Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand (2012)

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114 C h a p t e r 5 This chapter provides a concise guide to how the methodolog- ical issues and results presented in the previous chapters can best be incorporated into practical planning tools. Specific models and tables presented in earlier chapters are referred to as needed. trip-Based Four-Step Demand Framework In general, the four-step aggregate zonal framework is not suf- ficiently flexible to fully incorporate most of the model speci- fications tested in this project. However, a number of advances can readily be incorporated: • Segment the zonal population by income group. The effect of pricing on behavior is strongly related to income. In order to capture the effects of pricing somewhat realisti- cally, the population of each zone should be segmented into at least three or four income groups, and income should be included as a variable in all models, including mode choice, destination choice, trip generation, and auto ownership. The mode choice model results in described in Chapter 3 recommend specifications for including income as a modifier for the cost variable. Separate mode- specific constants can also be estimated for different income groups. • Use different auto paths for different income groups. If there are priced links in the auto network, then the shortest path through the network in terms of generalized time or generalized cost will vary with value of time (VOT), which in turn varies by income. For each income group, a VOT similar to the one used in the mode choice models should be used to calculate the generalized time along each path, and separate shortest-path skim matrices of travel time and toll cost should be created for each income group. This approach is used in the Puget Sound Regional Council (PSRC) trip-based models. • Include a toll–nontoll choice submodel in the mode choice. A toll–nontoll choice can provide more flexibility and real- ism to skim the best tolled path and the best nontolled path separately and model that choice as a nested, binary sub- choice in mode choice models. The New York mode choice models presented in Chapter 4 use such a structure, which can be used for either trip-based or tour-based models. In this case, different tolled path skim matrices should be pre- pared for each income group, but the best nontolled path can be the shortest time path, which is the same across income groups. • Include the effects of pricing and congestion and alternative modes in trip distribution and destination choice models. As described in Chapter 4, there are more comprehensive measures to use in location choice models than simply using the travel time by auto, which is often done in gravity-type distribution models. A better form is the inclusive value, or logsum, across all travel modes, which includes the effects of both pricing and congestion, and also takes into account accessibility by nonauto modes. The travel times and costs used in calculating the logsums should be for the most rep- resentative periods of the day for the trip purpose (unless, in the ideal case, the logsum is from a joint trip mode and time-of-day [TOD] choice model, as presented in Chapter 3, in which case all time periods of the day will be included in a representative way). Ideally, the logsum will be included as an impedance value in a discrete destination choice model. Several existing four-step model systems use destination choice models in place of gravity models, at least for the commute purpose (e.g., the Southern California Associa- tion of Governments and PSRC models). Even with a grav- ity-type model, however, it is still possible to normalize a mode choice logsum to use as an impedance variable, such as by dividing by the travel time coefficient to convert it into equivalent minutes of travel time. • Include an explicit auto ownership model and segment subsequent models by auto availability. Although auto Incorporation of Results in Operational Models in Practice

115 ownership models were not estimated in this study, they are included in most advanced-practice trip-based models, and examples can be found in the literature. The team includes this recommendation here to underline its impor- tance, because the most significant variables in mode choice models are those related to auto ownership, and auto owner- ship is responsive to changes in household size and income distributions, as well as changes in pricing and congestion. Trip generation, distribution, and mode choice models should then be segmented by both income and auto own- ership, with auto ownership divided into at least three seg- ments: (1) households with zero autos, (2) households with one or more autos but fewer autos than working adults, and (3) households with one or more autos per working adult. The mode choice models presented in Chapter 3 show the importance of those segmentation effects. Note that for nonwork trips, it may be best to define the segments in terms of autos per driving-age adult rather than per working adult. • Include accessibility variables in the auto ownership and trip frequency models. One major criticism of four-step models is that major changes in travel congestion or prices do not affect the upper-level models, such as trip generation, so they are not able to predict induced or suppressed trips. Chap- ter 3 describes how to specify accessibility variables to use in upper-level choice models. Although they are discussed in the context of activity-based models (ABMs), there is no rea- son why they cannot be used in four-step model frameworks, particularly as they are aggregate, traffic analysis zone–based measures defined for a limited number of specific population segments. Note that in order to include such variables in a trip frequency model, a regression model (Poisson regression is appropriate for count data) will be needed, rather than a simple cross-classification table. • Include explicit TOD choice models, ideally as joint mod- els with mode choice. Most four-step models in practice use fixed TOD factors that are not sensitive to the relative travel speeds and prices in different periods. To predict peak- spreading phenomena, explicit TOD choice models are needed. Although TOD models work best as activity and trip scheduling models within a tour-based, full-day model framework, they can still provide substantial benefit at the trip level, particularly to model the effects of TOD pricing. Using the basic specifications in Chapter 3 for when the TOD model is applied to car trips according to mode choice or when the model is estimated and applied jointly with a mode choice model, the TOD model provides the basic sensitivity TOD variations in pricing and congestion. Note that a TOD model will work best with at least five network assignment or skim periods for auto: pre-a.m. peak, a.m. peak, midday, p.m. peak, and post-p.m. peak. A TOD model can benefit from the use of even more periods, such as separate skims for the shoulders of the peak. Conversely, it would not be beneficial to include skim matrices for more times of day without also including a TOD choice model. As more and more of the improvements recommended above are incorporated into the aggregate trip-based frame- work, the inefficiencies in terms of computation and run time can become extreme. In particular, the amount of computa- tion in the zonal aggregate framework increases linearly with the number of population segments, and it can also increase substantially with the number of TOD periods (particularly if separate network skims are required for different income groups). Also, the full computation of mode choice logsums across all possible destination zones becomes prohibitive with large numbers of zones. In contrast, in microsimulation model frameworks in which each household is simulated, the run time does not increase substantially with the number of house- hold and person variables in the models, nor with the num- ber of time periods or the number of zones (particularly since sampling of destinations can be used). As a result, the more advanced features one wishes to incorporate into a trip-based four-step model, the more beneficial it becomes to move to an activity-based microsimulation framework, in which even more advanced features can readily be incorporated, as described below. advanced tour-Based, activity-Based Demand Models Many of the recommendations for tour-based ABMs parallel the ones provided for the trip-based four-step models described above. For activity-based microsimulation models, however, the possibilities are greater, and the issues tend to be some- what different. As described in Chapter 6, some of the issues may depend on whether the demand models are to be applied in combination with static or dynamic network assign- ment methods. For the SHRP 2 C10 project, for example, ABMs will be applied in combination with the Dynus-T and TRANSIMS network models. The same ABMs can (and will) also be applied in combination with more conventional static equilibrium assignment methods; however, the desired capa- bilities may differ. For advanced tour-based ABMs, the team recommends the following model specifications: • Represent as many determinants of VOT as possible, includ- ing residual heterogeneity (simulate a specific VOT for each person and tour). With ABMs applied with an agent-based microsimulation framework, it is possible to include a large variety of household, person, and trip characteristics in the models. The analyses in Chapter 4 indicate systematic

116 effects of a number of those characteristics on willingness to pay and VOT. A prototypical VOT function would be one such as in Chapter 3, including the effects of income, occupancy, mode, TOD, gender, age, tour purpose, and dis- tance, plus residual random variation. Since the latter term is represented as a standard deviation of a lognormal dis- tribution, then applying such a model in practice involves the following steps: (1) for a given tour and trip made by a given person, apply the VOT coefficients for the relevant household, person, trip, and tour characteristics to calcu- late the systematic portion of the cost and time coefficients; (2) use a random draw to stochastically draw the random portion of the time coefficient given the distribution and the standard deviation; and (3) combine the systematic and stochastic components of the time and cost coeffi- cients to calculate a person- and tour-specific VOT to use in the choice models for that simulated individual’s travel. • Use different auto paths for different VOT groups. If there are priced links in the auto network, then the shortest path through the network in terms of generalized time or gener- alized cost will vary with VOT. In contrast to the recommen- dation for trip-based models, for which income segmentation is the main determinant of VOT, an ABM that simulates a person- and tour-specific VOT (as recommended above) will have a specific VOT associated with every trip. So, the best strategy for producing different skims to feed back to the models is to segment the trips within different VOT groups (e.g., by quartiles). For each VOT group, the median VOT within that group should be used to calculate the general- ized time along each path, and separate shortest-path skim matrices of travel time and toll cost should be created for each income group. • Include a toll–nontoll choice submodel in mode choice. As recommended for trip-based models, including a toll– nontoll choice can provide more flexibility and realism to skim the best tolled path and the best nontolled path sepa- rately and to model that result as a nested binary subchoice in mode choice models at the trip level, and possibly at the tour level. The New York mode choice models presented in Chapter 4 use such a structure, which can be used for either trip- or tour-level models. Different tolled path skim matri- ces should be prepared for each VOT group, as described in the preceding paragraph, but the best nontolled path can be the shortest-time path, which is the same across VOT groups. • Include the effects of pricing and congestion and alternative modes in tour and trip destination choice models. As described in Chapter 3, the inclusive value, or logsum, across all travel modes, which includes the effects of both pricing and congestion and also considers accessibility by nonauto modes, should be used in any tour or intermediate-stop des- tination choice models. The travel times and costs used in calculating the logsums should be for the most representa- tive periods of the day for the tour or trip purpose (unless, in the ideal case, the logsum is from a joint trip mode and TOD choice model, as presented in Chapter 4, in which case all time periods of the day will be included in a representa- tive way). • Include accessibility variables in the upper-level auto own- ership and tour frequency and activity pattern models. Chapter 3 describes how to specify accessibility variables to use in upper-level choice models, which have been used in a number of recent ABM systems. This strategy should be followed as closely and comprehensively as possible in order to include consistent effects of pricing and congestion at all levels of the model system. Most ABM systems are suffi- ciently flexible to include such accessibility variables in a variety of ways. Even if the effects of variables are only mar- ginally significant in model estimation, it is still advisable to include them as long as the signs are correct. Note that there is not yet enough evidence for these variables to recommend specific coefficient values to use in general cases, although that may be possible in the near future after a number of additional ABM systems have been estimated. • Include explicit TOD choice models, ideally as joint models with mode choice. TOD models work best as activity and trip scheduling models within a tour-based, full-day model framework. The hybrid departure time and duration spec- ification described in Chapter 3 is recommended, with TOD and duration shift effects. Such models can be at both the tour level and the trip level, using the specifications of Chap- ter 3, whether the TOD model is applied to car trips accord- ing to mode choice or the model is estimated and applied jointly with a mode choice model. Note that with static assignment procedures, a TOD model will work best with at least five network assignment or skim periods for auto: pre- a.m. peak, a.m. peak, midday, p.m. peak, and post-p.m. peak. A TOD model can benefit from even more periods, such as separate skims for the shoulders of the peak. With dynamic traffic assignment (DTA), the level of service (LOS) can be fed back for a large number of time periods, since it is typical for those methods to work at a fine level of temporal detail. The methods for passing back LOS from a dynamic traffic simulation are discussed in the following section. Static and Dynamic traffic Simulation tools As explained in the beginning of this chapter, static network modeling tools used in conjunction with four-step demand forecasting and planning tools are not especially well suited to capture user responses to dynamic pricing schemes, conges- tion, and (un)reliability. Recommendations for improvements

117 in the application of these methods (see beginning of this chap- ter) include the main recommendation of segmentation of the demand matrices into classes with different VOT and other behavioral parameters. Segmentation is a commonly used approach to incorporate more demand-side realism in four- step aggregate procedures. It does not, however, accomplish much in terms of a more realistic representation of the supply side, particularly congestion dynamics and reliability. In addi- tion, the user class definitions are subject to a certain degree of arbitrariness, in addition to containing users with poten- tially distinct network path and mode choices. Furthermore, it adds considerably to the computational burden of applying these procedures. Most of the interest therefore lies in dynamic, simulation- based tools for network assignment. Microassignment meth- ods, which track individual particles, have become the state of the art in DTA models advancing to the early stages of practice. These methods provide a natural platform for incorporating the kinds of behaviorally rich demand-side tools developed as part of this project. The challenges in integrating individual-level ABMs and the pricing- and congestion-responsive behavior models developed here are discussed in detail in Chapter 4. Solutions to these challenges are developed and demonstrated in that chapter, in connection with a particle simulation-based dynamic equilibrium assignment methodology. As demonstrated, these methodological innovations are ready for implementation in connection with existing simulation-based network assignment tools. Note in this regard that the differences in the physics underlying the traffic propagation (simulation) per se (e.g., the traditional distinctions between micro- and mesosimulation approaches) are not directly relevant to the applicability of the network procedures developed and demonstrated as part of this work. The main requirement is that the approach repre- sents and tracks individual travelers as decision entities. Beyond that, whether vehicle propagation invokes robust and easy- to-calibrate relations among averages to determine speeds at which vehicles move, or detailed microscopic rules for car-following and passing maneuvers, is not essential to the procedures developed under this project. Four main modeling elements introduced in this work are essential to accomplish the objectives of the study, namely, to develop predictions of network flows and facility usage while capturing user responses to various forms of pricing, conges- tion, and reliability. These four elements, which are outlined in Figure 5.1, form the recommendations for advancing the state of the practice by implementing the methods developed for this project: 1. Expand the set of attributes typically considered in the route choice assumptions underlying traffic assignment methods beyond travel time to include cost (toll) and Figure 5.1. Summary of major network issues and proposed solutions.

118 reliability measures in the form of generalized cost. Most existing tools readily allow incorporating a link-level cost attribute in the path search procedures used to generate paths in the assignment process. However, incorporating reliability is more challenging, because most measures of reliability are not additive across links. An approach that circumvents this difficulty is presented in Chapter 4 and is summarized under Item 3 below; 2. Capture heterogeneity of network users (travelers) with regard to their willingness to pay as it is reflected in the relative valuation of the attributes affecting route selection, as well as other choice dimensions. As discussed, this could be accomplished in an approximate manner through seg- mentation of the user population and solution of a multi- class traveler assignment model with predefined classes, although it is shown in Chapter 4 that an approach based on a continuous distribution of VOT (or other choice attri- bute coefficient) is preferable and could be implemented in connection with any network-simulation–based network- loading procedure. Such an approach would require imple- mentation of a new parametric path-finding procedure, as well as relatively minor modification of the loading and updating process (from one iteration to the next). This procedure was successfully demonstrated for the New York best practice model network; 3. Generate path-level reliability measures in order to incor- porate reliability as an attribute in path choice decisions (and other choice dimensions as applicable). This is per- haps the most challenging of the elements of the method- ology developed to address the objectives of the study. For this reason, it is the subject of a separate research study under a SHRP 2 Reliability program (Project L04). In that project, the goal is to generate measures of reliability from micro, meso, and possibly macro traffic-simulation tools. In this work, a relatively simple approach was developed for planning applications that relies on a robust relation between the mean travel time per unit distance and the corresponding standard deviation of the mean travel time, also per unit distance. The normalization by the traveled distance is essential for the relation to hold. This relation can be applied directly at the route or origin–destination (O-D) level, thereby circumventing the nonadditivity issue noted in connection with Item 1 above. This relation builds on classic work in traffic science and has been extensively validated for simulated network results. In addition, it is currently being further tested using trajec- tory data from mobile vehicle probes in connection with SHRP 2 Project L04. Chapter 4 shows how this relation is applied directly at the path level to estimate reliability (in the form of standard deviation given the mean value). This approach could be readily implemented with any simulation tool; and 4. Cope with large-scale network issues by reducing compu- tational requirements. As simulation-based assignment methods, which are an essential platform for capturing user responses to pricing and reliability, are applied to realistic regional networks comparable to those typically used for static assignment applications, it is essential that their computational requirements become manageable. Simple, single-class applications with homogeneous users have long been executable on very large networks without much difficulty. Addressing the objectives of the present study required pushing the frontier with regard to the network size that may be executed with the advanced tools for het- erogeneous users. Through several computer science and algorithmic implementation techniques, it was possible to reduce the computational requirements for very large net- works (as shown with the New York data) and successfully demonstrate the computational reductions. These reduc- tions are associated primarily with the path-finding and equilibration algorithms developed for multiuser classes. Although additional improvement is undoubtedly possi- ble in this regard, the present implementation to New York demonstrates the feasibility of such a large-scale applica- tion and paves the way for bigger and faster procedures in the future. All the methods proposed in this study have been demon- strated in connection with a state-of-the-art simulation-based DTA methodology. The DYNASMART-P code provided the implementation platform, although the components of the implementation and modifications could be replicated in a straightforward manner in connection with any simulation- based DTA tool. In particular, these methods could be directly implemented in mesosimulation DTA models such as Dynamit-P, which follows a similar blueprint; Dynus-T, which is built directly on the basic DYNASMART-P platform; VISTA, which adapts a similar network representation and path-finding algorithmic structure in a modified simulation platform; and several other meso-DTA tools. Because these procedures apply primarily to the path-finding procedures and are independent of the simulation logic, they can be readily implemented with microlevel simulators, although the latter cannot at this stage address large-scale networks of the scale of the New York City regional network. This drawback has prompted several microscopic simulation software vendors to release mesoscopic versions of their tools (e.g., Aimsun). Application in TRANSIMS is also possible, though it requires more effort because of its elaborate router, which does not entail traditional path finding and would therefore require adaptation to its shortest-path computation method. Although the use of static assignment tools is not recom- mended in conjunction with studies of pricing schemes and reliability assessment, it is nonetheless possible to incorporate

119 some of the above methods and recommendations in static assignment tools. In particular, if path-based assignment approaches are used, it is possible to improve the route choice basis by implementing the recommended options. For instance, shortest-path-finding procedures can readily consider multiple attributes in a generalized cost function when these attributes are additive across links. Incorporating heterogeneity in user preferences can also be accomplished by using a parametric shortest-path method, originally pro- posed by Leurent (1993) and Dial (1997). Incorporating travel time variability is also possible, at least in aggregate form, using the same robust relation already discussed. With path-based assignment implementations, the structural dif- ferences between static and dynamic assignment become less pronounced, and it is possible to essentially adapt all the dis- cussion and methods to encompass static assignment tech- niques, although the critical time dimension of the problem would be inherently ignored. Integrated Demand and Network Models Two-Way Linkage Between Travel Demand and Network Supply Since the technologies of microsimulation have been brought to a certain level of maturity on both the demand side (ABM) and the supply (network) side (DTA), the challenge of ABM- DTA integration has become one of the most promising ave- nues in transportation modeling. Seemingly, the integration between the two models should be as natural and straight- forward as the integration concept between a four-step model and static traffic assignment, shown in Figure 5.2. The rela- tively simple integration of the demand and supply sides in the conventional framework is based on the fact that the input and output entities involved in the process have the same matrix structure. The four-step demand model produces trip tables needed for assignment, and the assignment procedures produce full LOS skims in the same matrix format needed for the four-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 it can be said 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, however, operate with individual par- ticles as modeling units (individual tours and trips) and can have compatible levels of spatial and temporal resolution. It might seem that exactly the same integration concept as applied for four-step models could be adjusted to account for a list of individual 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, which can never be incorporated in an aggregate framework. Indi- vidual 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 con- sideration of the actual technical aspects of implementation reveal some nontrivial issues that need to be resolved before the advantages offered by overall microsimulation framework can be taken. The specific problem is illustrated in Figure 5.3, which shows that the feedback provided by the DTA procedure does not cover all the needs of the ABM. The crux of the problem is that unlike the four step–static traffic assignment integration, the microsimulation DTA can only produce an individual trajectory (path in time and space) for the list of actually simulated trips. It does not automati- cally produce trajectories for all (potential) trips to other desti- nations and at other departure times. Thus, it does not provide the necessary LOS feedback to ABM at the disaggregate level for all modeled choices. Any attempt to resolve this issue by “brute force” would result in an infeasibly large number of calculations, since all possible trips cannot be processed by 4-step demand model Static assignment Trip tables LOS skims for all possible trips Figure 5.2. Integration of four-step model and static assignment. Microsimulation ABM Microsimulation DTA List of individual trips Individual trajectories for the current list of trips LOS for the other potential trips? Figure 5.3. Integration of ABM and DTA (direct).

120 DTA at the disaggregate level. In fact, the list of trips for which the individual trajectories can be produced is a very small portion of the all possible trips to consider. As shown in Figure 5.4, one of the possible solutions is to employ DTA to produce crude LOS matrices (the way they are produced by static traffic assignment) and use these LOS variables to feed the demand model. However, this approach, in the aggregation of individual trajectories into crude LOS skims, would lose most of the detail associated with DTA and the advantages of individual microsimulation (e.g., individual variation in VOT or other person characteris- tics). Essentially, with this approach the individual schedule consistency concept would be of limited value because travel times would be crude for each particular individual. Nevertheless, this approach has been adopted in many studies due to its inherent simplicity (Bekhor et al. 2011; Castiglione et al. 2012). Instead of the model integration ideas outlined above, the team proposes several new ideas that are currently being con- sidered and tested in the SHRP 2 L04 project. These ideas are explained in the subsequent sections. Activity-Based Model–Dynamic Traffic Assignment Integration Principles The emphasis in the L04 project is on truly integrating the demand and network models, not merely connecting them through aggregate measures in an iterative application. The team’s approach is based on the following principles: • Use of a fully disaggregate approach implemented at the disaggregate individual level (travel tours by person); • Conceptual integration of the demand and network simu- lation procedures to ensure a fully consistent daily schedule for each individual. This approach is principally different from the so-called “iterative loose coupling” of the demand and supply models. The basic travel unit exchanged between ABM and DTA is a travel tour, rather than an elemental trip; • Representation of user heterogeneity (individual travel varia- tions) in network-based choice processes, with implications for optimum-path computations; • Use of 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 that would call for one-shot simulations, versus recurrent congestion that 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; and • Use of 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 5.1. 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 sev- eral 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 yet been resolved in opera- tional models. The crux of the problem is that all trips and associated 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 inte- gration between the demand and network simulation mod- els. Also, both models should be brought to a level of temporal resolution that is sufficient for controlling the constraints (e.g., 5 minutes). 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 four-step Microsimulation ABM Microsimulation DTA List of individual trips Aggregate LOS skims for all possible trips Figure 5.4. Integration of ABM and DTA (aggregate feedback).

121 demand models or the static trip-based network simulation models because they operate with unconnected trips and do not control for activity durations at all. Also, in four-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). However, these improvements do not include trip details, and they do not control for feasibility of travel times within the tour framework (although travel time is used as one of the explanatory variables). Certain attempts to incorporate trip departure-time choice in a framework of trip chains have been made within DTA models (Abdelghany and Mahmas- sani 2003). However, these attempts were limited to a tour level only, and they also required a simplified representation of activity duration profiles. This constraint expresses con- sistency (i.e., the same number) in each row of Table 5.1. • 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 5.1. • Equilibrium Travel Times. Travel times between activities in the schedule generated by the demand model should cor- respond to realistic network travel times for the correspond- ing origin, destination, departure time, and route generated by the traffic simulation model with the given demand. While most of the four-step models and ABMs include a certain level of demand–supply equilibration, they are lim- ited to achieving stability in terms of average travel times. There is no control for consistency within the individual daily schedule. The challenge is to couple this constraint with the previous one; that is, to ensure individual schedule continuity with equilibrium travel times. This hard con- straint expresses consistency between trip departure and arrival times in the corresponding columns of Table 5.1 with the travel times obtained in the network simulation. Practi- cally, 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. 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 activ- ity episodes). However, this rescheduling process should Table 5.1. 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

122 obey utility-maximization rules over the entire schedule and cannot be effectively modeled by simplified proce- dures that adjust departure times for each trip separately. None of the existing operational ABMs explicitly controls for activity durations, although some of them control for entire-tour durations (such as the MTC ABM) or the dura- tion of the activity at the primary destination (as imple- mented in the SACOG ABM). DTA models that incorporate departure time choice have been bound to a simplified rep- resentation 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 5.1 with the schedule utility-maximization prin- ciple (or in a more general sense, with the observed tim- ing and duration pattern for activity parti cipation). In operational models, the focus has been primarily on out- of-home activities. It should be noted, however, that it is also important to preserve a consistent and realistic pat- tern of in-home activities (e.g., reasonable time constraints for sleeping and household activities), as well as take into account possible substitution between in-home and out-of-home durations for work, shopping, and discre- tionary activities. Schedule consistency with respect to all five constraints is absolutely essential for time-sensitive policies like congestion pricing. In reality, any change in the timing of a particular activity or trip spurred by a congestion pricing policy would trigger a chain of subsequent adjustments through the whole individual schedule. It can be shown that under certain cir- cumstances, 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 (PB Consult, Inc. 2005). In order 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 temporal dimension of activities and trips, but other choice dimensions can be effectively treated by each corresponding module, as shown in Figure 5.5. The mutual core ensures synchronization of time-related ABM and DTA components and is designed to achieve a full schedule consistency at the individual level. The ABM model generates tours with origins, destinations, and trip departure 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 Feasibility of adjusted schedules Tours with planned trip departure times and schedule delay costs Tours with simulated travel time and adjusted trip departure times Figure 5.5. Integration scheme of ABM and DTA.

123 times based on expected travel times (from the DTA) and TOD choice utilities. These can be converted to temporal activity profiles for each activity episode; the temporal activity profile is essentially an expected utility of activity participation for a given time unit. As discussed above, these temporal 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 on 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; it takes into account schedule delay cost, as well as interdependencies across trips on the same tour. These features have been recently added to the DTA algorithm and tested for DYNASMART-P (Abdelghany and Mahmassani 2003; Zhou et al. 2008). The capability of DTA to handle travel tours rather than trips is essential to ensure consistency between DTA and ABM. Indi- vidual choices are to be 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 on the basis of the feasibility of their adjusted schedules and the magnitude of the adjustments introduced by 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. After each tour has been adjusted, the synchronization module consolidates the entire daily schedule for each indi- vidual. Depending on the magnitude of adjustments, the schedule might result in an infeasible (or highly improbable) state in which tours are overlapped or activity durations have reached unreasonable values. The synchronization module informs the ABM which individual daily schedules have to be resimulated. Individuals whose schedules have to be resim- ulated will undergo a complete chain of demand choices based on the updated travel times. 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 acts as an 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, end times, and dura- tions) and trip trajectories (trip departure time, duration, and arrival time). This feedback is implemented as part of the tem- poral equilibrium between ABM and DTA, when all trip des- tinations 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 5.6. In this way, any change in travel time would affect activity dura- tions and vice versa. New methods for equilibrating ABM and DTA are pre- sented in Figure 5.7, in which two innovative technical solu- tions are applied 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 dimen- sions (number of trips, order of trips, and trip destinations) are fixed for each individual. Full advantage can then be taken of the individual schedule constraints and correspond- ing effects, as shown in Figure 5.6. The inner loop of temporal equilibrium includes schedule adjustments in individual daily activity patterns that occur when congested travel times 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 5.6. Consistent individual daily schedule.

124 are different from planned travel times. This action helps the DTA to reach convergence (inner loop), and is 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 would only be required to produce trajectories for a subset of origins, destinations, and departure times. In this case, the schedule consolidation is implemented though corrections of 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). Adjustment of the individual daily schedule can be formu- lated as an entropy-maximizing problem of the following form: min ln x i i i ii I i i i w x x d u y { } = × ×         + × ×∑0 ln ln y v z z i ii I i i i i pi τ         + × ×    = +∑ 1 1                = ∑ i I 0 5 1( . ) subject to , 1, 2, . . . , 1 (5.2)0 0 1 0 1 y x t i Ii j j i j j i∑ ∑= τ +   +   = + = − = − , 1, 2, . . . , (5.3)0 0 1 0 x t i Ij j i j j i∑ ∑= τ +   +   = = − = 0, 0, 1, 2, . . . , (5.4)x i Ii > = where i, j = 1, 2, . . . , I = trips and associated activities at the trip destination; i, j = 0 = activity at home before the first trip; i = I + 1 = (symbolic) departure from home at the end of the simulation period; xi, xj = 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, tj = actual time for trip to the activity that is different from expected; wi = schedule weight (priority) for activity duration; ui = schedule weight (priority) for trip depar- ture time; and vi = schedule weight (priority) for trip arrival time. The essence of this formulation is that in the presence of travel times that are different from the expected travel times that the user used to build the schedule, it will try to accom- modate new travel times in such a way that the schedule is preserved to the extent possible. This preservation relates to activity start times (trip arrival times), activity end times (trip departure times), and activity durations (Equation 5.1). The relative weights represent the priorities 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 cor- responding component close to the original schedule. Very large weights correspond to inflexible, fixed-time activities. The weights directly relate to the schedule delay penalties as described below in the section on travel time reliability mea- sures. The concept of schedule delay penalties relates to devi- ation from the (preferred or planned) activity start time (trip arrival time) only, but the schedule adjustment formulation allows for a joint treatment of deviations from the planned start times, end times, and durations. The constraints express the schedule consistency rule as shown in Figure 5.6. Equation 5.2 expresses departure time for each trip as a sum of the previous activity durations and travel times. Equation 5.3 expresses arrival time of each trip as a sum of the previous activity durations and travel times plus travel time for the given trip. The (symbolic) arrival time for the home activity prior to the first trip is used to set 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 Figure 5.7. Integration of ABM and DTA (split feedback).

125 the scale of all departure and arrival times. In this way, the problem is formulated in the space of activity durations, and the trip departure and arrival times are derived from the activity durations and given travel times. The solution of the convex problem can be found by writ- ing the Lagrangian function and equating its partial deriva- tives (with respect to activity durations) to zero. The equation takes the following form: (5.5) 1 1 x d y zi i j j u j j v j wj j i∏= × pi   × τ         > This solution is easy to find by using either an iterative bal- ancing method or the Newton–Raphson method. The essence of this formula is that updated activity durations are propor- tional to the planned durations and adjustment factors. The adjustment factors are applied considering the duration pri- ority. If the duration weight is very large, then the adjust- ments 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 pi j jy   and trip arrival adjustment τ j jz   can be interpreted as lateness versus the planned schedule if it is less than one and earliness if it is greater than one. Each trip departure or arrival adjustment fac- tor is powered by the corresponding priority weight. As a result, activity duration will shrink if there are many subsequent trip departures or arrivals (or both) that are later than planned. Conversely, activity duration will be stretched if there are many subsequent trip departures or arrivals (or both) that are earlier than planned. Overall, the model seeks the equilibrium (com- promise) state in which all activity durations, trip departures, and trip arrivals will be adjusted to accommodate the changed travel times while preserving the planned schedule compo- nents by priority. The team provides demonstration software and has 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 durations {xi = di}; 2. Update trip departure times with new travel times and updated activity durations using Equation 5.2; 3. Update trip arrival times with new travel times and updated activity durations using Equation 5.3; 4. Calculate balancing factors pi j jy   for trip departure times (lateness if less than one, earliness if greater than one); 5. Calculate balancing factors τ j jz   for trip arrival times (lateness if less than one, earliness if greater than one); 6. Update activity durations using Equation 5.5; and 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 for which more specific data on schedule pri- orities and constraints of different person types would be wel- comed. 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 also have schedule constraints. At this stage, the team suggests the default values shown in Table 5.2. 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. Incorporation of reliability in Demand Model The proposed methods of quantification of reliability should be incorporated in 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 a reliability term can be directly included in the utility function for highway modes. Further on, the reliability term will affect destination and TOD choice through mode choice logsums. In the same vein, it affects upper-level choice models of car ownership and activity–travel patterns though accessibility measures that represent simpli- fied destination choice logsums. As discussed in Chapter 3, the demand side of travel time reliability has been explored in detail in the SHRP 2 C04 project. In this section, the team pres- ents 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 using the weights recommended in Table 5.3. 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 the volume-to-capacity ratio or flow density parameter. However, perceived travel time is not a direct measure of travel time

126 reliability. It can be used as a surrogate when more advanced methods are not available, but it is less appealing behaviorally and it 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 sig- nificant 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 can be recommended as the first step for incorporation in operational models (many additional modifications and nonlinear transformations are analyzed in Chapter 3): (5.6)U a T b C c SD 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 = VOT; c/b = value of reliability (VOR); and c/a = reliability ratio (r = VOT/VOR). Recommended values for the parameters are summarized in Table 5.4. The parameters are segmented by travel purpose, household income, car occupancy, and travel distance. Schedule Delay Cost in Demand Model Several models were estimated in the SHRP 2 C04 research with schedule delay cost as described in Chapter 3. The majority of them were estimated using different stated prefer- ence settings in which either route or departure time served as the underlying travel choice dimension. The technical details for the inclusion of this method in an operational travel demand model have not yet been fully explored. As shown in Figure 5.8, the team outlines two possible approaches that differ in how and where the schedule delay cost compo- nent is calculated. In both approaches, the travel demand model (its TOD choice or activity scheduling submodel) produces a preferred departure time (PDT) and preferred arrival time (PAT) for Table 5.2. 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 = nonhome based. Table 5.3. Recommended Highway Travel Time Weight by Congestion Levels Travel Time Condition Weight Free flow 1.00 Busy 1.05 Light congestion 1.10 Heavy congestion 1.20 Stop start 1.40 Gridlock 1.80

127 Travel Purpose Examples of Population and Travel Characteristics Model Coefficients and Derived Measures Household Income ($/year) Car Occupancy Distance (mi) Time Coefficient with Distance Effect Cost Coefficient with Income and Occupancy Effects Cost for SD (min) VOT ($/h) VOR ($/h) Reliability Ratio Work and 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 (continued on next page) Table 5.4. Recommended Values of Parameters for Generalized Cost Function with Reliability

128 Travel Purpose Examples of Population and Travel Characteristics Model Coefficients and Derived Measures Household Income ($/year) Car Occupancy Distance (mi) Time Coefficient with Distance Effect Cost Coefficient with Income and Occupancy Effects Cost for SD (min) VOT ($/h) VOR ($/h) Reliability Ratio Nonwork 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 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 Note: SD = standard deviation. Table 5.4. Recommended Values of Parameters for Generalized Cost Function with Reliability (continued)

129 each trip based on the expected travel times (and known 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 scheduled 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 highway modes. The network simulation model assigns trips based on PDT without considering 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 yet been tested. The most realistic implementation approach for this scheme is a multiple-run framework, which is discussed below. In the second approach, the calculation of schedule delay cost is incorporated in the network model and is fed into the demand model. Perhaps the most behaviorally appealing aspect of this implementation approach occurs when the net- work simulation model is allowed to optimize PDT based on 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 implemented in a single-run framework; some testing of this approach has been 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 (e.g., work with fixed schedule, appoint- ments, ticketed shows), this might be ultimately the right 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 ap pr oa ch :s ch ed ul e de la y co st ca lc ul at io n in de m an d m od el 2n d ap pr oa ch :s ch ed ul e de la y co st ca lc ul at io n in ne tw or k m od el Figure 5.8. Incorporation of schedule delay cost calculation in ( top) demand model and (bottom) network model (mode choice).

130 approach. Some approaches to endogenously calculated PAT within the scheduling model as a latent variable were sug- gested by Ben-Akiva and Abou-Zeid (2007). Further research is needed to operationalize this approach within the frame- work of a regional travel model. Temporal Utility Profiles in Demand Model As described in detail in Chapter 3, using temporal utility profiles in the demand model is the most theoretically advanced approach, and its operationalization on the demand side requires that temporal utility profiles be defined for each activity. The attractive part of this approach is that these pro- files are indeed implicitly defined in the TOD choice model embedded in any ABM. However, conversion of the time-of- choice model output into 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 TOD choice model produces probabilities for each activity to be undertaken at a certain time in the form of a joint start (arrival) and end (departure) time probability over all feasible combinations P(ta, td) such as: P t ta d t t T t T d aa , ( . )( ) = == ∑∑ 0 1 5 7 These probabilities are defined for each activity, and they are not directly comparable across different activities. To convert the TOD choice probabilities into temporal utility profiles, an overall scale Uk for each activity k has to be defined. The util- ity profile could then be calculated as u t t U P t tk a d k a d, , ( . )( ) = × ( ) 5 8 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 TOD choice utility Vk(ta, td) used to calcu- late the probability P(ta, td). Hence, the following estimate of Uk can be suggested that is essentially the coefficient of travel cost in the TOD choice utility (it is assumed that this is a single coefficient not differentiated by departure or arrival time): U V t t Ck k a d ad = ∂ ( ) ∂ , ( . )5 9 However, these techniques are yet to be explored and fur- ther research is needed to unify TOD choice and temporal utility profiles. Also, even if the temporal utility profiles are available for each activity, their incorporation in an opera- tional travel demand model is not straightforward. In a cer- tain sense, two approaches similar to the approaches outlined above 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 minutes). The demand model (mode choice) would then 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. Incorporation of reliability in 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 in 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 restruc- turing of the network assignment model whether a user equilibrium static assignment or advanced DTA is applied. Essentially, the generic highway travel time variable in route choice should be replaced with segmented travel time by con- gestion levels with the weights recommended in Table 5.3. The highway LOS skims for the demand model have to be seg- mented accordingly. However, in the same way as 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 surrogate when more advanced methods are not available, but it is less appealing behaviorally, and it 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 5.9. 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 choices through mode choice logsums). However, implementation of

131 this method on the network simulation side proved to be more complicated than its incorporation in a demand model. Any demand model, whether four-step or ABM, inherently operates with entire-trip O-D LOS measures. Consequently, adding one more measure does not affect the model struc- ture. However, network simulation models that are efficient in large networks operate with link-based shortest-path algo- rithms for route choice. This results in the necessity of con- structing entire-route O-D LOS measures from link LOS measures. Although 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, which requires non- standard statistical dependences to be involved. In a multiple-run framework, this measure can be summarized from multiple simulations. However, the whole framework of multiple runs has to be defined in a consistent way across demand, network supply, and equilibration parameters. The SHRP 2 L04 project is specifically devoted to an analy- sis of these issues and a substantiation of the recommended methods. Schedule Delay Cost in Network Simulation The previous section outlines two possible approaches that differ in how and where the schedule delay cost component is calculated (see Figure 5.8). 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 simulation model assigns trips based on PDT without considering 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. The most real- istic implementation approach with this scheme is a multiple- run framework, which is discussed below. In the second approach, the schedule delay cost calculation is incorporated in the network model and is fed to the demand model. Perhaps the most behaviorally appealing implemen- tation of this approach occurs when the network simulation model is allowed to optimize departure time based on PAT and specified schedule delay penalties. This type of model can be implemented in a single-run framework; some testing of this approach has been 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 above for the schedule delay method can be adjusted within a temporal profiles framework. The first approach would employ the network simulation model to produce travel time distributions for each trip depar- ture time bin (30 minutes). The second approach would include temporal profiles in the network simulation, which 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). Currently, this method cannot be recommended for imple- mentation in real-size networks because of the many technical details that have to be explored on both demand and network supply size. However, it represents an important avenue for future research.