. 4-step demand model Static assignment Trip tables LOS skims for all possible trips Figure 3.2. Integration of ABM and DTA (direct). Microsimulation ABM Microsimulation DTA List of individual trips Individual trajectories for the current list of trips LOS for the other potential trips? Figure 3.3. Integration of ABM and DTA (aggregate feedback). Microsimulation ABM Microsimulation DTA List of individual trips Aggregate LOS skims for all possible trips be crude for each particular individual. Nevertheless, this approach has been adopted in many studies due to its inher- ent simplicity (Bekhor et al. 2011; Castiglione and Vovsha 2012). The emphasis in those studies was on using more dis- aggregation in the LOS skims (many more time periods, smaller zones, several VOT classes), but at a certain point, that also becomes unmanageable because of the sheer amount of data. (https://tfresource.org/Integrated_Travel_Demand- and-Network-Models.) The team proposes instead several new ideas that were considered and/or tested in the SHRP 2 C04 and L04 projects. These ideas are explained in the subsequent sections.

24 several trips and related out-of-home activities and essentially represents a fragment of the individual daily schedule. In reality, the observed individual schedules are always con- sistent in the sense that they obey time-space constraints and have a logical continuous timeline, in which all activities and trips are sequenced with no gaps and no overlaps. However, achieving full consistency has not been yet resolved in opera- tional models. The crux of the problem is that all trips and asso- ciated activities have to obey a set of hard (physical) and soft (consideration of probabilistic choices) constraints that can only partially be taken into account without a full integration between the demand and network simulation models. Also, both models should be brought to a level of temporal resolution that is sufficient for controlling the constraints (e.g., 5 min). The following constraints should be taken into account: • Schedule continuity. Activity start time should correspond to the preceding trip arrival time, and activity end time should correspond to the following trip departure time. This hard constraint is not controlled in either the 4-step demand models or the static trip-based network simula- tion models since they operate with unconnected trips and do not control for activity durations at all. Also, in 4-step models, the inherently crude level of temporal resolution does not allow for incorporating this constraint. In ABMs, starting from the Columbus model developed in 2004, cer- tain steps have been made to ensure a partial consistency between departure and arrival times, as well as duration at the entire-tour level (Vovsha and Bradley 2004). This, however, did not include trip details and does not control for feasibility of travel times within the tour framework (though travel time is used as one of the explanatory vari- ables). Certain attempts to incorporate trip departure time choice in a framework of trip chains have been made within DTA models (Abdelghany and Mahmassani 2003). However, these attempts were limited to a tour level only and also required a simplified representation of activity duration profiles. This constraint expresses consistency (i.e., the same number) in each row of Table 3.1. • Physical flow process properties. These hard constraints apply to network loading and flow propagation aspects in DTA procedures. Physical principles such as conservation of vehicles at nodes must be adhered to strictly (e.g., no vehicles should simply be lost or otherwise disappear from the system). This constraint accounts for feasibility of travel times obtained in the network simulation that are further used to determine trip departure and arrival times in the corresponding columns of Table 3.1. • Equilibrium travel times. Travel times between activities in the schedule generated by the demand model should corre- spond to realistic network travel times for the corresponding origin, destination, departure time, and route generated by the traffic simulation model with the given demand. While most of the 4-step models and ABMs include a certain level Table 3.1. Fully Consistent Individual Daily Schedule In-Home trips out-of-Home tours Activity Start end purpose Depart Arrive Activity Start end purpose Depart Arrive Sleeping, eating at home, errands 3:00 7:30 Escort 7:30 work 7:30 7:45 drop-off child at school 7:45 work 7:50 7:50 8:30 work 8:30 Shop 16:30 16:30 17:00 Shop 17:00 Return home 17:30 17:30 child care, errands 18:00 18:00 18:00 19:00 disc 19:00 disc 19:00 19:30 Theater 19:30 Return home 21:30 21:30 Resting, errands, sleeping 22:00 22:00 22:00 27:00 Note: disc = discretionary.

25 of demand-supply equilibration, they are limited to achiev- ing stability in terms of average travel times. There is no con- trol for consistency within the individual daily schedule. The challenge is to couple this constraint with the previous one, that is, ensure individual schedule continuity with equilib- rium travel times. This hard constraint expresses consistency between trip departure and arrival times in the correspond- ing columns of Table 3.1 with the travel times obtained in the network simulation. Practically, it is achieved within a certain tolerance level. • Realistic activity timing and duration. Activities in the daily schedule have to be placed according to behaviorally realistic temporal profiles (Parsons Brinckerhoff et al. 2013). Each activity has a preferred start time, end time, and duration formalized as a utility function with multiple components. In the presence of congestion and pricing, travelers may deviate from the preferred temporal profiles (as well as even cancel or change the order of activity episodes). However, this rescheduling process should obey utility-maximization rules over the entire schedule and cannot be effectively mod- eled by simplified procedures that adjust departure time for each trip separately. None of the existing operational ABMs explicitly control for activity durations [although some of them control for entire-tour durations as does the Metro- politan Transportation Commission’s activity-based model in Oakland, California] or the duration of the activity at the primary destination [as implemented in the Sacramento Area Council of Governments (SACOG) activity-based model. The SACOG model also controls for duration of activities at secondary destinations as part of the trip-level departure time/duration choice model (but only to the half- hour level of temporal resolution). DTA models that incor- porate departure time choice have been bound to a simplified representation of temporal utilities and limited to trip chains in order to operate within a feasible dimensionality of the associated choices when combined with the dynamic route choice. This soft constraint expresses consistency between activity start and end times in the corresponding columns of Table 3.1, with the schedule utility maximization principle (or in a more general sense with the observed tim- ing and duration pattern for activity participation). In oper- ational models, the focus has been primarily on out-of-home activities. It should be noted, however, that it is also impor- tant to preserve a consistent and realistic pattern of in-home activities (e.g., reasonable time constraints for sleeping and household errands), as well as take into account possible substitution between in-home and out-of-home durations for work, shopping, and discretionary activities. Schedule consistency with respect to all four constraints is absolutely essential for time-sensitive policies like congestion pricing. In reality, any change in timing of a particular activity spurred by the policy would trigger a chain of subse- quent adjustments through the whole individual schedule. It can be shown that under certain circumstances, an attempt to alleviate congestion in the a.m. period by pricing may result in worsening congestion in the p.m. period because of the compression of individual daily schedules that are forced to start later (Vovsha and Bradley 2006). To address all five constraints, the model system has to be truly integrated with a mutual core between the ABM and DTA modules. This mutual core has to fully address the tem- poral dimension of activities and trips, while other choice dimensions can be effectively treated by each corresponding module as shown in Figure 3.4. The mutual core ensures synchronization of time-related ABM and DTA components that operate along the temporal dimension and is designed to achieve a full schedule consis- tency at the individual level. The ABM model generates tours with origins, destinations, and trip departure times based on expected travel times (from the DTA) and time-of-day choice utilities. These can be converted to temporal activity profiles for each activity episode; the temporal activity profile is essen- tially an expected utility of activity participation for a given time unit. As discussed in the SHRP 2 C04 Report, these tem- poral activity profiles can be converted into schedule delay cost functions for each trip arrival time, which are input to the DTA model. The DTA model assigns each trip onto the network, deter- mines the route, and reschedules trip departure times based on the feasible travel times (which may be different from the expected travel times used in the ABM). This rescheduling is done based on the updated congested travel times and takes into account schedule delay cost as well as interdependencies across trips on the same tour. These features have been added to the DTA algorithm and have been tested for DYNASMART-P (Abdelghany and Mahmassani 2001; Zhou et al. 2008). The capability of DTA to handle travel tours rather than trips is essential to ensure consistency between DTA and ABM. After each tour has been adjusted, the synchronization mod- ule consolidates the entire daily schedule for each individual. Depending on the magnitude of adjustments, the schedule might result in an infeasible (or highly improbable) state in which tours overlap or activity durations have reached unrea- sonable values. The synchronization module informs the ABM which individual daily schedules have to be resimulated. Indi- viduals whose schedules have to be resimulated undergo a complete chain of demand choices based on the updated travel times. For the first few global iterations of the integrated model, all individual choices are resimulated even if the DTA was able to fulfill the planned schedule successfully. For subsequent iterations, after aggregate travel times have been stabilized, a (gradually diminishing) portion of individuals will be subject to demand resimulation, and these individuals will be chosen

26 on the basis of the feasibility of their adjusted schedules and the magnitude of the adjustments introduced by the DTA. The team’s research on equilibration of the integrated models has resulted in new procedures for directing the convergence algo- rithm toward a mutually consistent solution through selection of the fraction of individuals or households whose schedules may be replanned in each iteration. Individual Schedule Adjustments (Temporal Equilibrium) Integration of ABM and DTA at a disaggregate level of indi- vidual trips requires an additional model component to be developed. This component plays a role of interface that trans- forms the DTA output (individual vehicle trajectories with departure and arrival times for each trip simulated with a high level of temporal resolution) into schedule adjustments to the individual schedules generated by the ABM. The purpose of this feedback is to achieve consistency between generated activity schedules (activity start times, and times and dura- tions) and trip trajectories (trip departure time, duration, and arrival time). This feedback is implemented as part of temporal equilibrium between ABM and DTA when all trip destinations and modes are fixed but departure times are adjusted until a consistent schedule is built for each individual. Individual schedule consistency means that for each per- son, the daily schedule (i.e., a sequence of trips and activities) is formed without gaps or overlaps as shown in Figure 3.5. In this way, any change in travel time would affect activity durations and vice versa. According to Castiglione and Vovsha (2012), New methods of equilibration for ABM and DTA are pre- sented in Figure 3.6, which applies two innovative technical solutions in parallel. The first solution is based on the fact that a direct integration at the disaggregate level is possible along the temporal dimension if the other dimensions (number of trips, order of trips, and trip destinations) are fixed for each individual. Then, full advantage can be taken of the individual schedule constraints and corresponding effects as shown in Figure 3.5. The inner loop of temporal equilibrium includes schedule adjustments in individual daily activity patterns as a result of congested travel times being different from the planned travel times. Such adjustments very much help the DTA to reach convergence (internal loop) and are nested within the global system loop (when the entire ABM is rerun and demand is regenerated). The second solution is based on the fact that trip origins, destinations, and departure times can be presampled, and the DTA process is only required to produce trajectories for a subset of origins, destinations, and departure times. In this case, the schedule consolidation is implemented through corrections to the departure and arrival times (based on the individually simulated travel times) and is employed as an inner loop. The outer loop includes a full regeneration of daily activity patterns and schedules but with a subsample of locations for which trajectories are available (it also can be interpreted as a learning and adaptation process with limited information). Figure 3.4. Integration scheme of ABM and DTA. ABM DTA Population synthesis Usual work and school location Car ownership Activity generation and tour formation Destination choice (Planned) tour time-of-day Tour mode Stop frequency Stop location Trip mode and auto occupancy Parking lot choice (Planned • • • • • • • • • • • • ) trip departure time Network route choice Network loading Flow propagation Node processes Information strategies (Feasible) tour time-of-day (Feasible • • • • • • • ) trip departure time Mutual core: synchronization Schedule delay costs Schedule • • adjustmentsTours with planned trip departure and arrival times Temporal • • activity profiles Expected travel times Feasibilit • • y of adjusted schedules Tours• with planned trip departure times and schedule delay costs Tours• with simulated travel time and adjusted trip departure times

27 Adjustment of individual daily schedule can be formulated as an entropy-maximizing problem of the following form (Equation 3.1): min ln ln ln (3.1) 0 1 1 0 w x x d u y y v z zx i i I i i i i i i ii I i i i ii Ii ∑ ∑ ∑ × ×     + × × pi     + × × τ               { } = = + = which is subject to Equations 3.2, 3.3, and 3.4: , 1, 2, . . . , 1 (3.2)0 0 1 0 1 y x t i Ii j j i j j i ∑ ∑= τ +    +     = += − = − , 1, 2, . . . , (3.3)0 0 1 0 z x t i Ii j j i j j i ∑ ∑= τ +    +     == − = 0, 0, 1, 2, . . . , (3.4)x i Ii > = where i = 1, 2, . . . , I = trips and associated activities at the trip destination, i = 0 = activity at home before the first trip, i = I + 1 = (symbolic) departure from home at the end of the simulation period, xi = adjusted activity duration, yi = adjusted departure time for trip to the activity, zi = adjusted arrival time for trip to the activity, di = planned activity duration, pi = planned departure time for trip to the activity, ti = planned arrival time for trip to the activity, ti = actual time for trip to the activity that is different from expected, wi = schedule weight (priority) for activity dura- tion, ui = schedule weights (priority) for trip depar- ture time, and vi = schedule weight (priority) for trip arrival time. The essence of this formulation is that when the traveler experiences travel times that are different from those used to build the schedule, he or she will attempt adjustments that seek to preserve the schedule to the extent possible. Schedule preservation relates to activity start times (trip arrival times), activity end times (trip departure times), and activity dura- tions (Equation 3.1). The relative weights relate to the priori- ties of different activities in terms of start time, end time, and duration. The greater the weight, the more important it is for the user to keep the corresponding component close to the original schedule. Very large weights correspond to inflexible, fixed-time activities. The weights directly relate to the sched- ule delay penalties. However, the concept of schedule delay penalties relates to a deviation from the (preferred or planned) activity start time (trip arrival time) only, while the schedule Figure 3.5. Individual daily schedule consistency. 0 24 Activity i=0 Activity i=1 Activity i=2 Trip i=1 Trip i=2 Trip i=3 Activity i=3 Departure Arrival Duration Travel id iT i i Schedule i Figure 3.6. Integration of ABM and DTA (split feedback). Microsimulation ABM Microsimulation DTA List of individual trips Individual trajectories for the current list of trips Consolidation of individual schedules (inner loop for departure / arrival time corrections) Sample of alternative origins, destinations, and departure times Individual trajectories for potential trips

28 adjustment formulation allows for a joint treatment of devia- tions from the planned start times, end times, and durations. The constraints express the schedule consistency rule as shown in Figure 3.5. Equation 3.2 expresses departure time for each trip as a sum of the previous activity durations and travel times. Equation 3.3 expresses arrival time for each trip as a sum of the previous activity durations and travel times plus travel time for the given trip. (Symbolic) arrival time for the home activity prior to the first trip is used to set the scale of all departure and arrival times. This way, the problem is formulated in the space of activity durations, while the trip departure and arrival times are derived from the activity durations and given travel times. The solution to the convex problem can be found by writing the Lagrangian function and equating its partial derivatives (with respect to activity durations) to zero. It has the following form (Equation 3.5): (3.5) 1 ∏= × pi   × τ         > x d y z i i j j u j j v j i wj j i This solution is easy to find by using either an iterative balancing method or Newton-Raphson method. The essence of this formula is that updated activity durations are proportional to the planned durations and adjustment factors. The adjust- ment factors are applied considering the duration priority. If the duration weight is very large, then the adjustments will be minimal. The duration adjustment is calculated as a product of trip departure and arrival adjustments for all subsequent trips. The trip departure adjustment y j j pi  and trip arrival adjust- ment z j j τ  can be interpreted as lateness versus the planned schedule if it is less than 1 and earliness if it is greater than 1. Each trip departure or arrival adjustment factor is powered by the corresponding priority weight. As the result, activity dura- tion will shrink if there are subsequent trip departures and/or arrivals that would occur later than planned. Conversely, activity duration may be stretched if there are many subsequent trip departures and/or arrivals that are earlier than planned. Overall, the model seeks the equilibrium (compromise) state in which all activity durations, trip departures, and trip arrivals are adjusted to accommodate the changed travel times while preserving the planned schedule components by priority. The team has provided demonstration software and imple- mented many numerical tests with this model. In particular, the iterative balancing procedure goes through the following steps: 1. Set initial activity durations equal to the planned dura- tions {xi = di}. 2. Update trip departure times with new travel times and updated activity durations using Equation 3.2. 3. Update trip arrival times with new travel times and updated activity durations using Equation 3.3. 4. Calculate balancing factors y j j pi  for trip departure times (lateness if less than 1, earliness if greater than 1). 5. Calculate balancing factors z j j τ  for trip arrival times (lateness if less than 1, earliness if greater than 1). 6. Update activity durations using Equation 3.5. 7. Check for convergence with respect to activity durations; if not go to Step 2. Applying this model in practice requires default values for activity durations, trip departure times, and trip arrival times. This is an area in which more specific data are welcome on schedule priorities and constraints of different person types. This type of data is already included in some household travel surveys with respect to work schedules. It should be extended to include nonwork activities, many of which can also have schedule constraints. At this stage, the team suggests the default values shown in Table 3.2. If some activity in the schedule falls into more than one category (e.g., work and first activity of the day), the maxi- mum weight is applied from each column. Table 3.2. Recommended Weights for Schedule Adjustment Activity type Duration trip Departure (to activity) trip Arrival (at activity location) work (low income) 5 1 20 work (high income) 5 1 5 School 20 1 20 last trip to activity at home 1 1 3 Trip after work to NhB activity 1 5 1 Trip after work to NhB activity 1 10 1 NhB activity on at-work subtour 1 5 5 Medical 5 1 20 Escorting 1 1 20 Joint discretionary, visiting, eating out 5 5 10 Joint shopping 3 3 5 Any first activity of the day 1 5 1 other activities 1 1 1 Note: NhB = non–home-based activity.

29 Approaches to Quantifying reliability and Its Impacts Construction of User-Centric Network Reliability Measures In summary, the following two important aspects of the problem need to be taken into account when the user’s per- spective on reliability (and performance in general) is com- pared with the highway operations perspective: • The user perspective can be different and include many per- ceived components and weights compared with the physical measures of average travel time and reliability. The measure that looks the best and most statistically significant from the highway operations perspective might not be best when model- ing user responses. For example, the 95th percentile of travel time is favored in highway operations since it singles out the most critical cases of nonrecurrent congestion (mostly asso- ciated with traffic collisions, road works, special events, and extreme weather); see Cambridge Systematics, Inc. (2005) and Cambridge Systematics, Inc. et al. (2013). The current experience with models of individual behavior in the route choice context, however, indicates that the decision-making point at which users evaluate reliability lies rather some- where between the 80th and 90th percentile, that is, mixes of recurrent and nonrecurrent congestion; see Concas and Kolpakov (2009) and Parsons Brinckerhoff et al. (2013). • The user perspective is inherently an entire-trip perspective. Thus, the reliability measures for travel models and network simulation tools have to be synthesized at the O–D-route level, while the bulk of statistical evidence on highway operations is naturally collected at the facility/link level. This synthesis is not a trivial task, because practically all sensible reliability measures are inherently nonadditive (Institute for Trans- portation Studies 2008). This aspect is discussed in detail in the subsequent sections and constitutes one of the major challenges for the current project. Suggested Approaches to Quantifying Reliability Impacts on Highway Users In general, there are four possible methodological approaches to quantifying reliability either suggested in the research litera- ture or already applied in operational models: • Indirect measure: Perceived highway time by congestion levels. This concept is based on statistical evidence that in conges- tion conditions, travelers perceive each minute with a certain weight (Small et al. 1999; Axhausen et al. 2007; Levinson et al. 2004; MRC and PB 2008). Perceived highway time is not a direct measure of reliability since only the average travel time is considered (although it is segmented by congestion levels). It can serve, however, as a good instrumental proxy for reli- ability since the perceived weight of each minute spent in congestion is partially a consequence of associated unreli- ability. This is the simplest measure that can be readily incor- porated into both demand models and network simulation tools and equilibrated between them. • First direct measure: Time variability (distribution) measures. This is considered the most practical direct approach and has received considerable attention in recent years. This approach assumes that several independent measurements of travel time are known that allow for forming the travel time distribution and calculation of derived measures, such as variance, standard deviation, or buffer time (Small et al. 2005; Brownstone and Small 2005; Bogers et al. 2008). One of the important technical details with respect to the genera- tion of travel time distributions is that even if the link-level time variations are known, it is a nontrivial task to synthe- size the O–D-level time distribution (reliability “skims”) because of the dependence of travel times across adjacent links due to a mutual traffic flow. This implementation chal- lenge posed by issue is specifically addressed in the course of the project. This is a more complicated measure—primarily on the network simulation side. The network model has to incorporate travel time distribution measures (like variance or standard deviation) in the route choice and also generate the O–D reliability skims. This can be achieved only by using path-based assignment algorithms since the reliability measures are (in general) not additive by links. Recommen- dations are made how an equilibrium framework with these measures could be implemented. • Second direct measure: Schedule delay cost. This approach has been adopted in many research works on individual behavior in academia (Small 1982; Small et al. 1999). According to this concept, the direct impact of travel time unreliability is measured through cost functions (penalties expressed in monetary terms) of being late (or early) compared with the planned schedule of the activity. This approach assumes that the desired schedule is known for each person and activity in the course of the modeled period. This assumption, however, is difficult to meet in a practical model setting. This is a more sophisticated approach that is more difficult to implement. However, certain directions are outlined, including incorpo- ration of schedule delay penalties into the combined trip route and departure time cost. It was shown that under cer- tain assumptions on the shape of the earliness and lateness penalties, this approach can be reduced to the mean-variance approach (Fosgerau and Karlstrom 2007; Fosgerau 2008). • Third direct measure: Loss of activity participation utility. This method can be thought of as a generalization of the schedule delay concept. It is assumed that each activity has a certain temporal utility profile and individuals plan their schedules to achieve maximum total utility over the modeled period

30 (e.g., the entire day), taking into account expected (average) travel times. Then, any deviation from the expected travel time due to unreliability can be associated with a loss of participation in the corresponding activity (or gain if travel time proved to be shorter) (Supernak 1992; Kitamura and Supernak 1997; Tseng and Verhoef 2008). This approach recently was adopted in several research works on DTA for- mulation integrated with activity scheduling analysis (Kim et al. 2006; Lam and Yin 2001). It was shown that under spe- cific assumptions about the shape of temporal utility profiles of two consecutive activities, the expected generalized cost function that includes travel time variation impact can be reduced to the mean-variance approach (Engelson 2011). Similar to the schedule delay concept, however, this approach suffers from the data requirements that are difficult to meet in practice. The added complexity of estimation and calibration of all temporal utility profiles for all possible activities and all person types is significant. This makes it unrealistic to adopt this approach as the main concept for the current project. This approach, however, can be considered in future research efforts. Early research indicates that this approach may be the most promising theoretical avenue for a fully integrated ABM-DTA model formulation that can eliminate the need to equilibrate two separate models. Unfortunately, these meth- ods are currently applicable only in very small networks. A summary of the main features of the proposed approaches to quantifying reliability impacts on travel choices is presented in Table 3.3. Some clarification is needed regarding preferred arrival time (PAT) and its relation to time-of-day (TOD) choice. Travel demand (TOD choice) models in general predict the preferred departure time (PDT) for each trip, since this is the choice dimension that is controlled by the traveler. Arrival time in general is not controlled, and a PAT is not directly generated by travel demand procedures in a conventional ABM. If travel time is considered deterministic, PAT can always be derived from PDT by adding the travel time; thus TOD choice with deterministic travel times can be thought of as a (simplis- tic) simultaneous model for predicting PDT and PAT. How- ever, travel time reliability is ignored in this case. Also, even if times are deterministic within each time of day, as long as con- gestion causes average travel times to vary across times of day, some people may shift their travel away from their most pre- ferred time to avoid driving in congested conditions (even if it is perfectly predictable congestion). If travel time is considered probabilistic, PAT has to be either defined exogenously (assuming fixed scheduling constraints) or generated by the demand model before modeling PDT. If we assume that PDT is optimized by the traveler, conditional on the predetermined PAT with a full knowledge of travel time distribution, this leads to a model equivalent to the mean- variance approach in terms of the form of the generalized cost function. It is also possible to assume that PDT is optimized by the user based on the PAT and mean travel time only (e.g., by subtracting mean travel time from PAT). This would mean, however, that travel time reliability is ignored at least at the TOD-choice stage. The concept of temporal activity Table 3.3. Methods to Quantify Reliability Impacts on Travel Method Representation of travel time Impact on travel Choices through Generalized Cost Function Special Features Needed Perceived highway time by congestion levels Segmented by congestion levels Travel time is weighted by congestion levels. Mean-variance (travel time distribution measures) Mean (or mode), variance [or Sd(T ) or buffer time] Mean (or mode) and variance [or Sd(T ) or buffer time] are linearly included in generalized cost as loS components. Schedule delay distribution Expected schedule delay cost over travel time distribution is linearly included in generalized cost along with the mean travel time. Preferred arrival time (PAT) has to be defined externally or generated by the demand model. Temporal activity profiles distribution Expected loss in activity participation over travel time distribution is linearly included in gener- alized cost along with the mean travel time. Requirements for network simulation model with any of the methods above Travel time characteristics above have to be generated by network simulation model. generalized cost function above has to be incorporated into route choice. Requirements for travel demand model with any of the methods above generalized cost function above has to be incorporated into mode, time-of-day, destina- tion, and other choices. Note: Sd(T) = standard deviation of travel time.

31 profiles is a way to endogenize PAT within the demand model- ing (scheduling) framework. Incorporating reliability into demand Model The proposed methods of quantification of reliability should be incorporated into the demand model (ABM) with respect to subchoices such as tour and trip mode choice, destination choice, and TOD choice. In the typical ABM structure, a gen- eralized cost function with the reliability terms can be directly included in the utility function for highway modes. Further on, it will have an impact on destination and TOD choice through mode choice logsums. In the same vein, it has an impact on upper-level choice models of car ownership and activity-travel patterns through accessibility measures that represent simplified destination choice logsums. The demand side of travel time reliability has been explored in detail in the recently completed SHRP 2 C04 project. The relevant model structures and techniques are described in the Task 11 Report (Stogios et al. 2014). This section presents a concise overview of each method and its applicability in an operational travel demand model. Perceived Highway Time in Demand Model This method is easy to implement without a significant restruc- turing of the demand model. Essentially, the generic highway travel time variable in mode choice should be replaced with segmented travel time by congestion levels with the recom- mended weights shown in Table 3.4. For each level of conges- tion, the table provides approximate volume to capacity (V/C) ratios that can be used to classify highway network links after the traffic simulation. The weights applied have to be consistent between traffic assignment and mode choice. The table provides pivot points that can be interpolated between them linearly using V/C ratio or flow density parameter. However, perceived travel time is not a direct measure of travel time reliability. It can be used as a surrogate when more advanced methods are not available, but it is less appealing behaviorally and is not the main focus of the current research. Mean-Variance in Demand Model This method is easy to implement and does not require a significant restructuring of the demand model. Essentially, it requires an inclusion of an additional reliability term in the mode choice utility for highway modes. The following form of generalized cost component in the mode utility function (Equation 3.6) can be recommended as the first step for incor- poration into operational models. There are many additional modifications and nonlinear transformations analyzed in the SHRP 2 C04 project and described in the Task 11 Report (Stogios et al. 2014). ( )= × + × + × SD (3.6)U a T b C c T where T = mean travel time, C = travel cost, SD(T) = standard deviation of travel time, a = coefficient for travel time, b = coefficient for travel cost, c = coefficient for standard deviation of travel time, a/b = value of time (VOT), c/b = value of reliability (VOR), and c/a = reliability ratio (r = VOT/VOR). A summary of recommended values for the parameters is presented in Table 3.5. The parameters are segmented by travel purpose, household income, car occupancy, and travel distance. More details and the actual values for all coefficients can be found in (Parsons Brinckerhoff et al. 2013). Schedule Delay Cost in Demand Model There are multiple estimated models with schedule delay cost, as described in the Task 11 Report (Stogios et al. 2014). The majority of them were estimated using different stated pre- ference (SP) settings in which either route or departure time served as the underlying travel choice dimension. The techni- cal details for the inclusion of this method in an operational travel demand model have not yet been fully explored. The team outlines two possible approaches that differ in how and where the schedule delay cost component is calculated; see Figure 3.7. In both approaches, the travel demand model (its time-of- day choice or activity scheduling submodel) produces pre- ferred departure time (PDT) and preferred arrival time (PAT) for each trip based on the expected travel times (and known Table 3.4. Recommended Highway Time Weight by Congestion Level travel time Conditions Weight LoS V/C Free flow 1.00 A, B under 0.5 Busy 1.05 c 0.5–0.7 light congestion 1.10 d 0.7–0.8 heavy congestion 1.20 E 0.8–1.0 Stop start 1.40 F 1.0–1.2 gridlock 1.80 F 1.2+

32 Table 3.5. Recommended Values of Parameters for Generalized Cost Function with Reliability travel purpose examples of population/travel Model Coefficients and Derived Measures Household Income, $/year Car occupancy Distance, Miles time Coefficient Cost Coefficient Cost for SD(T) min Vot, $/h VoR, $/h Reliability Ratio work & business 30,000 1.0 5.0 -0.0425 -0.0026 -0.1042 9.9 24.3 2.45 30,000 2.0 5.0 -0.0425 -0.0015 -0.1042 17.2 42.3 2.45 30,000 3.0 5.0 -0.0425 -0.0011 -0.1042 23.9 58.5 2.45 30,000 1.0 10.0 -0.0425 -0.0026 -0.0521 9.9 12.1 1.23 30,000 2.0 10.0 -0.0425 -0.0015 -0.0521 17.2 21.1 1.23 30,000 3.0 10.0 -0.0425 -0.0011 -0.0521 23.9 29.2 1.23 30,000 1.0 20.0 -0.0425 -0.0026 -0.0260 9.9 6.1 0.61 30,000 2.0 20.0 -0.0425 -0.0015 -0.0260 17.2 10.6 0.61 30,000 3.0 20.0 -0.0425 -0.0011 -0.0260 23.9 14.6 0.61 60,000 1.0 5.0 -0.0425 -0.0017 -0.1042 15.0 36.8 2.45 60,000 2.0 5.0 -0.0425 -0.0010 -0.1042 26.1 64.1 2.45 60,000 3.0 5.0 -0.0425 -0.0007 -0.1042 36.2 88.6 2.45 60,000 1.0 10.0 -0.0425 -0.0017 -0.0521 15.0 18.4 1.23 60,000 2.0 10.0 -0.0425 -0.0010 -0.0521 26.1 32.0 1.23 60,000 3.0 10.0 -0.0425 -0.0007 -0.0521 36.2 44.3 1.23 60,000 1.0 20.0 -0.0425 -0.0017 -0.0260 15.0 9.2 0.61 60,000 2.0 20.0 -0.0425 -0.0010 -0.0260 26.1 16.0 0.61 60,000 3.0 20.0 -0.0425 -0.0007 -0.0260 36.2 22.2 0.61 100,000 1.0 5.0 -0.0425 -0.0013 -0.1042 20.4 50.0 2.45 100,000 2.0 5.0 -0.0425 -0.0007 -0.1042 35.5 87.1 2.45 100,000 3.0 5.0 -0.0425 -0.0005 -0.1042 49.1 120.4 2.45 100,000 1.0 10.0 -0.0425 -0.0013 -0.0521 20.4 25.0 1.23 100,000 2.0 10.0 -0.0425 -0.0007 -0.0521 35.5 43.5 1.23 100,000 3.0 10.0 -0.0425 -0.0005 -0.0521 49.1 60.2 1.23 100,000 1.0 20.0 -0.0425 -0.0013 -0.0260 20.4 12.5 0.61 100,000 2.0 20.0 -0.0425 -0.0007 -0.0260 35.5 21.8 0.61 100,000 3.0 20.0 -0.0425 -0.0005 -0.0260 49.1 30.1 0.61 Non-work 30,000 1.0 5.0 -0.0335 -0.0030 -0.0697 6.7 13.8 2.08 30,000 2.0 5.0 -0.0335 -0.0019 -0.0697 10.8 22.5 2.08 30,000 3.0 5.0 -0.0335 -0.0014 -0.0697 14.4 29.9 2.08 30,000 1.0 10.0 -0.0335 -0.0030 -0.0348 6.7 6.9 1.04 30,000 2.0 10.0 -0.0335 -0.0019 -0.0348 10.8 11.2 1.04 30,000 3.0 10.0 -0.0335 -0.0014 -0.0348 14.4 14.9 1.04 30,000 1.0 20.0 -0.0335 -0.0030 -0.0174 6.7 3.5 0.52 30,000 2.0 20.0 -0.0335 -0.0019 -0.0174 10.8 5.6 0.52 30,000 3.0 20.0 -0.0335 -0.0014 -0.0174 14.4 7.5 0.52 60,000 1.0 5.0 -0.0335 -0.0021 -0.0697 9.4 19.6 2.08 60,000 2.0 5.0 -0.0335 -0.0013 -0.0697 15.3 31.8 2.08 60,000 3.0 5.0 -0.0335 -0.0010 -0.0697 20.3 42.3 2.08 60,000 1.0 10.0 -0.0335 -0.0021 -0.0348 9.4 9.8 1.04 (continued on next page)

33 (continued)Table 3.5. Recommended Values of Parameters for Generalized Cost Function with Reliability travel purpose examples of population/travel Model Coefficients and Derived Measures Household Income, $/year Car occupancy Distance, Miles time Coefficient Cost Coefficient Cost for SD(T) min Vot, $/h VoR, $/h Reliability Ratio Non-work (continued) 60,000 2.0 10.0 -0.0335 -0.0013 -0.0348 15.3 15.9 1.04 60,000 3.0 10.0 -0.0335 -0.0010 -0.0348 20.3 21.1 1.04 60,000 1.0 20.0 -0.0335 -0.0021 -0.0174 9.4 4.9 0.52 60,000 2.0 20.0 -0.0335 -0.0013 -0.0174 15.3 8.0 0.52 60,000 3.0 20.0 -0.0335 -0.0010 -0.0174 20.3 10.6 0.52 100,000 1.0 5.0 -0.0335 -0.0017 -0.0697 12.2 25.3 2.08 100,000 2.0 5.0 -0.0335 -0.0010 -0.0697 19.8 41.1 2.08 100,000 3.0 5.0 -0.0335 -0.0008 -0.0697 26.2 54.6 2.08 100,000 1.0 10.0 -0.0335 -0.0017 -0.0348 12.2 12.6 1.04 100,000 2.0 10.0 -0.0335 -0.0010 -0.0348 19.8 20.5 1.04 100,000 3.0 10.0 -0.0335 -0.0008 -0.0348 26.2 27.3 1.04 100,000 1.0 20.0 -0.0335 -0.0017 -0.0174 12.2 6.3 0.52 100,000 2.0 20.0 -0.0335 -0.0010 -0.0174 19.8 10.3 0.52 100,000 3.0 20.0 -0.0335 -0.0008 -0.0174 26.2 13.6 0.52 Demand Network TOD choice Mode choice Route choice PDT PAT Travel time distribution Schedule delay cost Schedule delay penalty functions TOD choice Mode choice Route choice & PDT optimization PDT PAT Schedule delay cost Schedule delay penalty functions Demand Network 1s t a pp ro ac h: s ch ed ul e de la y co st ca lc ul at io n in d em an d m od el 2n d a pp ro ac h: s ch ed ul e de la y co st ca lc ul at io n in n et w or k m od el Figure 3.7. Incorporation of schedule delay cost into demand model (mode choice).

34 variations if used in the scheduling procedure and departure time optimization). In both approaches, schedule delay pen- alty functions are assumed known for each trip. The principal difference is in how the demand model interacts with the net- work simulation model to produce the expected schedule delay cost for each trip. In the first approach, schedule delay cost is calculated in the demand model as part of the mode utility calculation for high- way modes. The network simulation model assigns trips based on PDT without a consideration of PAT. The role of the net- work simulation model is to produce travel time distributions for each trip (through a single equilibrium run or multiple runs). Subsequently, schedule delay cost is integrated over the travel time distribution in the demand model. This scheme has not been tested yet. The most realistic implementation approach for this scheme is a multiple-run framework. In the second approach, the calculation of schedule delay cost is incorporated into the network model and is fed into the demand model. Perhaps, the most behaviorally appealing aspect of this implementation approach is when the network simulation model is allowed to optimize PDT based on the PAT and specified schedule delay penalties. This means that the route choice component is replaced with a joint route and departure time choice. This type of model can be imple- mented in a single-run framework, and some testing of this approach has been already reported (Zhou et al. 2008). In both cases, the main (technical) obstacle for practical implementation of the schedule delay approach is the neces- sity to generate PAT for each trip against which the schedule delay cost is calculated as a consequence of unreliable travel time. It is currently unrealistic to prepare PAT as an input to travel demand models, although for some trips with inher- ently fixed schedules (work with a fixed schedule, appoint- ments, ticket shows) this might be ultimately the right approach. Some approaches to endogenously calculated PAT within the scheduling model as a latent variable were sug- gested (Ben-Akiva and Abou-Zeid 2007). Further research is needed to operationalize this approach within the framework of a regional travel model. Temporal Utility Profiles in Demand Model This is the most theoretically advanced approach. Its opera- tionalization on the demand side requires that temporal util- ity profiles be defined for each activity. The attractive part of this approach is that these profiles are indeed implicitly defined in the time-of-day choice model embedded in any ABM. However, conversion of the time-of-day choice model output into the utility profiles with the necessary level of temporal resolution is not a trivial procedure and has yet to be developed and explored. The crux of the problem is that a time-of-day choice model produces probabilities for each activity to be undertaken at a certain time in a form of joint start (arrival) and end (departure) time probability over all feasible combinations P(ta, td) as in Equation 3.7: , 1 (3.7) 0 P t ta d t t T t T d aa ∑∑ ( ) = == These probabilities are defined for each activity, and they are not directly comparable across different activities. To con- vert the time-of-day choice probabilities into temporal utility profiles, an overall scale Uk for each activity k has to be defined. Then the utility profile could be calculated as in Equation 3.8: , , (3.8)u t t U P t tk a d k a d( ) ( )= × The overall scale reflects the importance of (a unit duration of) each activity versus generalized travel cost. General travel cost Cad is a part of the time-of-day choice utility Vk(ta, td) used to calculate the probability P(ta, td). Thus the following esti- mate of Uk can be suggested that is essentially the coefficient for travel cost in the time-of-day choice utility, assuming that this is a single coefficient not differentiated by departure or arrival time (Equation 3.9): , (3.9)U V t t C k k a d ad ( ) = ∂ ∂ However, these techniques are yet to be explored and fur- ther research is needed to unify time-of-day choice and tem- poral utility profiles. Also, even if the temporal utility profiles are available for each activity, their incorporation into an operational travel demand model is not straightforward. In a certain sense, two approaches similar to the approaches out- lined in Figure 3.7 for the schedule delay method can be adjusted to the temporal profiles framework. The first approach would employ the network simulation model to produce travel time distributions for each trip departure time bin (30 min). Then, the demand model (mode choice) would convert these distributions to estimates of activity participation loss using temporal activity profiles. This approach has never been applied and its details have yet to be explored. The second approach would include temporal profiles in the network simulation that would require a simultaneous choice of network routes and departure times for the entire daily schedule (or each travel tour to make this model more realistic). Theoretical constructs of this type and corresponding experiments in small networks have been reported (Kim et al. 2006; Lam and Yin 2001). However, at the current time, the second approach cannot be recommended for implementation in real-size networks.

35 Incorporating reliability into Network Simulation This section presents a concise overview of each method of quantification of travel time reliability from the perspective of its inclusion in an operational network simulation model. This means that the reliability measure of interest has to be incorporated into the route choice and generated at the O–D level to feed into the demand model. Perceived Highway Time in Network Simulation This method is easy to implement without a significant restructuring of the network assignment model, whether a user equilibrium static assignment or advanced DTA. Essen- tially, the generic highway travel time variable in route choice is replaced with segmented travel time by congestion levels, with the recommended weights shown in Table 3.4. The high- way LOS skims for the demand model have to be segmented accordingly. However, in the same way as mentioned for a demand model, perceived travel time is not a direct measure of travel time reliability for network simulation. It can be used as a sur- rogate when more advanced methods are not available, but it is less appealing behaviorally and is not the main focus of the current research. Mean-Variance in Network Simulation This method requires an inclusion of an additional reliability term (standard deviation, variance, or buffer time) in the route choice generalized cost along with the mean travel time and cost as shown in Equation 3.9. Further on, the correspondent O–D skims for the reliability measure have to be generated to feed to the demand model (mode choice and other choice through mode choice logsums). However, implementation of this method on the network simulation side proved to be more complicated than its incorporation into a demand model. Any demand model, whether 4-step or ABM, inherently operates with entire-trip O–D performance measures. Conse- quently, adding one more measure does not affect the model structure. However, network simulation models that are effi- cient in large networks operate with link-based shortest-path algorithms for route choice. This results in the necessity to construct entire-route O–D performance measures from link performance measures. While mean travel time and cost are additive by link, the reliability measures are not in a general case. This represents a significant complication that has to be resolved. Even if an explicit route enumeration is applied, which means that several entire O–D routes are explicitly considered in route choice, it is not trivial to incorporate a reliability measure like standard deviation, variance, or buffer time. In a single-run framework, this measure has to be generated based on the traf- fic flow versus capacity characteristics that require nonstandard statistical dependences to be involved. In a multiple-run frame- work, this measure can be summarized from multiple simula- tions. However, the whole framework of multiple runs has to be defined in a consistent way across demand, network supply, and equilibration parameters. The next section is specifically devoted to an analysis of these issues and a substantiation of the team’s recommended methods. Single-run and multiple-run equilibration frame- works are discussed in subsequent chapters. Schedule Delay Cost in Network Simulation The previous section outlined two possible approaches that differ in how and where the schedule delay cost component is calculated (see Figure 3.7). With the first approach, schedule delay cost is calculated in the demand model as part of the mode utility calculation for highway modes. The network sim- ulation model assigns trips based on PDT without a consider- ation of PAT. The role of the network simulation model is to produce travel time distributions for each trip (through a sin- gle equilibrium run or multiple runs). Subsequently, schedule delay cost is integrated over the travel time distribution in the demand model. The most realistic implementation approach with this scheme is a multiple-run framework. In the second approach, the schedule delay cost calculation is incorporated into the network model and is fed to the demand model. Perhaps the most behaviorally appealing implementation of this approach is when the network simu- lation model is allowed to optimize departure time based on the PAT and specified schedule delay penalties. This type of model can be implemented in a single-run framework, and some testing of this approach has been already reported (Zhou et al. 2008). In both cases, the main (technical) obstacle for practical implementation of the schedule delay approach is the necessity to generate PAT (externally or endogenously in the demand model scheduling procedure) for each trip against which the schedule delay cost is calculated as a consequence of unreliable travel time. Further research is needed to operationalize this approach in the framework of a regional travel model. Temporal Utility Profiles in Network Simulation Two approaches similar to the approaches outlined for the schedule delay method can be adjusted within a temporal pro- files framework.

36 The first approach employs the network simulation model to produce travel time distributions for each trip departure time bin (30 min). The second approach includes temporal profiles in the network simulation that require a simultaneous choice of network routes and departure times for the entire daily schedule (or each travel tour to make this model more realistic). Theoretical constructs of this type and correspond- ing experiments in small networks have been reported (Kim et al. 2006; Lam and Yin 2001). Currently, this method cannot be recommended for imple- mentation in real-size networks because of many technical details that have to be explored on both demand and network supply size. However, this represents an important avenue for future research. Single-run Versus Multiple-run Approach The incorporation of reliability factors into the models can be done in either of two principal ways: • Implicitly in a single model run. In this case, travel time is implicitly treated as a random variable; and its distribution, or some parameters of this distribution, such as mean and variance, are described analytically and used in the model- ing process. • Explicitly through multiple runs (scenarios). In this case, the travel time distribution is not parameterized analytically but is simulated directly or explicitly through multiple model runs with different input variables. There are pros and cons associated with each method. The vision emerging from this research is that both methods are useful and could be hybridized to account for different sources of travel time variation in the most adequate and computationally efficient way. In particular, the team consid- ers single-run analytical methods whenever possible, since they are generally preferable both from a theoretical point of view, particularly for network equilibrium formulations, and in terms of a more efficient use of computational resources in application. Generally, the factors that can be described by means of analytical tools and probabilistic distributions relate to the baseline demand and capacity estimates, day-to- day variability in travel demand, impact of weather condi- tions, traffic control, route choice, meso effects associated with traffic flow physics, and individual driver behavior. Fac- tors that can probably be better modeled through explicit scenarios, rather than captured by probabilistic distributions, mostly relate to special events, road works, and occurrence of incidents. Some of the factors—such as day-to-day fluctuations in demand, weather conditions, and traffic control—can be modeled in both ways, and the best approach will be deter- mined in the course of the project. It should also be noted that an explicit simulation by scenarios is in itself based on a proba- bilistic distribution of input parameters (such as parameter- ized probability of occurrence of a certain event). However, the principal difference is that the resulting variation in travel times is generated through multiple simulation runs, rather than derived analytically from the distribution of input vari- ables in a one-time network simulation. Single-Run Framework Accounting for Link Correlations by Distance-Based Scaling The team proposes an approach that is based on the following line of reasoning supported by empirical evidence. Consider a route r that consists of two successive links a and b with identical length (da = db) and identical parameters of travel time distribution on each link (T˜a = T˜b and sa = sb = s). If we assume that travel time distributions on these links are inde- pendent, the entire-route parameters can be calculated as in Equation 3.10: ; ; 2 (3.10)0.5d d d T T Tr a b r a b r  = + = + σ = σ × If we assume that the travel time distribution on these links is perfectly correlated (as in a case when there is no inter- section between the links, just a formal node), then consider Equation 3.11: ; ; 2 (3.11)d d d T T Tr a b r a b r  = + = + σ = σ × Comparing Equation 3.10 and Equation 3.11, a general formula for standard deviation can be written as Equation 3.12: 2 (3.12)1rσ = σ × −η where parameter 0 ≤ h ≤ 0.5 represents the level of correlation between travel times on the links that constitute the path. The closer the parameter value is to 0.5 the more independent the links are, and consequently, they tend to mitigate travel time variation on each other. The closer the parameter value is to 0, the more correlated the links are and there is no mitiga- tion of travel time variations on the links along the route. Now, instead of discrete links, consider elemental distance units (e.g., miles) and also assume that there is a basic rela- tionship between travel time variance and mean established for the elemental unit (link of unit length) in the form of Equation 3.13: (3.13) d T T d ( )σ = γ × −

37 This particular form is chosen since it is logical to expect that the variation should tend to zero when average travel time tends to the minimal (free-flow) time. This is appropriate for planning applications in which travel time variability is mea- sured in an aggregate fashion (i.e., between average hourly travel times for consecutive days). If an individual-level varia- tion is taken into account, a certain level of variance is observed even at the free-flow condition and a more appropriate form would be Equation 3.14: (3.14) d T d σ = γ × The empirical evidence currently in hand indicates that the values of parameter g should be in the range of 0.2 to 0.3 for average hourly travel times and in the range of 0.8 to 1.2 for individual trajectories depending on the facility type. By substituting Equation 3.13 or Equation 3.14 into Equa- tion 3.12, and taking into account that the route has a number of elemental units equal to its length, we obtain the following expressions for aggregate-level and individual-level variances accordingly (Equations 3.15 and 3.16): (3.15) 1d d d T T dr r r r r r r r r r( )( ) ( ) ( )σ = σ × = σ × × = γ × − ×−η −η −η (3.16)1d d d T dr r r r r rr r r( ) ( ) ( )σ = σ × = σ × × = γ × ×−η −η −η These formulas can be used in practical applications as a heuristic approximation of the route standard deviation func- tion of the entire route congested travel time over the free- flow travel time. Relationship Between Mean and Standard Deviation of Time per Unit Distance The attractiveness of this approach is that there is a body of empirical evidence supporting a linear dependence between the travel time (per unit distance) standard deviation and mean at both the elemental link and route level. For example, research undertaken by Hani Mahmassani’s group at the Uni- versity of Texas in the late 1980s, using data collected using the chase-car technique, exhibited such a linear relation (Jones et al. 1989). The proposed approach that has been extensively tested in the course of the current project is based on a relationship between mean travel time per unit distance and its variability established at the entire-route level. This is a simple but robust model suggested by the traffic flow theory. It is formu- lated in the following way (Equation 3.17): (3.17)1 2t E t( ) ( )σ ′ = θ + θ × ′ + ε where t′ = route travel time per unit distance, s(t′) = standard deviation of route travel time per unit distance, E(t′) = mean value of route travel time per unit distance, q1, q2 = estimated coefficients, and e = random error. Calibration results for this model based on the GPS traces from the Seattle Traffic Choices Study (Puget Sound Regional Council 2007) are presented in Figure 3.8. The path-level coef- ficients are recommended for application in the framework of path-based assignment algorithm. Dependence Between Mean and Standard Deviation of Route Travel Time Another piece of empirical evidence that travel time mean is a good predictor of variance is taken from SHRP 2 Project L03, Analytical Procedures for Determining the Impacts of Reliability Mitigation Strategies (Cambridge Systematics, Inc. et al. 2013). It is presented in Figure 3.9. Several outliers presented at the figure correspond to a one-time lane closure. The L03 authors adopted a nonlinear approximation function, though a linear one would fit the data equally well. This formula reduces the problem of constructing a variance characteristic for the O–D-path from link variances to a single parameter hr applied in combination with the route length. The presence of a route-specific multiplier (dr)hr explains why, though the linear dependence can be statistically confirmed for a wide range of links and routes, very different slopes are observed for different routes. In general, the longer is the route and the lower is the level of correlation between the links on the route, the lower will be the route-level variance that is expressed in a smaller slope. This formula is also in a principal agreement with the route- level empirical formula developed on the basis of the data from Leeds, United Kingdom, region (Arup 2003). The Arup formula is written in the following way (Equation 3.18): 0.148 (3.18) 0.781 0.285 T T T d r r r r r  ( )σ = ×    × − It can be equivalently rewritten as Equation 3.19 for better compatibility with Equations 3.15 and 3.16, which are dis- cussed above: 0.148 (3.19) 0.781 0.285T T T dr r r r r   ( )σ = ×    × × − Another equivalent transformation of the Arup function is useful for compatibility with the graphs in Figure 3.9, in which

38 (a) (b) (c) Figure 3.8. Standard deviation of trip time per unit distance as a function of average time per unit distance (Mahmassani et al. 2013). (a)  O–D level, (b)  path level, and (c)  link level. Figure 3.9. Travel time variance as a function of average time (Cambridge Systematics, Inc. et al. 2013).

39 the standard deviation per mile is contrasted to the average time per mile and takes the following form (Equation 3.20): 0.148 1.6 (3.20) 1.781 0.781 0.285  ( )σ = ×    ×     × − d T d d T d r r r r r r r where d T r r = free-flow speed, and 1.6 = scaling coefficient from kilometers to miles. The scaling coefficient is not needed for the other distance terms in the formula since it would be canceled out. The Arup functions for different speed limits and distances are presented in Figure 3.10 for different assumptions regard- ing trip length and speed limits. In general, the longer the trip, the lower variability is, and the higher the free-flow speed, the greater variability is. Interestingly, the Arup function is essentially convex with respect to the coefficient of variation (i.e., it assumes that time variability grows faster than average travel time when conges- tion grows); the functional form adopted in the SHRP 2 L03 study suggests concavity (i.e., some saturation effect when travel times are somewhat stabilized at high levels of congestion becoming “reliably bad”), while the Northwestern researchers on the L03 team adopted a linear function. It should be men- tioned, however, that the level of empirical data in hand does not currently allow for an unambiguous choice with respect to these functions. In practical terms, they all perform similarly to a linear function in the range of most frequently observed levels of congestion; the principal differences between the functions begin at very high levels of congestion for which, normally, only a few observations are available. By comparing Equation 3.19 with Equations 3.15 and 3.16, we can say the following: • Both formulations are similar and relate the standard devi- ation to mean travel time (proportionately) and distance (inversely proportional with a power coefficient between -0.5 and 0.0). These two factors relate to the obvious effects for which a certain consensus has been reached. The first factor states that the longer the average congested travel time, the greater its variability. The second factor states that the longer the route distance is, the stronger the mitigation effects associated with imperfect correlation between the links would be. • The Arup formula has an additional multiplier that is the Congestion Travel Time Index. Overall, with this multi- plier, it makes standard deviation an exponential (rather than linear) function of the average congested travel time. Empirical data so far developed in the current project do not confirm this and instead indicate a linear dependence rather than an exponential one. Also, this multiplier is not additive by links (in addition to the distance-based term), which com- plicates its practical application. The team’s intention is to have an analytical dependence with a single non-additive- by-links term and a single route-level parameter to calibrate. • The Arup formula postulates a certain value for the distance- based exponential scale (-0.285) regardless of the level of correlation of link travel times along the route. The team pro- poses to have a route-specific parameter -0.5 ≤ -hr ≤ 0 that is calibrated based on the specific network configuration and demand flow structure. To further simplify the approach and reduce it to essentially a link-based assignment algorithm without explicit route enumeration, the team also proposes to calibrate the distance-based scale for each O–D pair rather than each network route. This is yet another empirical com- ponent but it has a certain behavioral basis since the O–D measure is dominated by a few chosen (good) routes. Endogenous Distance-Based Scaling The basic idea is that if multiple network loadings {vna}n are available (e.g., by exploiting multiple iterations of equilibrium assignment or, alternatively, by randomly varying the demand Figure 3.10. Travel time variance as function of average time.

40 matrix), both the link-level and O–D-level travel time vari- ances can be calculated in a way that gives rise to the following estimation method for scaling parameter (Equation 3.21): (3.21) 1 dij ij a a A ij ij ∑( ) = σ σ −η ∈ where dij = distance skim based on the shortest path at free-flow time, sa = link standard deviations for travel times across loadings, sij = standard deviation for O–D travel time skimmed by the shortest path for each iteration, and Aij = loadings between origin i and destination j. The following setting and algorithm can be outlined for a practical application (i.e., iterative traffic assignment), where n now denotes the iteration number: 1. Assume an initial link generalized cost function of the form ca = T˜a(va) + l × sa[T˜a(va)] according to Equation 3.13 or Equation 3.14, where parameter l represents a reliability ratio with a normal value of 0.8. 2. Set a matrix of distance-based scales according to the assumption of independence between link travel times hij = 0.5. 3. Assign demand Wij to the shortest paths at zero volumes to obtain zero iteration volumes {va0}. 4. Set iteration counter n = n + 1. 5. Recalculate link generalized cost functions can+1 = T˜a(van) + l × sa[T˜a(van)]. 6. Assign demand Wij to the shortest paths at volumes {van} to obtain next iteration volume directions {wan+1}. In the path building procedure, scale the variance-related component of the link generalized cost functions to account for the correlation pattern can+1 = T˜a(van) + l × sa[T˜a(van)] ⁄ (dij)1-hij. 7. Calculate new weighted link volumes for the current itera- tions 1 1 1 1 1v n w n n van an an{ }= + −+ + + . 8. Calculate O–D travel time skims. 9. Recalculate travel time standard deviations for links and O–D pairs across iterations, and recalculate the scaling factors by Equation 3.21. Go to Step 4. It is appropriate to use inter-iteration variability to esti- mate the correlation scaling factors (that essentially reflect the common demand flows going through different links) but not to estimate the standard deviation in travel times directly. Inter-iteration variability has not much relation to real world variability and does not correspond to the actual sources of travel time variability (except for some relation to route choice). Mechanically, variation across iterations could be used to provide a direct measure of standard deviation at the O–D level, without going through this process. However, that method would hardly produce reasonable estimates. In reality, some congestion is more reliable than others; so even across links, variability is not perfectly correlated with mean travel time or speed. The described process broadly allows for incorporation of that difference by applying weights by facility type. The distance scaling factors in Step 9 could be calculated using a weighted sum of link SD(T)s in this case. Nonmonotonic Relationship Between Mean and Standard Deviation There have been some research approaches in which a non- monotonic relationship between the mean and standard deviation of travel time was advocated (Bates et al. 2002; Eliasson 2006). This effect is due to the serial correlation between different values of standard deviation and mean across observations taken at successive points in time. It results in a two-fold function with one part corresponding to growing congestion and the other part corresponding to congestion release. While this effect is plausible and in a certain sense similar to two-fold volume- delay functions advocated by many researchers, this curve in Bates et al. (2002) was obtained as a result of a hypothetical one-link experiment with many specific assumptions regarding the sources of travel time. In Eliasson (2006) it was based on automatic travel time measurements on selected urban links. Thus, more empirical data are needed to substantiate this type of nonmonotonic function for the entire O–D route. Another possible type of nonmonotonic relationship was the focus of discussion at the special session on travel time reliabil- ity at the 89th Annual Meeting of the Transportation Research Board in 2010. Some researchers advocated that at a high level of congestion, travel time variation should be reduced since travel time becomes “reliably bad.” Again, there is currently very little empirical evidence to support this effect (Brennand 2011). In particular, it was generally agreed that when the recur- rent congestion grows, the relative impact of nonrecurrent congestion (e.g., due to a traffic collision) will not be mitigated, but rather exacerbated. Multiple-Run Framework Addressing Feedback with Simulation Models Linking travel demand forecasting to traffic microsimulation is one of the most important aspects of the current project. The simulated traffic conditions (described not only in terms of average travel time, but as travel time distributions with reli- ability measures) should be fed back to choices of travel route, travel mode, departure time, and other possible choice dimen- sions (including destination choice and even the decision to travel at all—i.e., trip frequency/generation choice).

41 Incorporating average travel time in the feedback mecha- nism has become a routine part of travel demand and traffic assignment models. Traffic assignment models operate with (average) generalized cost combined with (average) travel time and (average) cost expressed in travel time units. This measure is directly used in route choice embedded in the network simu- lation procedure. Further on, travel time and cost skims are used to form mode choice utilities. The other choice dimen- sions (time-of-day choice, destination choice) include either mode-choice logsums or time/cost skims, depending on the structure of the model. The incorporation of travel time reliability into the feed- back mechanisms, however, is not trivial since the travel time reliability measure in itself requires several iterations with varied demand and supply conditions. The reliability measure can be introduced in the generalized cost function of route choice (in addition to average travel time and cost). Then, the route generalized cost (or separate time, cost, and reliability skims) can be used in the mode choice and upper level mod- els. This technique, however, would only address one iteration feedback of (previously generated) reliability on average travel demand. The fact that both demand and supply fluctuations affect reliability creates a major complication. In other words, the equilibration scheme should itself incorporate the process of generating of reliability measures. The general suggested structure that resolves this issue is pre- sented in Figure 3.11. It includes the travel time variation mea- sure of reliability as the only practical option within the project time and budget. The key technical feature of this approach is that the very top and bottom components—average demand and average travel time—are preserved as they function in the conventional equilibration scheme, while the reliability mea- sures are generated by pivoting off the basic equilibrium point. The distribution of travel times is modeled as the composi- tion of three sets of probabilistic scenarios: (1) demand varia- tion scenarios, (2) network capacity scenarios, and (3) network simulation scenarios. Each set of scenarios has its own group of factors that cause variation. The final distribution of travel times is generated as a Cartesian combination of the demand, capacity, and simulation scenarios. It is essential to have a static demand-supply equilibrium point (between the average demand and supply) explicitly modeled for two reasons, to • Define the basic travel demand patterns (at least in pro- babilistic terms) off which the variation (scenarios) can be pivoted. • Provide the background level of congestion and associated fragility of traffic flows from which the probability of breakdowns can be derived. Average demand is a function of both average travel time and reliability (through measures like buffer time). It is assumed that the average demand and the corresponding equilibrium point are simulated separately for each season (if seasonal varia- tion is substantial), day-of-week (if there is a systematic varia- tion across days of week), and time-of-day period conditions, although there is a linkage across the demand generation steps for different periods of a day (especially if an advanced activity- based model is applied). The demand fluctuation scenarios are created by application of several techniques (e.g., Monte Carlo variation) and auxiliary models (e.g., special events model) described in the subsequent sections. In addition to feeding back the resulting average travel times and reliability measures to the average demand genera- tion stage (i.e., having a global feedback), two additional (internal) feedback options will be considered: 1. Internal feedback of scenario-specific travel times through route choice adjustments in the network simulation proce- dure. In this option, travel demand and network capacity are considered fixed. However, route choice can change from iteration to iteration because of the factors associated with traffic control, incidents, individual variation of driving habits, and dynamic real-time pricing, if applied. The net- work simulation can also incorporate the probability of flow breakdown. In the course of this project, the corresponding network simulation algorithm and route choice feedback mechanism will be established first. Then, this module will be employed within the demand-supply equilibrium frame- work (second internal feedback and global feedback). Average demand Demand scenarios Network capacity scenarios Season Day of week Time of day Special events Day-to-day individual variation Weather Work zones Network simulation scenarios Traffic control Dynamic pricing Incidents Day-to-day individual variation Scenario-specific travel times Travel time distribution Average travel times Conventional Buffer time, STD Schedule adjustments Route adjustments Figure 3.11. Implementation of feedback with demand and network scenarios.

42 2. Internal feedback of travel time distributions (and any derived measure of reliability) to the demand scenario through schedule adjustments of trip departure times. In this option, the demand scenario (in terms of trip genera- tion, distribution, and mode choice) is considered fixed, while the trip departure time can change from iteration to iteration as the result of travel time fluctuations modeled by the network capacity and network simulation scenar- ios. The purpose of this feedback is to stabilize trip depar- ture times for each demand scenario. This feedback is applied within the global equilibrium loop. The details of the demand generation process and its sensi- tivity to reliability measures depend on the type of travel demand model. The team plans to address both traditional (4-step) trip-based travel demand models and advanced activity-based models. The activity-based modeling frame- work represents a more promising counterpart to microscopic and mesoscopic network simulation models because of their more compatible temporal resolution. Advanced activity- based models in practice already operate with 30–60-minute demand slices, while traditional 4-step models typically oper- ate with broad 3–4-hour periods. For a 4-step travel demand model, the following dimension and components of travel demand can be included in the equilibrium framework and incorporate reliability measures: • Mode choice, in which utility functions for highway modes (drive alone, shared ride) can include buffer time or any other reliability measure; • Trip distribution, in which the travel impedance function can include mode choice logsum or directly include reli- ability measures; • Trip time-of-day choice, specifically for highway modes, in which the peak (and other period-specific) factors can include period-specific reliability measures; and • Trip generation, which can be made sensitive to accessibility measures (destination choice logsums) that can include reli- ability measures along with average travel time and cost. It should be noted that it may not be easy to incorporate all of these features into 4-step models. This has been part of the motivation for development and adoption of activity-based models by planning agencies over the past two decades. For an activity-based travel demand model, the following dimension and components of travel demand can be included in the equilibrium framework and incorporate reliability measures: • Mode choice, in which utility functions for highway modes (drive alone, shared ride) can include buffer time or any other reliability measure; • Primary destination choice, in which the travel impedance function can include mode choice logsum or directly include reliability measures; • Stop frequency and location choices for chained tours that are also based on travel impedance functions with reliabil- ity measures; • Tour generation models (daily activity-travel pattern), which can be made sensitive to accessibility measures (des- tination choice logsums) that can include reliability mea- sures along with average travel time and cost; and • Tour time-of-day models (daily schedule), which can be made sensitive to time-specific reliability measures. It should be mentioned that despite certain similarities between the 4-step and activity-based models in their approaches to incorporating reliability feedback, there are some important principal differences. In particular, 4-step models operate with aggregate zonal flows, so that any demand response to reliability will be identical for all trips within the same segment. In contrast, activity-based models are based on individual microsimulation, which opens the way to imple- ment the feedback on the individual level, at which point additional individual variation can be taken into account. Also, the utility coefficients in activity-based microsimulation models can be effectively randomized, taking into account individual variation of value of time and value of reliability. technical Aspects of Scenario Formation Practical implementation of the equilibrium mechanism shown in Figure 3.11 requires the establishment of certain rules for scenario formation, as well as specific technical aspects for the combination of different sources of travel time variability. The team envisions the following general imple- mentation scheme: • All three types of scenarios are defined as discrete cases with a predetermined number of states. These discrete states are randomly generated at each global iteration; however, the number of states and the core probabilistic distributions are prepared in advance. It should be men- tioned that even with a small number of states generated in each dimension, the Cartesian combination of them can easily reach a number that would result in unrealistic run- times for simulations (especially in large urban networks). Thus, generally, two to three random scenarios for each factor would be enough. A fractional factorial design can be effectively employed to reduce random variation. • Scenarios associated with travel demand and network capacity are simulated first since they are assumed indepen- dent. Then they are combined in a Cartesian way. Travel

43 demand scenarios in turn are combined with scenarios for special events and day-to-day variation scenarios that are also assumed independent. Network simulation scenarios are combined with scenarios for weather conditions and scenarios for work zones that are also assumed indepen- dent. For example, assume that for each of the four dimen- sions we generate two scenarios. This would already result in 2 × 2 × 2 × 2 = 16 combined basic scenarios. Taking into account that day-to-day variation in travel demand con- tributes 60% to 70% of the observed variability in travel times, we may generate more scenarios (three or four) for this particular factor. This would make the total number of possible combined scenarios 24 or 32. A fractional factorial might also be adequate here, allowing for more scenarios for each dimension while keeping the total number of com- binations realistic. The goal is to come up with a realistic distribution of travel times across a wide range of combina- tions of conditions—not to test every combination. • Each of the 16 basic scenarios is simulated, taking into account several possible network simulation scenarios. Each network simulation scenario is essentially a full run of net- work simulation with certain randomly drawn parameters that relate to traffic control, dynamic pricing algorithm, incidence occurrence, and individual route choice and driv- ing style. On top of these randomized factors, a flow break- down probability will be applied. If we implement three runs for each scenario, it would result in 3 × 16 = 48 simula- tions. This would supply travel time distribution for each O–D pair with the necessary degree of details. Essentially, any of the applied reliability measures (standard deviation; 80th, 85th, 90th, or 95th percentile) can be derived from this distribution. Parallel processing can be effectively employed for multiple simulation runs. Since the core 16 scenarios for travel demand and network capacity have been defined, the simulation runs can be implemented independently. • Trip tables associated with special events will be pre- calculated for each venue and randomly chosen from the list based on the frequency (as described in the next subsection). These tables will be added to the core trip table generated by the demand model. • The core trip table will be randomized as described in the next subsection to account for day-to-day individual variation. • The weather condition scenarios will be randomly chosen from the frequency table that will contain two to three weather-related states that are significantly different from the travel condition point of view. Dependent on the chosen region for simulation, the states will be classified as normal, rainy, and/or snowy/icy. For each of the weather condi- tions different from the normal, network capacities and/or volume-delay functions will be adjusted to account for the additional difficulty of driving. • The scenarios associated with work zones will be con- structed based on the observed/planned frequency of link/ lane closures by road type for the time-of-day periods of the simulation. Based on the defined frequencies, some network links/lanes will be disabled in the traffic simulation process. The methodological and implementation details associated with scenario formation are described in Chapter 6. They are described again in connection with the applications presented in Part 3 of this report. Travel Demand Scenarios Individual travel behavior is inherently stochastic from the perspective of the modeler. Except for work and school com- muting, most of the trips are not implemented on a daily basis. Even for commuting trips that are the most stable demand component of travel, there is an average weekday attendance factor (trips per workplace) of around 0.8 because of vaca- tions, sickness, days off, work in other locations, and so on. This means that a 5% spike in traffic flow can be just a com- bination of random individual trip frequencies. It can be said that the random variation in individual travel behavior is a consequence of small special events unknown to the modeler. There are probably some opportunities to move some of the uncertainty attributed to random individual behavior into the systematic variation category. For example, one can speculate that there might be a seasonal effect in workplace attendance. However, in general, randomness of individual behavior cannot be eliminated from the travel forecasting process, and it should be explicitly incorporated into the new generation of travel models. The team suggests two possible and different approaches to incorporating this factor. Approach 1. One of the natural options is embedded in the demand microsimulation structure of activity-based models. These models operate with parameterized probabilities that are converted into travel choices by using Monte Carlo (or sometimes more elaborate discretizing method); see Vovsha et al. (2008) for technical details. Thus, a certain level of vari- ability can be effectively modeled by changing random num- ber seeds in the microsimulation process (so-called Monte Carlo variability). This option is comparatively simple to imple- ment, and it will be fully explored in the current project for both travel choices and route choice in the traffic simulation. This approach is difficult to operationalize for a 4-step model that operates with aggregate flows. The conceptual limita- tions of this approach have to be understood nonetheless since Monte Carlo variability does not have a systematic rela- tionship to real world variability. Approach 2. Another possible approach that is equally appli- cable to 4-step and activity-based models is estimating variation

44 in aggregate demand (trip table) based on the observed variation in link traffic counts. This approach has been successfully used in the framework of the SHRP 2 C04 project. In this approach, a set of trip tables (demand scenarios) can be created (pivoting off the average trip table) that, when assigned, would replicate the observed distribution of traffic counts for each link. With this approach, continuous or repeated traffic counts taken multiple times for each link are sorted by scenarios. Contempo- raneous counts are included in the same scenario, and the cor- relation patterns between links with a significant common flow are taken into account (e.g., adjacent links). After the counts have been sorted by scenarios, the trip table is adjusted to each scenario (corresponding count values). The process is first cali- brated for the base year. Then the variation proportions can be calculated (for each O–D pair) and applied in forecasting. Application of this approach with DTA when discrete trips and tours are simulated instead of aggregate O–D flows requires some modifications. Individual trips or tours are (randomly) replicated and/or deleted based on the correction coefficients. When trips are replicated, the exact times and exact network entry/exit nodes are randomized to avoid extra “lumpiness.” Special events represent one of the more important factors that contribute to nonrecurrent congestion on the demand side. A good operational classification of planned special events is provided in Fox et al. (2003) and is reproduced in Table 3.6. Parsons Brinckerhoff is currently developing a special events, activity-based model for the Phoenix metropolitan area, which represents an additional component added to the regional travel demand model. Different from the core demand model that is based on a household travel generation process in which tours/trips are produced by households and then attracted to the potential destinations, the special events model is based on the reverse logic. The flow attracted to the venue is estimated first, and then the origin trip ends are distributed across the region. The model is segmented by the special event/ generator type and includes the following major components: • First, the yearly frequency and total daily patronage of the venue is estimated, as well as the distribution by time-of- day periods. • The mode choice model is applied for each relevant time- of-day period (when the venue is open for visitors). Utili- ties are obtained for every valid mode and production/ attraction pair, and logsums are computed. • The relative attractiveness of each production (residential) zone is computed for each time-of-day period, and event trip attractions by attraction zone are distributed to each production zone, according to the relative attractiveness of the production zone compared with all production zones. • Utilities are recomputed and probabilities are computed for every valid mode and production/attraction pair. The trips between each zone pair are allocated to the modes available by applying the mode choice probabilities. • The trips are assigned to the appropriate network. Table 3.6. Classification of Special Events event type examples Demand Characteristics discrete/recurring event at a permanent venue Planned special events include sporting events, concerts, shows, theater, festivals, and conventions occurring at permanent multi-use venues (e.g., arenas, stadiums, race- tracks, fairgrounds, amphitheaters, convention centers) Predictable starting and ending times; known venue capacity; anticipated demand typically known; advance ticket sales; concentrated arrival and departure demands continuous long-term exhibitions, museums, multiple-day conferences (e.g., TRB annual meeting) occurrence often over multiple days; patrons arrive and depart during the event day; less reliance on advance ticket sales; capacity of venue not always known; occurrence sometimes at tempo- rary venues; variation in parking availability Street use less frequent public events such as parades, fireworks dis- plays, bicycle races, sporting games, motorcycle rallies, seasonal festivals, and milestone celebrations at tempo- rary venues; temporary venues such as parks, streets, and other open spaces with limited roadway and parking capacity and undefined spectator capacity occurrence on roadway requiring closure; specific starting and predictable ending times; capacity of spectator viewing area not known; spectators typ- ically not charged or ticketed; variation in parking availability; impacts on emergency access and local services Regional/multiple-venue olympic games, international festival, world championship occurrence of events at multiple venues at or near same time; ingress and egress operations for con- current events that occur at same time; parking areas that service demand from different events during the day Rural Farm market or festival Rural area and possible tourist destination; high attendance events attracting event patrons from a regional area; limited roadway capacity; area lack- ing regular transit service

45 A model of this type naturally lends itself to a traffic simu- lation incorporating reliability. The probability of the event occurring during the simulation run is estimated based on the frequency for each venue. In each generated demand sce- nario, some of the randomly selected special events will be included. To better control for variability across different demand scenarios, the random selection process can be orga- nized with “no replacement” rules. Network Capacity Scenarios Network capacity can be significantly affected by the weather conditions and road works that require closure of some lanes or entire road segments for some period of time. The impacts of weather conditions on road capacity can also be explicitly taken into account in the network simulation through param- eters of car following. To include these factors in the network simulation, the following technical steps will be implemented: • Weather conditions. A categorization of possible weather conditions will be implemented for the given season and hour with probability for each particular condition to occur. Then for each condition that is different from nor- mal, network capacities and speed functions will be adjusted accordingly. • Work zones. The probability of lane/road segment closure for maintenance or other purpose will be calculated for all facil- ity types. According to this probability, in the network simu- lation, some network links are fully or partially disabled. If special events are associated with some predetermined road closures (in addition to the demand spike associated with the event), this factor can be combined with road works in the network scenario formation. Details that relate to these factors are discussed in the pilot applications. Network Simulation Scenarios For a given combined demand and network capacity sce- nario, there are two major factors that can significantly affect travel time reliability (and specifically relate to nonrecurrent congestion): incidences and traffic flow breakdowns. Ways to parameterize the probability of these factors occurring, and the associated practical techniques to incorporate them into network simulations, have been discussed in detail in the Task 7 Report (Stogios et al. 2014). In the framework of mul- tiple simulation runs (implicitly associated with different days), these factors form scenarios of network simulation. It should be stressed that due to these factors, different simulation runs can produce very different travel times even though the demand and network capacity are fixed. Drivers’ response to changing network conditions is subject to different time scales. This has to be taken into account when forming the equilibration strategies. For example, route choice can change in response to a collision or work zone. However, this is not a long-term equilibrium state for the network. Varying time scales affect equilibration (fixed versus equilibrated versus one-pass) in the context of recurrent and nonrecurrent congestion. This section explains the differences between equilibrium in different time scales. This is of special relevance for modeling nonrecurrent congestion that cannot be considered as a state of equilibrium but is rather a one-pass event. Recurrent congestion in general is recognized as an example of a well-equilibrated state in which multiple highway users tried different routes (presumably on different days) and eventually reached a certain level of convergence (average day). Recommendations are made on how an equilibration time scale can be properly accounted for. A wide range of travel choices with very different time scales for traveler responses are affected by travel time reli- ability. Short-term responses include travel dimensions such as network route choice (including any portion of the route when new travelers’ information becomes available), route type choice (toll versus nontoll and/or managed lanes versus general-purpose lanes), trip departure times, and possibly mode choice (if a transit option is competitive). Because the perception of travel time reliability generally stems from observed variability over time, it requires a certain learning curve and experience from travelers to perceive it and respond to changes in it, although an advance information system that would provide reliability estimates along with the shortest and/or average travel times can change this drastically. Mod- els that are based on the distribution of travel times imply that the travelers have a good idea about this distribution, which probably means in practical terms at least 5–10 recent trips along the route at the same time of day. It is yet to be explored how the modeling assumptions about travelers’ knowledge and information match the reality, but this is largely the same problem with the conventional models that operate with average travel time. The assumptions about drivers’ per- fect knowledge and immediate response to changes in average travel times are seen to be essential for making the models analytically simple and operational, but they might be quite far from reality. recommendations for Future research Several important research directions have become clear in the course of the current project. Many of them relate to more advanced methods of incorporation of travel time reli- ability, specifically schedule delay cost and temporal activity

46 profiles. However, improving travel demand models and net- work simulation tools in this direction is closely intertwined with a general improvement of individual microsimulation models. The following specific recommendations for future research are made: • Continue research on advanced methods for incorporation of travel time reliability into demand models and network simulations tools, including the schedule delay cost approach and temporal utility profile (loss of activity participation) approach. As part of such research, continue research and development of path-based assignment algorithms that incorporate travel time reliability and can generate a trip travel time distribution in addition to mean travel time. • Continue research on schemes for the integration of advanced ABM and DTA that can ensure a full consistency of daily activity patterns and schedules at the individual level and behavioral realism of traveler responses. In this regard, enhancement of time-of-day choice, trip departure time choice, and activity scheduling components are essential to address. This relates to the conceptual structure of these models and their implementation with respect to temporal resolution. • Encourage additional data collection on the supply side of activities and on scheduling constraints, including the dis- tribution of jobs and workers by schedule flexibility, clas- sification of maintenance and discretionary activities by schedule flexibility, as well as developing approaches to forecast related trends. • Continue research and application of multiple-run model approaches and associated scenario formations, for both the demand and network supply sides. The team’s synthe- sis and research have shown that a conventional single-run framework is inherently too limited to incorporate some important reliability-related phenomena such as nonre- current congestion due to a traffic incident, special event, or extreme weather condition. • Incorporate travel time reliability in project evaluation and user benefit calculations. Restructure the output of travel models to support project evaluation and user benefit cal- culations with consideration of the impact of improved travel time reliability.

47 C h A p t e r 4 Introduction This chapter describes the framework and the functional requirements for the inclusion of travel time reliability esti- mates in transportation network modeling tools, with par- ticular focus on stochastic traffic simulation models. The framework identifies phenomena and behaviors that account for the observed variability in network traffic performance, and unifies all particle-based simulations at the microscopic and mesoscopic levels. Recognizing that the requirements development process is focused on the uses of traffic opera- tional models in agencies at the local, metropolitan, regional, and state levels, the functional requirements are developed for different resolutions and scales. In addition, a repeatable framework is proposed to model travel time variability induced by incidents and random events, recognizing the difference between so-called recurring and nonrecurring congestion due to various sources. Incorporating travel time reliability into stochastic traffic simulation models has the primary objective of enabling the off-line evaluation of traffic network performance, including assessment of management interventions, policies and geo- metric configuration, and so forth, as well as both short-term and long-run impacts of policies aimed at improving travel time and service reliability. Longer-term impact evaluation entails integrating reliabil- ity considerations in equilibrium planning models. An ideal integration would bring together reliability-sensitive network simulation models with micro-level activity-based demand models. However, practical approaches consistent with the current state of the practice can also be formulated. In addition to off-line applications, reliability-sensitive simulation models can support the design and implementa- tion of real-time operational decisions. The design of online traffic information and management strategies calls for sto- chastic simulation tools that are capable of modeling recur- rent and nonrecurrent congestion and generating reliability measures in real time. Framework Traffic operations and planning models generally require both demand and supply inputs. Travel demand could be static (for planning models), dynamic (for planning and operational models), or in the form of activity schedules (for activity-based models). In virtually all applications, actual travel demand cannot be perfectly forecast and is subject to a variety of dis- turbances, including special events, day-to-day variation in individual behavior, (unfamiliar) visitor traffic, and diversion from temporary unavailability of alternative modes. On the supply side, the operational capacity of network elements could be assumed as fixed, stochastic, or systematically vary- ing with traffic conditions through actuated signal controls, ramp metering, dynamic tolls, and so on. Unreliability sources that affect supply-side attributes consist of incidents, work zones, weather, traffic control, dynamic pricing, and varia- tion in individual driving behavior. These variations in demand and supply affect the movement of vehicles and the propagation of traffic flow, resulting in different travel times for drivers traveling on the same link or path or between a given origin–destination (O–D) pair. Therefore, travel time variability, at the individual or aggregated levels, could be quantified based on the simulation results, in particular, vehicle trajectories. Commonly used reliability measures include the probability of arriving on time, the Travel Time Index (ratio of the mean experienced travel time to the free mean travel time), the variance (or standard deviation) of experienced travel times, and various descriptive statistics that can be derived from the distribution of travel times, which is the most general and complete way of character- izing travel time variability across a population of drivers in a network. Figure 4.1 presents a general framework for incorporating reliability aspects into modeling tools used to support traffic operations and planning applications. The framework recog- nizes the different sources of unreliability and their interac- tion with the key components of network simulation models. Functional Requirements of Stochastic Network Simulation Models

48 Depending on the model’s intended purpose, data availability, and resource constraints for executing a particular study, appropriate assumptions can be formulated and inputs speci- fied regarding (1) the demand-side and supply-side character- istics, and (2) the variation sources to be included in the model. In addition, the specific travel time reliability measures can be accordingly selected. For example, if activity schedules of trip makers are available or are of interest, an activity-based travel simulation model can be used, considering some or all of the sources of variation in demand and supply and the probabil- ity of arriving on time for each traveler could be produced as a model output. Incorporating reliability into operations modeling tools entails three main components: (1) the Scenario Manager, which captures exogenous unreliability sources such as spe- cial events, adverse weather, work zone and travel demand vari- ation; (2) reliability-integrated simulation tools that model sources of unreliability endogenously, including user hetero- geneity, flow breakdown, collisions, and so forth; and (3) the vehicle Trajectory Processor, which extracts reliability informa- tion from the simulation output, namely, vehicle trajectories. Accordingly, the methodological framework for incorporat- ing reliability into stochastic network simulation models is shown in Table 4.1. Figure 4.1. Incorporating reliability measures into traffic operations and planning models. Travel Demand - Static - Dynamic - Activity schedule Network Capacity - Deterministic - Stochastic - Adaptive Simulation Model - Microscopic - Mesoscopic - Macroscopic Output - Individual level - Aggregated Demand Variation - Special events - Day-to-day variation in individual behavior - Visitors - Closure of alternative modes Supply Variation - Incidents - Work zones - Weather - Variation in individual driver behavior - Traffic control - Dynamic pricing Measure of Reliability - Travel time distribution - Probability of certain delay - Reliability proxies Table 4.1. Methodology Framework Input (exogenous sources) Scenario Manager Demand • Special events • day-to-day variation • visitors • closure of alternative modes Supply • Incidents • work zones • Adverse weather Simulation model (endogenous sources) existing simulation tools with suggested improvements Demand • heterogeneity in route choice and user responses to information and control measures • heterogeneity in vehicle type Supply • Flow breakdown and incidents • heterogeneity in car following behavior • Traffic control • dynamic pricing output Vehicle trajectory processor • Travel time distribution • Reliability performance indicators • user-centric reliability measures

49 Functional requirements Traffic operation models need to model variations in demand and supply sides as well as capture traffic physics. They are also expected to support system management decision mak- ing to control reliability, produce reliability-related measures, and retain flexibility to adapt to various agency and policy environments. The functional requirements for traffic opera- tion models needed to estimate travel time variability are summarized in Figure 4.2. Model Variations from Different Sources According to previous research (Cambridge Systematics, Inc. 2005, Figure 2.3), seven major factors account for approxi- mately half of all traffic delay and, therefore, a great deal of the uncertainty associated with travel time: (1) traffic incidents, (2) work zones, (3) weather (4) special events, (5) traffic con- trol devices, (6) fluctuations in demand, and (7) inadequate base capacity. In addition, factors such as variation in indi- vidual driver behavior, dynamic pricing, and closure of alter- native modes also increase travel time unreliability. Therefore, the traffic operation models should be capable of recognizing and representing both demand- and supply-side causes of variability, due to different sources. Furthermore, rather than affect travel time reliability sepa- rately, these factors often interact, which requires the ability to model all or any combination of the unreliability causes in one operational model. For example, adverse weather events may affect (supply-side) pavement conditions due to precipi- tation, as well as (demand-side) travel decisions as travelers may adjust their departure time or mode or cancel their trips. In addition, severe weather conditions could increase the probability of flow breakdown and traffic collisions. There- fore, traffic operation models intended to capture travel time variability need to model the impacts of weather events in all related components, including demand variation, traffic flow model, flow breakdown prediction, and collision prediction. Characterize Inherent Probabilistic Phenomena: Traffic Physics To capture the causes of unreliability in traffic, models should capture to the extent possible the underlying physics of the associated processes and phenomena. For example, density can be considered both a cause and an effect of unreliability. Figure 4.2. Functional requirements. Model variation in demand • Special events • Day-to-day variation in individual behavior • Visitors • Closure of alternative modes Model supply-side variations • Incidents • Adverse weather • Work zones and special events Characterize traffic physics • Variation in individual driver behavior • User heterogeneity in route choice and responses to information and control measures • Inherent randomness in individual maneuvers • Collective Effects: Flow breakdown and its impact on travel time Support management decision making • Traffic control strategies, integrated system management • Traveler information systems • Dynamic pricing • Closure of alternative modes Produce reliability related output • Construct travel time distributions by link, segment, trip, and for the entire system • Calculate reliability performance indicators • Generate user-centric (experienced, perceived) reliability measures Retain flexibility to adapt to various agency and policy environments

50 When density goes above a threshold, the vehicle-to-vehicle interactions become a dominant factor. While density can be considered a result of these other variables, at a certain thresh- old, density might itself be an independent random variable contributing to instability, such as flow breakdown. In particular, both systematic variations in individual driver behavior and inherent randomness in individual maneuvers— including driver’s choice of speed, gap acceptance, and lane changing—account for considerable observed variability in traffic speeds and resulting travel times. Interdriver behav- ioral differences are essential for capturing certain congestion dynamics. For instance, the presence of aggressive drivers and conservative drivers in the traffic stream gives rise to traffic dis- turbances that may increase in intensity (creating congestion and even traffic breakdowns) or dampen with time (Daganzo 1999). Most critically, these models should capture the col- lective effects that arise from the inherent randomness in driving behavior, namely, flow breakdown and its impact on travel time. In addition, behavioral models that may be embedded in traffic simulation models need to account for user hetero- geneity in route choice and responses to information and control measures. For example, when provided with travel time information, users could choose whether to react to such information and decide how to evaluate the reliability aspect in choosing their paths. Support System Management Decision Making As explained earlier, traffic controls and dynamic pricing affect travel decisions, flow distribution, and thus experienced travel times. Therefore, operations/traffic control strategies and trav- eler information systems need to be incorporated into the modeling process intended to quantify travel time variability. In particular, traffic control strategies can be either explicitly modeled in a microsimulation setting or included implicitly through intersection capacity. In both cases, adaptation/ optimization algorithms can be applied. Alternatively, infor- mation systems could be incorporated into the traffic simula- tion models by emulating the real-time information process and its resulting effect on the route (and possibly departure time in the case of pretrip information) choices of highway users both pretrip and at intermediate points along the trip. Moreover, traffic management actions, including control strategies, integrated system management, traveler information systems, dynamic pricing, and closure of alternative modes, are essential supply-side actions to alleviate congestion and possi- bly improve travel time reliability. As such, it is essential that traffic operation models be able to represent such actions and capture their impact on system performance. Produce Reliability-Related Output The main intended functionality of reliability-sensitive traffic operation models requires the generation of an array of per- formance indicators and figures of merit that allow model users to characterize the existing variability and interpret its impact from the standpoint of the quality of traffic service experienced by users. A general approach to characterizing variability is examining the travel time distribution, which reflects the net result of the combination of recurring and nonrecurring congestion as found in real networks. It is there- fore desirable for the traffic simulation models to produce travel time distributions by link, path, and trip (O–Ds). In addition, these models are expected to produce reliability- related performance measures. In particular, from the sys- tem operator’s perspective, reliability performance indicators for the entire system should allow comparison of different network alternatives and policy and operational scenarios. This could facilitate decision making in regard to actions intended to control reliability and evaluation of system per- formance. In addition, it is essential to reflect the user’s point of view, by producing user-centric reliability measures, which describe user experienced or perceived travel time reliability. The reliability-related output processing is realized through the vehicle Trajectory Processor, which is discussed in detail in Chapter 7. Retain Flexibility to Adapt to Various Agency and Policy Environments As the ultimate goal of this project is to develop practical operational tools that could be eventually applied by metro- politan planning organizations (MPOs), departments of transportation (DOTs), and other agencies for testing pro- posed projects and policies, the developed approaches need to be designed in a flexible way to adapt to various agency and policy environments. This means application to a range of problems in terms of geographic scope, time frame, stage in the development process, and target impact. As such, incor- porating reliability is of interest for both planning and opera- tions applications, as well as for operational planning activities. As noted previously, this means having sensitivity to an array of policy interventions and operational measures, including various highway pricing options such as real-time adaptive pricing. Real-time adaptive pricing is considered a particularly promising strategy to regulate travel demand and improve reliability of the highway system. In addition, the operations models need to recognize the primary applications for which reliability information may be required, calibration require- ments, and ability/needs of typical agencies to leverage such capabilities.

51 Quantifying Travel Time Variability As one of the key functional requirements is concerned with producing reliability-related output, the operations models need to generate travel time distributions by link, path, and trip (i.e., O–Ds), as well as reliability performance measures for the entire system. This section describes the challenges in characterizing travel time variability and associated correla- tions, followed by the methods to construct travel time distri- butions. After that, the relation between mean and standard deviation of travel time per unit distance is examined; this illustrates an important property of travel time variation in a traffic network and provides a basis for a practical approach for deriving travel time variability measures from measured or simulated average values. Challenges in Characterizing Network Variability and Correlations Characterizing the reliability of travel in a network necessar- ily entails representing the variability of travel times through the network’s links and nodes along the travel paths followed by travelers, taking into account the correlation between link travel times. Variability of Travel Time Through Links and Nodes Empirical studies have confirmed that the distribution of travel time along a link or through a network is generally not sym- metrical, indicating that the mean and median values would not be the same. The distribution is highly skewed with a flat and long right tail. Under free-flow conditions/off-peak the dis- tribution of travel times has a shorter right tail. Li et al. (2006) suggested that a lognormal distribution best characterizes the distribution of travel time when a large (in excess of 1 hour) time window is under consideration, especially in the presence of congestion. However, when the focus is on a small departure time window (e.g., on the order of minutes), a normal distribu- tion appears more appropriate. In addition, Sohn and Kim (2009) used the generalized Pareto distribution (GPD) in com- puting percentiles, as a travel time reliability index, to recognize the asymmetry in the travel time distribution. The morning peak (7 a.m. to 9 a.m.) travel times collected on a freeway section of I-405N in Southern California are used to estimate the distribution of travel time. The Travel Time Index data show that the mean (1.59) and the median (1.48) are to the right of the mode (0.96), which suggests a positive- skewed (right-skewed) distribution. In Figure 4.3, the his- togram is plotted as an approximate density estimator. In addition, the data are fitted to a lognormal distribution. Capturing the variability of travel times in the form of link- level distributions is not sufficient for characterizing the reli- ability of travel. Equally important are travel times by movement through the nodes (intersections), particularly delays associ- ated with left-turning movements, which may differ consider- ably from the delays experienced by through and right-turning vehicles. The intersection delay can be calculated analytically using queuing models, in which vehicles arrive at an inter- section controlled by a traffic light and form a queue (McNeill 1968; van den Broek et al. 2004). Alternatively, the delays can be measured directly or extracted from vehicle trajectories generated from traffic simulation models. Correlation Between Link Travel Times In addition to the individual link and movement delay distri- butions, a particularly vexing issue is the strong correlation between travel times in different parts of the network, gener- ally in proportion to distance; that is, adjacent links are likely to experience delays in the same general time period than unconnected links. Therefore, even if the link-level time vari- ations are known, it is a nontrivial task to synthesize the O–D- level and path travel time distribution because of the dependence of travel times across adjacent links due to a mutual traffic flow. The correlation phenomenon in network travel times is a direct result of the topological nature of a network and the strong interactions it induces. Capturing these correlation patterns is generally very diffi- cult when only link-level measurements are available. More important, given that a vehicle typically traverses a large num- ber of links along its journey, deriving path-level and O–D- level travel time distributions from the underlying link travel time distributions, even when the multivariate covariance pat- tern is known and available, is an extremely unwieldy and ana- lytically forbidding task for all but very limited special cases. Figure 4.3. Distribution of link travel times during peak period (7 a.m. to 9 a.m.).

52 Constructing Travel Time Distributions To quantify travel time variability, the traffic simulation tools need to support various uncertainty analysis methods such as Monte Carlo simulation, sensitivity analysis, and scenario planning. Monte Carlo method. Many of the travel time unreliability factors mentioned earlier fall into the area in which the ran- domness can be parameterized and probabilities can be assigned based on the known parameters of the demand and/ or supply. The Monte Carlo method considers random sam- pling of probability distribution functions as model inputs to produce hundreds or thousands of possible outcomes. Based on the probabilities of different outcomes occurring, namely, realizations of travel times, one can construct the resulting travel time distribution. Scenario-based approach. Some of the travel time unreliabil- ity factors—such as collisions, flow breakdown, and special events—can be modeled by constructing a few discrete sce- narios and then conducting single-point estimation for each scenario. Various combinations of input variables are manually chosen (such as normal conditions, collision or flow break- down on a road section, and football games) and the results recorded for each “what if” scenario. Therefore, given the sched- ule of a particular event (e.g., traffic signal plans, dynamic pric- ing schemes, and football games) or the probability of an event occurring (e.g., collision, flow breakdown), travel time variabil- ity can be computed based on the outcomes of the scenarios. Sensitivity analysis. Sensitivity analysis techniques can also be used to study how the variation in travel time can be appor- tioned, qualitatively or quantitatively, to different sources of travel time unreliability in the input of the traffic operation models. Network Travel Time: Mean and Standard Deviation The relation between mean and standard deviation of travel times per unit distance is discussed in this section. By establish- ing a linear or near-linear relation between these two variables, we can easily estimate the variance of travel time based on mean travel time. Note that the travel time needs to be normal- ized by distance, that is, travel time per unit distance (or the inverse of the space mean speed) as shown in Equation 4.1. 4.1t t d ( )′ = where t ′ = travel time per unit distance, t = travel time, and d = distance. The assumption of the linear relation between mean and standard deviation of travel time per distance can be written as in Equation 4.2: ( ) ( ) ( )δ ′ = + ′ 4.2t a b E ti where d(t ′) = standard deviation of t ′, E(t ′) = mean value of t ′, and a,b = coefficients. This relation, originally suggested in Herman and Prigogine’s work on the characterization of network traffic quality, was verified empirically with traffic measurements using vehicle probes (Jones 1988; Mahmassani et al. 1989). Simulation results on two real-world networks are presented next to further explore the relation between mean and standard deviation of travel times. Simulation Results: Travel Time from Irvine Network The simulation experiment is conducted using the Irvine test- bed network shown in Figure 4.4. DYNASMART had been calibrated for this network using real-world observations, obtained from multiple-day detector data. This network has 326 nodes (70 of which are signalized), 626 links (57 of which have road detectors), and 61 traffic analysis zones (TAZ). The morning peak of 7 a.m. to 9 a.m. is chosen as the study period. The time-dependent O–D demand profile for 7 a.m. to 9 a.m. (58,450 vehicles) is calibrated using traffic counts. Assuming user equilibrium is reached, the experienced travel time and travel distance of each vehicle can be extracted Figure 4.4. Irvine network.

53 from the vehicle trajectories. The travel time per mile can therefore be computed for each vehicle. In Figure 4.5, each data point represents the mean and standard deviation of travel times per mile for vehicles departing in a 1-minute interval. Therefore, there are 120 data points for 2-hour demand. The plot shows that the mean and standard deviation of network travel time per distance are linearly related; namely, greater variability in travel time is associated with more congested traf- fic conditions (i.e., longer travel time per mile). In reality, collecting experienced travel times for an entire population of drivers would be very costly, if at all practical. In most cases, only a small portion of the population might be expected to be equipped with GPS devices and report their experienced travel times. To explore the possibility of correctly calibrating the mean-standard deviation relation of travel time per distance using a portion of travel time data, the team randomly chose 10% of vehicles in the network and computed the mean and standard deviation of travel time per distance. In Figure 4.6, each data point represents the mean and stan- dard deviation of travel times per mile for vehicles departing in a 5-minute interval. There are 24 data points corresponding to the base case and the case with 10% sample, respectively. By comparing Figure 4.5 and Figure 4.6, we can see that the slope remains almost unchanged when the aggregation interval var- ies from 1 minute to 5 minutes. In addition, the statistics com- puted from 10% of the population (i.e., 10% sample case) can characterize the mean-standard deviation relation of the entire population (i.e., 100% sample case). Simulation Results: Travel Time from the CHART Network Additional simulation experiments were conducted on the CHART (Coordinated Highways Action Response Team, Maryland) network, shown in Figure 4.7. The network pri- marily consists of the I-95 corridor between Washington, D.C., and Baltimore, Maryland, and is bounded by two belt- ways (I-695 Baltimore Beltway to the north and I-495 Capital Beltway to the south). The network has 2,241 nodes, 3,459 links, and 111 traffic analysis zones (TAZ). A 2-hour morning peak dynamic O–D demand table estimated for the network is used in the experiments. Following the same procedure introduced previously for the Irvine network, the mean and standard deviation of travel time per mile are plotted in Figure 4.8 for the 100% popula- tion sample and the 10% population sample, respectively. Similar patterns are obtained for the CHART network as for the Irvine network, that is, (1) the mean and the standard deviation of network travel time per mile are linearly related, and (2) 10% of the population can produce almost the same mean-standard deviation relation as the entire population. As the demand level affects the degree of congestion in the network, and thus the travel time and its variability, mean- standard deviation relations under different demand levels are examined and compared in Figure 4.9. In particular, the low- demand case corresponds to 80% of the peak hour demand, and the high-demand scenario corresponds to 100%. Figure 4.5. Network mean travel time per unit distance and standard deviation of travel time per unit distance, Irvine network. Figure 4.6. Comparison of mean versus standard deviation relation at different sampling rates, Irvine network.

54 Figure 4.7. CHART network. Figure 4.8. Comparison of mean versus standard deviation relation at different sampling rates. Figure 4.9. Comparison of mean versus standard deviation relation at different demand levels. Finally, the mean-standard deviation relations of the two networks are compared, as plotted in Figure 4.10. The ranges of mean travel time per mile are comparable (i.e., 1.4–1.9 minutes per mile), which indicates similar congestion levels. However, the CHART network shows lower travel time vari- ability in general. Therefore, it is suggested that the mean- standard deviation relation provides a “signature” for a given network and so should be calibrated for each network. Trajectories: A Unifying Framework One way to circumvent the challenges described in the previ- ous section with regard to travel time correlation across links and nodes, and the dependence of link travel times on the movement performed at the downstream node, is to obtain or measure the path- and/or O–D-level travel times as a complete entity instead of by construction from link-level distributions. In a simulation model, this means obtaining the travel times over entire or partial vehicle (or “particle” trajectories, using plasma physics terminology). Regardless of the specific reliabil- ity measures of interest, to the extent that these can be derived from the travel time distribution, the availability of particle

55 trajectories in the output of a simulation model enables construction of the path- and O–D-level travel time distri- butions of interest, as well as the extraction of link-level dis- tributions. As such, the key building block for producing measures of reliability in a traffic network simulation model is particle trajectories and the associated experienced tra- versal times through entirety or part of the travel path. Vehicle Trajectory Data The vehicle trajectory contains the traffic information and itinerary associated with each vehicle in the transportation network. Each trajectory is associated with a set of nodes (describing the path), the travel time on each link along the path, the stop time at each node, and the cumulative travel/ stop time. It could also include lane information for micro- scopic models. Obtain Vehicle Trajectory from Direct Measurements Conventional sensors (e.g., inductive loop detectors) can measure traffic stream parameters at an aggregated level, such as flow (the number of vehicles passing over the detector per unit of time) and occupancy (the proportion of time that a vehicle is located directly above the detector). Yet, develop- ments in information and communication technologies— such as mobile phones with embedded GPS sending precise locations and prevailing speeds to a centralized traffic control center, and low-cost wireless sensors on the roads providing a snapshot of current traffic conditions—offer opportunities to obtain traffic data at less aggregated levels, including record- ing vehicle trajectories. For example, the Federal Highway Administration’s Next Generation Simulation (NGSIM) project collected vehicle trajectories on a segment of Highway 101 in Los Angeles using digital video cameras. The INRIX Smart Dust Network collects anonymous, real-time GPS probe data from over 1 million commercial fleet, delivery, and taxi vehicles. In addition, vehicle trajectories can be measured or inferred from the matching of automatic number plate rec- ognition (ANPR) data, moving vehicle observers, and toll tag data from systems such as California’s FasTrak system. Direct trajectory measurement enables consistent theoretical devel- opment in connection with empirical validation. Obtain Vehicle Trajectory from Microsimulation and Mesosimulation Models Because it is predicated on particle trajectories, which could be obtained from both micro- and meso-level simulation models, the team’s framework for producing reliability output unifies all particle-based simulations, regardless of whether the physics underlying vehicle propagation and interactions are captured through microscopic maneuvers or through ana- lytic forms. Regardless of how microscopic the modeling approach might be, so long as it is particle-based and not flow- based, the framework is applicable. Figure 4.11 shows an example of vehicle trajectory output files. The first block pertains to vehicle number 16645. This vehicle has exited the network by the time this file has been generated (Tag = 2). The origin zone for this vehicle is 5 and the destination zone is 9. This vehicle responds to variable message sign (VMS) information (Class = 5). The upstream node of its generation link is 103; the downstream node of the generation link is 102; and the destination node is 11. The departure time is 70.20 minutes, and the total travel time is 8.49 minutes. The vehicle has 18 nodes in its path, is of vehicle type 1 (passenger car), and has an occupancy level (i.e., level of occupancy, or LOO) of 1. The next line lists the complete path from the origin to the destination (excluding the upstream node of the genera- tion link), namely, node numbers 102, 160, 102, 103, 151, 97, 89, 4, 3, 24, 5, 27, 28, 32, 35, 39, 40, and 11. Figure 4.10. Comparison of mean versus standard deviation relation for two networks.

56 The next line shows the time instance, relative to the depar- ture time, at which the vehicle exited nodes 102, 160, 102, 103, 151, 97, 89, 4, 3, 24, 5, 27, 28, 32, 35, 39, 40, and 11, which are 0.80, 0.90, 1.60, 2.20, 3.00, 3.40, 3.80, 5.00, 5.50, 5.90, 6.00, 6.30, 6.70, 7.10, 7.30, 7.60, 8.20, and 8.40 minutes, respectively. The next line shows the travel times on links 102→160, 160→102, 102→103, 103→151, 151→97, 97→89, 89→4, 4→3, 3→24, 24→5, 5→27, 27→28, 28→32, 32→35, 35→39, 39→40, and 40→11, which are 0.80, 0.10, 0.70, 0.60, 0.80, 0.40, 0.40, 1.20, 0.50, 0.40, 0.10, 0.30, 0.40, 0.40, 0.20, 0.30, 0.60, and 0.20 minutes, respectively. The next line shows accumulated stop times at nodes 102, 160, 102, 103, 151, 97, 89, 4, 3, 24, 5, 27, 28, 32, 35, 39, 40, and 11, which are 0.60, 0.60, 1.20, 1.36, 1.42, 1.44, 1.47, 2.22, 2.57, 2.57, 2.57, 2.57, 2.57, 2.57, 2.57, 2.57, 2.57, and 2.57 minutes, respectively, and so on. Vehicle Trajectory Processor The vehicle Trajectory Processor is introduced to extract reliability-related measures from the vehicle trajectory out- put of the simulation models. As shown in Figure 4.12, inde- pendent measurements of travel time at link, path, and O–D level can be extracted from the vehicle trajectories, which allows for constructing the travel time distribution. Reliability- related measures can then be derived from the distribution. Alternatively, some of the measures can be computed directly from the travel time data, such as 95th percentile, standard deviation, and probability of on time arrival. In particular, to quantify user-centric reliability measures, which describe user experienced or perceived travel time reliability, the expe- rienced travel time and the departure time of each vehicle are extracted from the vehicle trajectory. By comparing the actual and the preferred arrival times, the probability of on time arrival can be computed. Note that the preferred arrival time is an input of the model, which could be obtained from sur- veys, drawn from statistical distributions parametrically calibrated to observed data (Zhou et al. 2008), or simply spec- ified by the planner to generate performance measures. Extract Travel Time Information As explained, the key building block for producing measures of reliability in a traffic network simulation model is particle trajectories and the associated experienced traversal times through entirety or part of the travel path. Travel time vari- ability at link, path, and O–D levels can be extracted from the trajectories generated by micro- or mesosimulation models. Construction of Travel Time Distribution To produce travel time distributions by link, path, and trip (O–Ds) using simulation models, the following procedures are suggested. Figure 4.11. Example of vehicle trajectory output. **** Output file for vehicles trajectories **** ================================================= This file provides all the vehicles trajectories Veh # 16645 Tag= 2 OrigZ= 5 DestZ= 9 Class= 5 UstmN= 103 DownN= 102 DestN= 11 STime= 70.20 Total Travel Time= 8.49 # of Nodes= 18 VehType 1 LOO 1 102 160 102 103 151 97 89 4 3 24 5 27 28 32 35 39 40 11 ==>Node Exit Time Point 0.80 0.90 1.60 2.20 3.00 3.40 3.80 5.00 5.50 5.90 6.00 6.30 6.70 7.10 7.30 7.60 8.20 8.40 ==>Link Travel Time 0.80 0.10 0.70 0.60 0.80 0.40 0.40 1.20 0.50 0.40 0.10 0.30 0.40 0.40 0.20 0.30 0.60 0.20 ==>Accumulated Stop Time 0.60 0.60 1.20 1.36 1.42 1.44 1.47 2.22 2.57 2.57 2.57 2.57 2.57 2.57 2.57 2.57 2.57 2.57 Figure 4.12. Framework of vehicle Trajectory Processor. Travel time distribution Performance indicators: – Travel time variance – 95th Percentile Travel Time – Buffer Index – Planning Time Index – Frequency that congestion exceeds some expected threshold Vehicle trajectories Travel time by lane, link, path and trip (O-D) User-centric measures: – Probability of on time arrival – Schedule delay – Volatility Experienced vehicle travel time and actual departure time Preferred arrival time

57 Variation among Vehicles 1. Perform one simulation run. 2. Extract link (path or O–D) travel time for each vehicle. Each vehicle produces a sample point. 3. Construct link (path or O–D) travel time distribution based on the sample points obtained in Step 2. time-of-Day Variation 1. Perform one simulation run. 2. Extract link (path or O–D) travel time for each time inter- val (e.g., 5 minutes). Each time interval produces a sample point. 3. Construct link (path or O–D) travel time distribution based on the sample points obtained in Step 2. Day-to-Day Variation 1. Perform multiple simulation runs. Each run corresponds to 1 day. 2. Extract link (path or O–D) travel time for each run. 3. Construct link (path or O–D) travel time distribution for average values and for a certain period of day (e.g., a.m./ p.m. peak, mid-day). Figure 4.13 shows an example of constructing path travel time distribution from simulation results. The experienced travel times of all the vehicles traveling on a particular path (highlighted in the figure) are extracted from vehicle tra- jectories. The histogram of travel time per mile is plot- ted, from which a probability distribution function can be estimated. Reliability Performance Indicators From the system operator’s perspective, reliability performance indicators for the entire system should allow comparison of different network alternatives and policy and operational scenarios. This could facilitate decision making in regard to actions intended to control reliability and evaluation of system performance. The following reliability measures can be derived from the travel time distribution or computed from the travel time data directly. • 95th percentile travel time: How much delay will be on the heaviest travel days. • Buffer Index: Extra time so traveler is on time most of the time, computed as difference between 95th percentile travel time and mean travel time, divided by mean travel time. • Planning Time Index: Total time needed to plan for an on- time arrival 95% of the time, computed as 95th percentile travel time divided by free-flow travel time. • Frequency that congestion exceeds some expected threshold: Percentage of days or time that mean speed falls below a certain speed. User-Centric Reliability Measures In addition to the reliability performance indicators, it is essential to reflect the user’s point of view, as travelers will adjust their departure time, and possibly other travel decisions, in response to unacceptable arrival in their daily commute (Chang and Mahmassani 1988). The following user-centric reliability measures describe user experienced or perceived travel time reliability: • Probability of on time arrival: The probability of a traveler arriving at his/her destination on time. • Schedule delay: The amount of time that a traveler arrives at his/her destination late (or early, in which case the sched- ule delay is negative), compared with the preferred arrival time. • Volatility and sensitivity to departure time: Travel time fluc- tuation over time and its sensitivity to departure time changes. As shown in Figure 4.14, during some periods travel time changes dramatically, while at other times it Figure 4.13. Path travel time distribution example. Fr eq ue nc y (v eh ) Travel Time per Mile (min/mile)

58 remains relatively stable. Therefore, travel time is more sensitive to the departure time in the periods with high volatility. Empirical evidence suggests that certain travelers opt to leave early or late so as to avoid such periods. Model Variability and Its Sources in traffic Simulation tools To address the functional requirements related to modeling variability and its sources we need to identify phenomena and behaviors that account for the observed variability in network traffic performance and determine the most effec- tive approach for modeling these phenomena at both micro- scopic and mesoscopic levels. The key question to address from a modeling standpoint has to do with the determinism with which an inherently stochastic phenomenon can be rep- resented. This section discusses the sources of variability and the incorporation of these variability sources into traffic operation (simulation) models. Taxonomy of Variability Sources Several sources of variability need to be distinguished. They are demand- versus supply-side, exogenous versus endoge- nous, and systematic versus random. Examples in each cell of the resulting taxonomy are shown in Table 4.2. The variability in system performance that is at the center of interest in this project has both systematic causes, which can be modeled and predicted, as well as causes that to the team can only be modeled as random variables—which occur according to some probabilistic mechanism. There is a con- tinuum between what may be captured as systematic versus what is viewed as a random process with partially or fully known characteristics. Incorporation of Variability into Traffic Operations Models: A Conceptual Approach Ideally, one would want to endogenize (i.e., capture within the model itself) the phenomena that cause the variability experi- enced in network travel times. It is at this level that differences will be manifested between different simulation approaches, including micro versus meso versus macro, as well as between the different behavioral rules that may be embedded in a given simulation model. The general approach to modeling these phenomena would be to incorporate as much as possible, and as may be supported by existing or in-progress theories and behavioral models, the causal or systematic determinants of variability; the remaining inherent variation would then be added to the representa- tion through suitably calibrated probabilistic mechanisms. To increase the model’s usefulness and responsiveness to various reliability-improving measures, the team’s philosophy is to push as much as possible the portion of the total variation from the unexplained (noise) side of the equation to the systematic observable portion. This approach can be implemented at both micro- and mesosimulation levels. Notwithstanding the desire for explanation, the portion of variability that must be viewed Table 4.2. Examples of Taxonomy of Variability Sources exogenous endogenous Demand Systematic Seasonality Route choice Random Transient surge diversion Supply Systematic lane closure Breakdown/ capacity drop Random collision occurrence Merge capacity Figure 4.14. Within-day travel time variation. Sharp increase Source: Caltrans Performance Measurement System (PeMS), I-405N at Jeffrey, June 1, 2007.

59 as inherent or “random” is likely to remain substantial. This has important implications for how the models are used to produce reliability estimates and how these measures are interpreted and, in turn, used operationally. Figure 4.15 illustrates the framework for modeling variabil- ity and its sources in the traffic simulation models. Different from deterministic models, the stochastic network simulation models capture random variation in the input and produce corresponding output in the form of probability distributions. Both systematic and random variation exist in the input of the model, namely, X(t) + eX(t), where X(t) represents the system- atic variation and eX(t) indicates the random variation that possibly varies with time as well. By simulating traffic physics and human behavior, the travel time distribution can be obtained as Y[X(t)] + eY(tX). Model Demand-Side Variations The focus in this study is primarily on modeling the variability in network performance experienced under a given demand pattern. In other words, exogenous variation in demand pat- terns is not of primary concern, though the team assumes that the overall analysis framework recognizes such variation and allows consideration of scenarios under different demand realizations, with both systematic and transient demand load variation. Demand-side behaviors deeply interact with the perfor- mance of the traffic system, namely, route choice and user responses to information and control measures. These have remained outside the realm of traditional microsimulation tools, in which route choice typically meant application of aggregate turning percentages at junctions as exogenous events. Meso models developed for operational planning applications and ITS deployment evaluation introduced these behaviors explicitly into the realm of network traffic simulation models. These are now recognized as integral to any network-level simulation tool. Model Supply-Side Variations Systematic endogenous sources have generally been at the core of what traffic simulation models seek to capture and repro- duce. To deal with these sources of variability, bifurcations and chaotic behavior need to be addressed; that is, when do natu- ral inherent fluctuations become more serious sources of dis- ruption and/or major delay? Users expect some degree of variability; purely random sources of randomness (i.e., white noise) tend to cancel out over long trajectories. However, in some cases, successive maneuvers amplify and lead to disrup- tions. Flow breakdown is such an example, in which time lags and sudden reactions may combine with traffic becoming unstable and the throughput dropping considerably. Supply-side behavior parameters, such as gap acceptance and lane changing in microsimulation models, can be viewed as randomly distributed across the population of drivers in a given application, to be calibrated and externally specified, though they play a key role in determining various aspects of network performance through the rules included in the sim- ulation logic. In addition, existing models view collisions as exogenous random events that occur according to some probabilistic distribution input by the user. A recent review by Hamdar and Mahmassani (2008) showed that all existing car follow- ing models used in traffic simulation tools effectively pre- cluded the occurrence of collisions as an explicit constraint. Alternative car-following models that explicitly produce col- lisions were proposed by Hamdar et al. (2008) and are cur- rently under further development. Figure 4.15. Model variability in traffic simulation.