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

Chapter: Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies

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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Suggested Citation:"Chapter 4 - Network Simulation Procedures to Support Congestion and Pricing Studies." National Academies of Sciences, Engineering, and Medicine. 2012. Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand. Washington, DC: The National Academies Press. doi: 10.17226/22689.
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Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

89 C h a p t e r 4 This chapter discusses approaches for integrating models of user behavior in network modeling and simulation frame- works to support analysis and evaluation of pricing and other congestion-related measures. It also showcases the application of such integrated demand–network simulation procedures in an actual large-scale regional network: the New York City (NYC) best practice regional network. To the team’s knowledge, the network considered in this application is the largest network (in terms of number of links and nodes, as well as simulated vehicles and trip makers) to which a simulation-based dynamic traffic assignment (DTA) procedure has been applied. The three major sections of this chapter present (1) a general overview and recommended methods of network simulation modeling, with a focus on an integrated multi dimensional network choice model framework; (2) a demonstration of the proposed model framework with an application to the NYC regional network to support congestion and pricing studies; and (3) a summary of network simulation. Mathematical formulations and solution algorithms for the proposed integrated model are presented in greater detail in Appendix A. Details of the calibration proce- dure and its application for the estimation of time-dependent origin–destination (O-D) demand with multiple vehicle types are provided in Appendix A. General review and recommended Methods of Network Simulation The review of and recommendations for network simulation are divided into four subsections as follows: • Summary of the challenges of integrating user decisions in network simulations models; • Presentation of an integrated multidimensional network choice model framework to support congestion and pricing studies; • Presentation of a simulation-based column generation solu- tion framework to solve the proposed problem; and • Presentation of algorithmic procedures and discussion of associated challenges for applying the proposed solution method to large-scale regional networks. Integrating User Decisions in Network Simulation Models: Summary of Challenges A regional transportation model is a mathematical representa- tion of travel demand and network supply in a metropolitan area. The travel demand side is a result of interactions among various economic and social activities in the region. The network supply side generally includes a highway network and a transit network for the region. The highway network consists of arterials, freeways, and toll roads; the transit network rep- resents all public transportation modes, such as buses, ferries, and trains. Generally two types of travel demand models, trip-based models and activity-based models (ABMs), rep- resent travel activities and choices of travel destinations, frequency of travel, mode, and so forth. The network supply model represents how a given travel demand is distributed and propagated through a transportation network, namely traffic assignment, which essentially assigns the travel demand (i.e., trips or activity chains) to the transportation network links and determines the corresponding service levels of the transportation network elements. Network models used in practice have typically followed static assignment procedures, which assume that traffic flows and associated trip times are constant over time. Because these assumptions do not capture observed temporal patterns of congestion build up and dissipation in actual networks, analysts have moved toward DTA procedures. Static traffic assignment models typically rely on analytical link volume- delay functions (e.g., the Bureau of Public Roads function) to capture the dependence of level of service (LOS) on flow levels. In DTA models, traffic simulation procedures have Network Simulation Procedures to Support Congestion and Pricing Studies

90 increasingly been used to realistically capture traffic dynamics in practice. Most state departments of transportation (DOTs) and metropolitan planning organizations (MPOs) rely on static regional transportation models that have often been developed over several decades. In general, these static models execute travel demand and network supply models separately, in a sequential process, or introduce some elementary feedback loop between them. It has long been recognized that the travel demand side (especially frequency of travel, mode choice, and so forth) is influenced by the network supply side. From a realistic behavioral standpoint, integrating travel demand (especially for mode choice) with network supply (traffic assignment model) is required to address a wide range of transportation options and demand management policies (e.g., congestion pricing) in a regional large-scale transporta- tion system. As noted, conventional static assignment models assume stationary traffic states, in conjunction with simplified route choice assumptions and link volume-delay functions. As such, their applicability is severely limited for the evaluation of dynamic transportation management policies (e.g., dynamic pricing) over relatively short time scales (e.g., 5 or 15 minutes). DTA models with an underlying network traffic simulator provide a more realistic representation of traffic in terms of congestion, queues, and dynamic route choice than static traffic assignment models, especially for travelers’ choices of using toll versus nontoll roads over time. Simulation-based DTA models have been successfully applied to conduct analyses of pricing, reliability, and conges- tion at a corridor level. For example, such analyses were part of an integrated corridor management tool applied to the CHART network between Baltimore, Maryland, and Washington, D.C. (Zhou et al. 2008; National Cooperative Highway Research Program 2009) using a simplified multinomial logit modal choice model. However, corridor models are not intended as a substitute for regional models, but as an effective comple- mentary tool to achieve a more detailed level of analysis. The corridor models are useful for a detailed analysis of a route under congestion, and specifically for a better representation of facility-level choices between managed lanes and general- purpose lanes, as well as issues such as queuing phenomena and congestion at toll plazas. Decision-support tools to evaluate congestion-pricing policies call for a regional-level integrated user decision and DTA model incorporating multidimensional network choice behavior. In particular, since most current travel demand models used by state DOTs or MPOs (e.g., modal choice models) are rather complex due to the large network size and the presence of multiple modal alternatives at the regional level, this combined model requires a seamlessly and correctly integrated modeling framework to connect DTA models with available well-calibrated travel demand models. Accordingly, this study aims to demonstrate how to integrate a travel demand model with a simulation-based DTA model to support congestion and pricing studies in a large-scale regional transportation network using the NYC regional transporta- tion network as an extended example. The study provides a foundational framework that represents an evolution from current practice toward a conceptually, theoretically, and methodologically sound approach to address heterogeneous user responses to congestion, pricing, and reliability in large- scale regional multimodal transportation networks. The integration of travel demand and dynamic network simulation models to support congestion and pricing studies in large-scale regional transportation networks gives rise to several challenges, including the following: • Capturing user responses to congestion, pricing, and reli- ability is best accomplished through microsimulation of individual traveler decisions in a network platform. These responses must be considered in a network setting, not at the facility level, and the time dimension is essential to evaluating the impact of congestion pricing and related measures. Hence, a dynamic analysis tool is required; • Incorporating heterogeneity of user preferences is an essen- tial requirement for modeling user responses to pricing in a network setting, as discussed in Chapter 3. New algo- rithms that exploit parametric multicriteria shortest-path procedures allow travelers’ value of time (VOT), which determines users’ choice of path and mode in response to prices, to be continuously distributed across the population of travelers. Efficient implementations of these algorithms have been demonstrated for large network applications for the first time as part of this study; • Simulation-based DTA models have gained considerable acceptance in the past few years, yet adoption in practice remains in its infancy, especially for large-scale regional transportation networks. The current generation of available models only considers fixed, albeit time-varying, O-D trip patterns. Greater use and utility will result from consider- ation of a more complete set of travel choice dimensions and incorporation of user attributes, including systematic and random heterogeneity of user preferences; • Algorithms for finding equilibrium time-varying flows have been based on the relatively inefficient method of successive averages. Its implementation in a flow-based procedure did not scale particularly well for application to large metro- politan networks. New implementations of the method of successive averages and other algorithms that exploit the particle-based approach of DTA simulators have been pro- posed and demonstrated on large-scale regional transporta- tion networks (Sbayti et al. 2007; Lu et al. 2009); and • Regional networks are large-scale applications of network models and require substantial computational time and

91 memory storage for the various algorithmic components of these procedures, especially shortest-path calculation, traffic simulation, and traffic assignment. In addition, large-scale regional networks require large amounts of memory to store data for path calculation and traffic simulation, as well as traffic assignment. The next section presents an integrated model frame- work to evaluate pricing and reliability to overcome the above mentioned challenges. The proposed integrated model framework is a demonstration of a trip-based integration of a well-calibrated modal choice model in practice and a simulation-based dynamic traffic microassignment model. However, this framework is sufficiently flexible to incorpo- rate other dimensions than modal choice, such as destination choice and departure time choice, from the demand side. In addition, this framework can be readily extended to an activity- based integration of demand models and an activity-based dynamic traffic microassignment model. Integrated Model Framework to Evaluate Pricing and Reliability Problem Statement and Assumptions The starting point is a network of links and nodes representing the study area and a population of travelers with desired origins, destinations, and activity times reflecting their daily activity schedules. The problem considered here is downstream of the activity-scheduling process, whereby activity patterns have been mapped onto trips with known origins, destinations, and departure times. However, it is also possible to define the problem at the daily activity pattern formation or choice level with full integration of the supply-modeling procedures with the higher-level activity choices. The basic methodological framework presented here could be readily expanded to accommodate such integration, albeit with richer path-finding procedures in the combined travel activity time–space network and heavier computational burden. The focus here is limited to demonstrating practical procedures to achieve integration of a rich multimodal path- and mode-choice process in the network-modeling process. A more formal statement of the problem and key assump- tions is as follows. Given a time-varying network G = (N, A), where N is a finite set of nodes and A is a finite set of directed links, the time period of interest (planning horizon) is dis- cretized into a set of small time intervals, H = {t0, t0 + Dt, t0 + 2Dt, . . . , t0 + TDt}. Here t0 is the earliest possible departure time from any origin node, Dt is a small time interval during which no perceptible changes in either traffic conditions or travel cost (or both) occur, and T is a large number such that the intervals from t0 to t0 + TDt cover the planning horizon H. The time-dependent zonal demand qwt over the study horizon represents the number of individual travelers of an O-D pair w (w ∈W) at departure time t (t ∈T). The set of available modes is denoted as M. The integrated model in this study is designed to find a dynamic network equilibrium mode–path flow pattern by recognizing multiple dimensions of network choice behavior (i.e., mode choice decision, highway user hetero geneity, and reliability of route choice). Essentially, this is an integrated dynamic traveler mode–path assignment problem on a multimodal transportation network. Recognizing Dynamic Mode Choice Decision Associated with each mode m is the mode flow ymwt, "m ∈ M, w ∈ W, t ∈ T and corresponding mode choice probability pmwt(y), "m ∈ M, w ∈ W, t ∈ T, where y = {ymwt "m ∈ M, w ∈ W, t ∈ T} is the mode flow vector for all O-D pairs and departure times. A key behavioral assumption for the mode choice decision is as follows: in a random utility maximization framework, each traveler chooses a mode that maximizes his or her perceived utility. With no loss of generality, the choice probability of each mode pmwt(y), "m ∈ M, w ∈ W, t ∈ T can be determined as follows: Pr max , , , (4.1) p y U y U y m M w W t T m wt m wt m M m wt( ) ( ) ( ){ }= =  ∀ ∈ ∈ ∈ ∈ where Umwt(y) is a utility function of mode m and Pr[•] is a choice probability function. Note that the utility function U mwt is a function of travelers’ characteristics, mode attributes, and a random term that determines the structure of the choice model. The exact form of Pr[•] is defined by the underlying random error structure of the choice model. Daganzo and Sheffi (1977) defined the static stochastic user equilibrium (SUE) condition as follows: no user can reduce his or her perceived travel time by unilaterally changing routes. The team has extended this static SUE condition to the dynamic context and defined a time-dependent mode choice SUE (TDMSUE) as follows: For each O-D pair w and for each assignment–departure time interval t, no traveler can reduce his or her perceived mode travel cost or disutility by unilaterally changing modes. Given the assumptions and definitions above, the mode choice problem is to find a SUE mode flow pattern, y = {ymwt "w ∈ W, t ∈ T, m ∈ M}, satisfying the TDMSUE defi- nition. This essentially means that the attribute values used in the mode choice model, particularly the LOS attributes, are mutually consistent with the results of the traffic simulation assignment model obtained by splitting the travelers to modes and subsequently assigning them to routes.

92 Multiple Attributes (Criteria) in Highway Route-Choice Process The solution of the mode choice problem gives an equilibrium mode flow pattern, ymwt, "w ∈ W, t ∈ T, m ∈ M, which forms the input for a multiclass dynamic user equilibrium traffic- assignment problem. In other words, the mode choice model provides the relative fractions of users by different modes, including those whose choices entail automobile use as driver or passenger on the highway network. The path choices of these users and the associated network performance measures are consistent with the resulting multiclass dynamic user equilibrium problem defined here. The main features of the problem addressed here entail the response of users not only to attributes of the travel time experienced on average by travelers on a particular path at a given time, but also to the prices or tolls encountered and the reliability of travel time. Accordingly, users are assumed to choose a path that mini- mizes a generalized cost or disutility that includes three main path attributes: travel time, monetary cost, and a measure of variability to capture reliability of travel. Denote by GCk wtm(a) the experienced route generalized cost perceived by travelers with VOT a between O-D pair w departing at time t and using mode m and route k: , , , , (4.2) GC TT TC TTSD k K w t m k wtm k wtm k wtm k wtm( ) ( ) α β = + α × + β × ∀ ∈ where TT and TC denote the travel time and travel cost, respec- tively, and TTSD is the standard deviation of the travel time with subscripts and superscripts as already defined for route k, mode m, and O-D pair w. The parameters a and b denote the coefficients of the travel cost and travel time standard devia- tion, respectively; they are interpreted as VOT and value of reli- ability, respectively, as discussed in the previous chapters. Recognizing Highway User Heterogeneity In the above generalized cost expression, the parameters a and b represent individual trip maker’s preferences in the valuation of the corresponding attributes. As shown in Chapter 3, these preferences vary across travelers in systematic ways that may be captured through user sociodemographic or trip-related attributes or in ways that may not be directly observable. Variation in user preferences for the different travel choice attributes is referred to as heterogeneity. Both a and b in the generalized cost expression above may vary across users. However, to realistically capture the effect of pricing and its impact on different user groups, it is essential to represent the variation of user preferences in response to prices, captured here through the parameter a. Accordingly, the focus is on cap- turing heterogeneous VOT preferences across the population of highway users. Preferences for reliability may also reflect heterogeneity, and the same approach used here for VOT may be extended to incorporate both. It should be noted, however, that the empirical estimation analysis reported in the previ- ous chapter suggests that heterogeneity in VOT is much more significantly present than in the preferences for reliability. To reflect highway user heterogeneity, VOT in this study is treated as a continuous random variable distributed across the population of travelers, with a density function f(a) > 0, "a ∈ [amin, amax], and ∫amax aminf(a)da=1, where the feasible range of VOT is determined by a given closed interval [amin, amax]. The distribution of VOT can be calibrated using discrete choice modeling techniques with random coefficient specifi- cations, as shown in Chapter 3 using New York data. Accord- ingly, the VOT distribution is assumed known for assignment purposes. As discussed, in the New York application the cor- responding coefficient b is taken as a constant across users when a is specified as a random variable distributed across the user population. The time-dependent O-D demands for the entire range of VOT over the planning horizon (i.e., ywtm(a), "w ∈ W, t ∈ T, m ∈ M, a ∈ amin, amax) can be obtained based on a given mode flow pattern ymwt, "w ∈ W, t ∈ T, m ∈ M. The analyst is interested in solving for xk wtm(a), "w ∈ W, t ∈ T, m ∈ M, k ∈ K(w, t, m), a ∈ amin, amax, the route flow for users with VOT a between O-D pair w departing at time t and using mode m and route k, and the corresponding experienced route generalized cost GCkwtm(a). Note that although the mode choice utility function also reflects one’s VOT, and in some instances reliability, the speci- fications used in practice for mode choice and route choice tend to differ markedly, and hence may not be directly comparable. For instance, mode choice models incorporate a richer array of sociodemographic attributes, as well as more refined definitions of travel time components (e.g., waiting time versus in-transit time) that affect mode valuation differentially. Accordingly, it is not expected that coefficients will be the same in models for these different choice dimensions. Ideally, a more complete activity-choice model formulation may achieve consistency in attribute valuation, but this is not expected in the models currently used in practice. Generating Reliability Measures As noted, travel time reliability is another important measure in the choice procedure. To incorporate this measure in the integrated model, it is necessary to devise a method to gener- ate it for the respective paths and O-D pairs in connection with the movement of vehicles through the network. The reliability measure in this application is generated by a method that exploits a robust relation found to hold between the standard deviation and the mean values of the travel time per unit

93 distance. This method is best applied directly at the path level (between given origin and destination). In addition to the relation proving more robust at the path (O-D) level than at the link level, this approach circumvents the need to include this attribute in shortest-path labeling procedures. It also circum- vents the challenging issue of link travel time correlations and the resulting nonadditivity across links defining a given path. It is observed that, in general, the standard deviation of travel time per distance increases with its mean value. It is assumed that there is a linear relationship between the mean travel time per unit distance and its standard deviation, which is (4.3)0 1TTSDMILE b b MEANTTMIL= + × The method leverages a robust relation that is shown to hold between the standard deviations and the mean values of the travel time per unit distance. First established in research con- ducted by Mahmassani and co-workers (Mahmassani and Her- man 1987; Mahmassani and Tong 1986; Chang and Mahmassani 1988; Stephan and Mahmassani 1988) using actual traffic observations, the relation has been investigated in greater depth using both actual traffic data and simulation experiments. This relation has been shown to be more robust at the path (O-D) level than at the link level. By using this relation, the proposed solution algorithm circumvents the need to include link-level reliability measures in shortest-path labeling procedures and the challenging issue of correlations of link travel time. In this study, the relation between standard deviation (reli- ability measure) and the mean values of the travel time per unit distance is estimated using a linear regression model based on simulated vehicle trajectories on the network (here, the New York metropolitan regional network) under consideration. From the regression analysis (see Figure 4.1), the reliability mea- sure is generated using the equation represented in the figure. This approach provides a very efficient procedure for com- bining reliability sensitivity with heterogeneous preferences for mean and standard deviation of travel time using the generalized cost function in Equation 4.2. Multicriterion Dynamic User Equilibrium Route Choice Decision A key behavioral assumption made for the route choice decision is that each trip maker would choose a route that minimizes the route generalized cost function. Specifically, for trips with VOT a, a path k* ∈ K(w, t, m) will be selected if and only if GCk* wtm(a) = min{GCk wtm(a)k ∈ K(w, t, m)}. Based on this assumption, the multiclass multicriterion dynamic user equi- librium (MDUE), a multiclass multicriterion and dynamic extension of Wardrop’s first principle, is defined as follows: For each O-D pair w, mode m, and assignment–departure time interval t, no traveler can reduce his or her experienced route generalized cost with respect to his or her particular VOT a by unilaterally changing path. This definition implies that, at MDUE, each traveler is assigned to a path with the least generalized cost with respect to his or her own VOT. The next section presents an integrated multidimensional network choice model framework for the problem under consideration. Conceptual Framework: Integrated Multidimensional Network Choice Model To solve the integrated dynamic traveler mode–path assign- ment problem in multimodal transportation networks, the analyst essentially wants to determine the number of travelers for each alternative (i.e., mode and path) and the resulting temporal–spatial loading of vehicles and travelers. The sequence of the integrated multidimensional network choice is traveler’s mode choice, ride-sharing choice, and vehicle generation, as well as vehicle route choice and simulation. Figure 4.2 shows the integrated multidimensional simulation- based dynamic microassignment conceptual framework. This framework gives the procedure and evolution of traveler’s equi- librium mode choice, ride-sharing choice, vehicle generation, vehicle equilibrium route choice, and traffic simulation. Time-Dependent Traveler Origin–Destination Demand and Characteristics Demand input for the integrated model consists of a set of time-dependent traveler O-D trips and corresponding individual characteristics, such as income, auto ownership, purpose, and VOT, which are used in both mode and route choice procedures. In this study, the time-dependent traveler O-D demand is generated directly from the New York Metro- politan Transportation Council’s best practice model (NYBPM) y = 0.2207x - 0.4787 R2 = 0.4769 0 5 10 15 20 25 30 0 10 20 30 40 50 60 Mean Travel Time per Mile (min/mile) St an da rd D ev ia tio n (m in /m ile ) Figure 4.1. Standard deviation versus mean of travel time per unit distance.

94 (Vovsha, Donnelly, and Gupta 2008; Vovsha, Donnelly, and Chiao 2008; Chiao and Vovsha 2006; PB Consult, Inc. 2005; Vovsha et al. 2002). The NYBPM is a static tour-based model that includes individual characteristics by a microsimulation model based on social and economic characteristics of the pop- ulation, such as employment status. From a set of given time- of-day (TOD) distributions in the NYBPM tour-based model, 30-minute interval time-varying traveler O-D trips with 13 modes can be generated for interval traveler trips between internal zones (i.e., zones inside the NYC regional network). External demand comprises trips from, to, or between external zones (i.e., zones outside the NYC regional network); these trips are all auto trips. External vehicle trips are not involved in the mode choice part, but will be considered in the route choice and network simulation part. In addition to the TOD pattern generated from the NYBPM model, a 15-minute interval auto trip (i.e., single-occupant vehicle [SOV] and high-occupancy vehicle [HOV]) TOD pattern is estimated based on historical detector data. This study combines the TOD patterns from both models to define the final departure-time pattern. Accordingly, demand in this study consists of individual travelers, and the mode choice is a disaggregated choice or microassignment procedure; that is, each traveler selects his or her best mode based on a Monte Carlo simulation technology and choice probabilities of available alternatives in his or her choice set. Note that this framework can further integrate an activity chain–based DTA model by replacing the under- lying trip-based DTA model with an activity-based DTA model. In this study, the integrated model is restricted to a trip-based model. Figure 4.2. Framework of the integrated multidimensional network choice model.

95 Nested Logit-Based Mode Choice Model With the above time-dependent traveler O-D demand with individual characteristics for internal zones, the mode choice model is used to determine the mode to be chosen for each traveler according to his or her individual characteristics (e.g., income, auto ownership, age) and mode attributes (LOS) at each departure time. There are 13 modes considered in this study, as shown in the nested logit mode choice model structure in Figure 4.3. Note that the auto travelers (i.e., SOV, HOV2, and HOV3) can fur- ther choose their corresponding routes with minimum expe- rienced generalized cost with respect to their VOT in the MDUE route choice and network simulation procedure. More importantly, this study allows flexible forms of both mode and route choice models; that is, it does not restrict the cost function of route choice function to be the same as the mode choice model. This flexibility is essential in practice, as specifications and calibrations of mode choice and route choice model may use different functions and data. Therefore, both mode choice and route choice models can be used with any well-calibrated choice models and utility functions. The mode choice model in this study is a nested logit model, which is appropriate when the set of alternatives faced by a decision maker can be partitioned in subsets (nests). In multi- modal regional transportation systems, travelers face drive- alone, ride-sharing, transit, and taxi choices. The nested logit mode choice model shown here reflects one of the best com- binations of individual characteristics and mode attributes in the utility functions. The utility function is shown in Equation 4.4: (4.4)U V V Vmwt mwt Biwt Bjwt m j i wt Bi wt Bj i wt = + + + ε + ε + ε where Vm wt = systematic utility for mode m; V wtBi = systematic utility for nest Bi, "i = 1,2,3 in Level 1; V wtBj = systematic utility for nest Bj, "j = 1,2, . . . , 7, 8 in Level 2; ewtBi, e wt Bji, ewtmji = random terms for each level that are inde- pendent to each other and are identically and independently distributed extreme value with scale parameters µ1, µ2, µ3, respectively; VLBi = logsum for nest Bi; and VLBj = logsum for nest Bj. Accordingly, the nested logit choice probabilities, marginal probabilities, and conditional probabilities can be evaluated by the following equations: Pr 1 (4.5) 1 3 1 3 1 1 1 i e e e VL i VL i i VL i VL i i Bi Bi Bi Bi∑ ∑ ( ) = = [ ]( ) ( ) ( ) ( ) µ ′ µ ′= ′ − µ ′= Pr 1 (4.6) 2 2 2 j i e e e VL j VL j j B VL j VL j j B Bj Bj i Bj Bj i ∑ ∑( ) = = [ ] ( ) ( ) ( ) ( ) µ ′ µ ′∈ ′ − µ ′∈ Pr 1 (4.7) 3 3 3 m j i e e e V m V m m B V m V m m Bj j ∑ ∑( ) = = [ ]( ) ( ) ( ) ( ) µ ′ µ ′∈ ′ − µ ′∈ Pr Pr Pr Pr (4.8)m m j i j i i( ) ( )( ) ( )= × × Pr (4.9)p mmwt ( )= Root TaxiSOV HOV and Transit HOV2 HOV3 HOV4 CR TR Taxi 13121110987654321 DTRDCRWCRTollTollTollTollNon- Toll Non- Toll Non- Toll Non- Toll WTR Figure 4.3. Nested logit mode choice model.

96 The result of the mode choice model is to assign a mode to each traveler. Because the majority of traffic interaction in the transportation networks is vehicle to vehicle, especially for highway networks, it is necessary to map travelers to vehicles, especially for those ride-sharing travelers, according to occu- pancy levels. The next section gives a ride-sharing choice and vehicle-generation procedure to connect the mode choice results to vehicle trips, which is the input for the MDUE route choice and network simulation model. Ride-Sharing Choice and Vehicle-Generation Model The mapping from travelers with mode choice to vehicle trips is a key element in the integrated model because it provides the essential demand input to the route choice and dynamic network simulation and assignment procedure. Most available regional models distinguish trips between internal zones and trips from, to, or between external zones; only internal trips are involved in the mode choice procedure, while modes of external trips are predefined. However, in the network simulation and assignment procedure, internal vehicle trips and external vehicle trips will be interacted with each other. Accordingly, the proposed ride-sharing choice and vehicle-generation model includes two components: ride- sharing choice and internal vehicle generation, and appending external vehicle trips to the vehicle demand. The ride-sharing choice is intended to address the carpool- ing behavior of HOV travelers, which is a procedure to map travelers to vehicles based on origin, destination, and departure time, as well as occupancy level (i.e., HOV2, HOV3, and HOV4). For a set of travelers with the same origin, destination, departure time, and occupancy level, there are three mapping methods: (1) deterministic simple mapping, (2) deterministic sorted mapping, and (3) random mapping. Deterministic simple mapping simply selects s (where s is the occupancy level) travelers in the traveler set sequentially. Deterministic sorted mapping selects s travelers sequentially in a sorted traveler set in which the sorted criterion can be the VOT of each traveler. Random mapping uses a Monte Carlo simulation process to randomly select s travelers in the traveler set. Following the procedure of ride-sharing choice of HOV travelers, this procedure generates internal vehicles based on the results of ride-sharing choice. After generating vehicles for all the inter- nal zones, this model appends vehicles for external zones. The procedure of ride-sharing choice and vehicle generation is shown in Figure 4.4. Figure 4.4. Ride-sharing choice and vehicle-generation model.

97 The mode choice model, ride-sharing choice, and vehicle- generation procedures result in a time-varying vehicle O-D demand pattern that consists of a set of multiclass vehicles with distinct individual origin, destination, departure time, occupancy level, VOT, and so forth, for the route choice and network simulation procedure. The next section describes the multidimensional simulation-based dynamic microassignment system used in the route choice and network simulation proce- dure in this study to assign routes to each vehicle. Multidimensional Simulation-Based Dynamic Microassignment System To support pricing and congestion, a multidimensional simulation-based dynamic microassignment system was devel- oped to address the MDUE route choice behavior. The system features the following three components: (1) traffic simulation (or supply), (2) traveler route choice behavior, and (3) path set generation. These components have become relatively standard in state-of-the-art simulation-based assignment procedures, following a blueprint originally developed for FHWA in the form of the DYNASMART simulation–assignment method- ology (Jayakrishnan et al. 1994). Accordingly, the simulation capabilities used in this work are interchangeable with almost any particle-based simulator that tracks individual vehicle trajectories in a micro or meso flow-modeling framework. However, the algorithmic procedures for equilibrium seek- ing differ across platforms. In particular, the algorithms for finding a TDUE with heterogeneous users have, to the team’s knowledge, only been implemented in conjunction with DYNASMART-P. However, these procedures could be adapted with most of the microassignment tools. The traffic simulator— DYNASMART (Jayakrishnan et al. 1994) in this case—is used to capture the traffic flow propagation in the traffic network and evaluate network performance under a given set of mode and route decisions made by the individual travelers. Given user behavior parameters, the traveler route choice behavior component aims to describe travelers’ route selection decisions (i.e., the MDUE route choice model in this study). The third component, path set generation, is intended to generate real- istic route choice sets for solving the traveler assignment problem. Figure 4.5 depicts the flowchart of the system. A general overview and recommended methods for a simulation-based solution approach to the TDUE assignment problem are presented below, and mathematical formulations and solution algorithms are presented in the Mathematical Formulations of the Integrated Multidimensional Network Choice Model and Solution Algorithms for the Integrated 1. Input and Initialization 2. Multidimensional Choice Set Generation for Multiple User Classes (Parametric Analysis Method Based Bi-Criterion Time-Dependent Least-Cost Path Algorithm) 3. Multi-Class Dynamic User Equilibrium Network Micro-Assignment (OD pairs, Modes, Departure times, VOTsubintervals, and Paths) 4. Multi-Class Dynamic Network Simulation (Particle-based meso-scopic simulator) DTA Loop Time-Varying Network Performance (Time, Cost, and Reliability etc.) Road Network (SOV and HOV) Traveler Characteristics (Value of Time, Value of Reliability etc.) Initial Network Performance (Time, Cost, and Reliability etc.) Time-Dependent Vehicle Demand (SOV and HOV) Road Pricing Scheme Time-Varying Network Multi- Class Flow Pattern (Link and Path Flows) 5. Output Results Figure 4.5. Multidimensional simulation-based dynamic microassignment system.

98 Multidimensional Network Choice Model sections within Appendix A. The following sections present an overview of a simulation-based iterative solution framework to solve the integrated model and present the some key issues in the integrated model, specifically route choice and path compu- tations including reliability, a column-generation solution framework, and algorithms and challenges for large-scale applications. Simulation-Based Iterative Solution Framework Overview of Solution Framework The TDMSUE-MDUE problem is to find both equilibrium travelers’ mode choice and equilibrium vehicles’ route choice with a given time-dependent traveler demand. The TDMSUE problem is solved by a projected gradient-based descent direc- tion method. However, it is not practical to enumerate the complete set of feasible routes for solving the MDUE problem in a realistically sized transportation network. To capture the individual choice behavior and traffic dynamics, the simulation-based DTA algorithmic framework disaggregates the O-D demands into individual vehicles. Only a portion of paths would have a nonzero probability of carrying vehicles in an MDUE solution. This study uses the trajectories of vehicles as a proxy to store the feasible path set, using what is referred to as the vehicle-based implementation technique (Lu et al. 2007), to optimize computer memory use and eliminate many otherwise unrealistic paths. To avoid explicit enumer- ation of all feasible routes, the study applies a column- generation approach to generate a representative subset of paths with competitive costs to augment the feasible path set. The parametric analysis method (PAM) is applied to obtain a set of breakpoints that partition the entire VOT interval into multiple subintervals. A projected descent direction method is used to solve the resulting MDUE problem in a restricted (reduced) path set; this is called the restricted multiclass multi criterion dynamic user equilibrium (RMDUE) problem in equations (see Solution Algorithm for the Integrated Multidimensional Network Choice Model section in Appendix A for more detail). Route Choice and Path Computations Including Reliability The main impediment for solving the MDUE problem of interest is due largely to the relaxation of VOT from a constant to a continuous random variable. This relaxation leads to the need to find an equilibrium state resulting from the inter- actions of (possibly infinitely) many classes of trips, each of which corresponds to a class-specific VOT, in a network. If, in the extreme case, each trip maker (or class) requires its own set of time-dependent least-generalized cost paths, finding and storing such a grand path set is computationally intrac- table and memory intensive in (road) network applications of practical sizes. In order to circumvent the difficulty of find- ing and storing the least-generalized cost path for each indi- vidual trip maker with different VOT, PAM is proposed to find the set of extreme efficient path trees, each of which minimizes the parametric path generalized cost function (Equation 4.2) for a particular VOT subinterval. The idea of finding the set of extreme efficient paths to which hetero- geneous trips are to be assigned is based on the assumption (Dial 1997; Marcotte and Zhu 1997) that in the disutility minimization-based path choice modeling framework with convex disutility functions, all trips would choose only among the set of extreme efficient paths corresponding to the extreme points on the efficient frontier in the criterion space. Essentially, the PAM bicriterion time-dependent least-cost path (BTDLCP) algorithm has two important roles to play in solving the proposed problem: (1) it transforms a continuous distributed VOT into multiple user classes, and (2) it generates a time-dependent least-cost path tree for each user class, which subsequently defines a descent search direction for the MBDUE traffic assignment problem. A novel approach is developed for this study to generate and incorporate reliability measures in route choice and sup- porting path computation. The method leverages a powerful relation that is shown to hold between the standard deviation and the mean values of the travel time per unit distance. By combining this approach with the multiple paths produced by the parametric shortest-path methods used to reflect hetero- geneity in user preferences, a very efficient implementation has been devised and tested in this work. Thus, for the given path set corresponding to the various classes of users (determined by the parametric shortest-path procedure), the corresponding reliability measure is estimated directly at the path level, and relabeling of the paths is then performed for the various classes, taking reliability valuation into consideration. This approach provides a very efficient procedure to combine reliability sensi- tivity with heterogeneous preferences for mean and standard deviation of travel time consistent with the generalized cost expression in Equation 4.2. The PAM-based path-generation procedure including the reliability measure is shown in Figure 4.6. Implementation Steps of Solution Framework The simulation-based column-generation iterative solution framework for the TDMSUE-MBDUE problem includes four main steps, depicted in Figure 4.7. The steps are 1. Input and initialization; 2. Nested logit mode choice; 3. Ride-sharing choice and vehicle generation; and

99 4. Multidimensional simulation-based dynamic micro- assignment. Column Generation–Based MDUE Solution Algorithm The column generation–based MDUE solution algorithm incorporating different vehicle classes (low-occupancy vehicles [LOVs] and HOVs) is outlined below, and its flowchart is presented in Figure 4.8. Algorithms and Challenges for Large-Scale Applications Computation and storage of least-generalized cost paths for time-dependent equilibrium problems constitute the major computational challenge for the algorithms described in this section. The parametric shortest-path procedures for random coefficient utility models represent a major breakthrough that allows consideration of heterogeneous users in a practical network setting. To alleviate the memory-demanding require- ments of the flow-based DTA models, a vehicle-based technique is implemented. Vehicle-based implementations circumvent storing the grand path set and path assignment sets explicitly whereby the path information is extracted from vehicle tra- jectories, and thus provide considerable savings in memory requirements in the process. To this end, vehicle-based imple- mentations of equilibrium methods and parametric shortest- path procedures are two major advances. Nonetheless, the scale of the networks of interest imposes additional computational burdens on the solution algorithm that require further considerations of the design of the algo- rithms and their implementation schemes. These are developed and illustrated on the New York regional network in this study. The bottleneck here is again the computational time required for time-dependent least-generalized cost path calculation. Two features in the implementation of PAM are introduced in conjunction with the New York application: (1) adjusting the step size in PAM and (2) gap-based shortest-path selection. Both features aim at reducing the computation time. Step Size Adjustment in Parametric Analysis Method In the outer loop, PAM is invoked to find the set of bicrite- rion time-dependent extreme efficient paths, to which all the trips with different VOTs are assigned, and the correspond- ing set of breakpoints (i.e., VOTs, aI = {a0, a1, . . . , ai, . . . , aI amin = a0 <a1 < . . . < ai< . . . <aI = amax}) that partitions the entire feasible range of VOT [amin, amax] and hence defines multiple classes of trips, where each class includes the trips with VOT a ∈ [ai-1, ai), "i = 1, . . . , I. Starting from the low- est possible VOT, the bicriterion time-dependent shortest- path algorithm continuously solves for the time-dependent least-generalized cost (TDLGC) path tree rooted at each des- tination for a given VOT interval and determines the upper bound of that VOT interval, for which the TDLGC path tree remains optimal, until reaching the highest possible VOT. In order to move from the current VOT segment to the next one and obtain a different TDLGC path tree, a small value D needs to be added to the current breakpoint ai. This implies that travelers cannot distinguish differences in VOT below D per minute. The value of D also implicitly sets an upper bound for the number of VOT segments generated in PAM, with a value of max min( )α − α ∆ . The feasible range of VOT is given by the closed interval [amin, amax] and can be estimated from survey data. As a result, D is a fixed given value. PAM requires a full run of BTDLCP calculations for finding one VOT segment, which is time consuming on a large-scale network. In order to reduce the computational time, D can be set to a larger value. As indicated elsewhere, D implies the indifference band in VOT 1. PAM of VOT α based on TT and TC and calculate shortest path tree for each VOT αi 2. Construct a set of minimum generalized cost (i.e., TT and TC) path set for all VOT αi 3. Relabeling minimum generalized cost path by including the reliability measure for each VOT αi Figure 4.6. PAM-based path-generation procedure including reliability measure.

100 Step 1. Input and Initialization 1.1 Input: Time-dependent multimodal traveler O-D demand with individual characteristics (income, auto ownership, and purpose), network, and initial network level of services (time, cost, and reliability etc.) 1.2 VOT generation: Generate VOT for each traveler based on Monte Carlo simulation with given VOT distribution Step 2. Nested Logit Mode Choice 1.3 Initialization: Set mode choice loop ml = 0 2.1 Input of travelers with individual characteristics and mode attributes 2.2 Mode choice set construction systematic utility calculation 2.3 Nested logit choice probability calculation 2.4 Descent direction finding and mode choice update Step 3. Ride Sharing Choice and Vehicle Generation 3.1 Input of travelers with mode choice 3.2 Ride sharing choice and vehicle generation 3.3 Append external vehicles 2.5 Output travelers with mode choice 3.4 Output vehicles Step 4. Multidimensional Simulation-Based Dynamic Micro-Assignment 4.3 Solving the restricted MDSUE problem. 4.3.4 DTA inner loop stop checking: g(x)<= , or il=ilMax 4.3.1 Initialization. Set inner loop il=0. Read network performance and assignment from last outer loop 4.3.2 Multiclass path assignment 4.3.3 Multiclass dynamic network loading 4.1 Input and initialization 4.1.1 Input: Time-dependent vehicle demand, network, road pricing scheme 4.1.2 Initialization: Set DTA out loop ol = 0. Perform a dynamic network loading to obtain network performance 4.2 Parametric analysis of VOT and path generation 4.2.1 Bi-criterion dynamic shortest path calculation to define multiple user classes and shortest path trees 3.4 DTA out loop stop checking: no new path, or ol=olMax 3.5 Mode choice loop stop checking: ml=mlMax, or g(y)<= Stop 4.2.2 Relabeling shortest path by including reliability Y Y Y N N N Figure 4.7. Simulation-based column-generation solution framework.

101 among travelers and should be set to a small value. Increasing the value of D in a small network may lead to inaccurate and unrealistic predictions of flow distribution patterns, whereas in a large-scale network the flow patterns will remain valid. This claim can be validated through a simple example. For the sake of simplicity, the generalized cost does not include reliability in this example. However, for a given path, reliability does not vary with VOT; therefore, the following illustration remains valid once the reliability term is added into the generalized cost. In PAM, the generalized cost perceived by travelers with VOT a from O-D pair w at departure time t along path k ∈ K ~ (w, t, m, ai) is given in Equation 4.2. In PAM, the BTDLCP algorithm calculates a time-dependent least-cost path tree for a given a rooted at every destination node based on the generalized cost described in Equation 4.2. The scale of the network influences the algorithm with regard to the proportion of the paths using tolled links in the path set. In this extreme case, every path found by BTDLCP uses the tolled link, thus making the algorithm very sensitive to VOT. If the value of a is changed to a + D, another path tree may Figure 4.8. Flowchart of MDUE solution algorithm.

102 be obtained that differs considerably from the current one in a small network. When D is large, a lot of information may be lost when generating the least-cost path tree, resulting in inaccurate flow distribution patterns for a small network. This inaccurate result will be avoided in large networks due to only a small portion of paths using tolled links; thus, the least- cost path trees are more robust. In this case, setting a larger value for D would not result in a significant loss in the total path set generated by the BTDLCP algorithm. Gap-Based Selection Technique in Parametric Analysis Method The other modification to reduce computational effort is a gap-based selection technique for time-dependent shortest- path calculation. Essentially, the path-finding algorithm is applied only to a fraction of the destination zones, selected on the basis of the gap values of vehicles arriving at that destina- tion. After sorting the destination zones according to their gap values, PAM is invoked in the outer loop for the worst 1/n of these destination zones to obtain new VOT partitions and update the previous path set with new paths (if any) found by the bicriterion time-dependent shortest-path algorithm. For the rest of the destination zones, the path sets and VOT partitions remain the same. An integrated multidimensional network modeling pro- cedure for supporting congestion and pricing studies was presented above. In the next section, an application of the proposed integrated procedure using the NYBPM regional network is demonstrated. Demonstration Using New York regional Network Building a Large-Scale Network Model: Summary of Challenges In general, because of their ability to represent network oper- ational characteristics, simulation-based DTA models require more detailed network information than comparable static assignment models. Traffic control signs and signals, left turns, and other movement capabilities at a node are mainly (and crudely) represented in the link performance function in a static network, whereas a dynamic model requires more accurate information on junction control and allowed move- ments at each phase at a signalized intersection, as well as careful definition of each downstream movement at a node. Basically, there is no direct method of (correctly) converting a static network model into a dynamic network model in one shot using only the existing data obtained from the provided static network model database. Smart conversion of the exist- ing database, use of external information sources, and more importantly, use of engineering judgment are essential parts of building a large-scale dynamic network model. In sum, models developed for static assignment applica- tion generally exhibit a variety of drawbacks that render them inappropriate for dynamic network analysis, including • Oversimplified representation of junctions, especially free- way interchanges, for correct operational simulation; • Absence or incorrect control information at junctions and lack of a reliable electronic database of control devices and control parameters at signalized junctions; • Poor definition of origin and destination zones, including treatment and connection of centroids and external traffic generators; • Insufficient specification of the operational attributes of links and junctions for the purpose of traffic simulation; and • Absence of time-varying O-D information, which must be synthesized from available static matrices, coupled with traffic counts sometimes taken in mutually different time periods. Conversion of Existing Network for Dynamic Analysis The regional NYBPM includes 28 counties from a tristate area divided into 3,586 internal traffic analysis zones. The counties include • Ten counties from the New York Metropolitan Transportation Council area; • Two other counties from New York State; • Thirteen counties from the North Jersey Transportation Planning Authority area; • One other county from the state of New Jersey; and • Two counties from the state of Connecticut. The zones are mainly concentrated in NYC; these include • 2,449 zones from New York State; • 740 zones from the state of New Jersey; • 397 zones from the state of Connecticut; and • 111 external zones for travel entries to and exits from the network. The NYBPM network also contains • 53,395 links; and • 31,812 nodes. The DTA model converted from the static TransCAD model can be seen in Figure 4.9, and Figure 4.10 shows the DYNASMART-P model. Details of the conversion steps and procedures applied in the process are described in the Application to New York Regional Network section in Appendix A. These include procedures to

103 Figure 4.9. TransCAD model of the NYBPM network. Figure 4.10. DYNASMART-P model of the New York network.

104 adjust the representation of geometric features of interchanges to support operational simulation and to assess, assign, and verify properties of junctions and specification of movements at junctions. The conversion also includes the preparation of the various required and optional input data files for the simulation. The properties of the resulting DYNASMART-P network are described below. Zone Information There are 3,697 zones. Of these, 3,586 are internal; only 111 are external. Node and Control Information There are 28,406 nodes. Control information for the nodes is as follows: • 3,816 uncontrolled; • 2,625 yield signed; • 12,944 all-way stop signed; • 8,054 actuated controlled; and • 967 two-way stop signed. Link and Type Information The 68,490 links on the network are classified as follows: • 6,026 freeways; • 169 freeway HOV links; • 56,102 arterials; • 37 HOV arterial links; • 150 highways; • 2,688 on-ramps; and • 3,318 off-ramps. Pricing Information There are 297 tolled links; of these, 291 use static tolling and only six use dynamic tolling. As seen in Figure 4.11, most of the pricing is nondistance based except along the I-95 New Jersey Turnpike corridor. Tolling on the major bridges and tunnels is as follows: • The George Washington Bridge, Lincoln Tunnel, Holland Tunnel, Goethals Bridge, Outerbridge Crossing, and Bayonne Bridge are dynamically tolled bridges; Figure 4.11. Pricing information for the New York network.

105 • The Verrazano-Narrows Bridge, Bronx-Whitestone Bridge, Brooklyn-Battery Tunnel, Queens Midtown Tunnel, Throgs Neck Bridge, Triborough Bridge, Marine Parkway-Gil Hodges Memorial Bridge, Cross Bay Veterans Memorial Bridge, and Henry Hudson Bridge are the bridges and tunnels tolled in New York metropolitan area; and • The Tappan Zee Bridge, Bear Mountain Bridge, Kingston Rhinecliff Bridge, Mid Hudson Bridge, and Newburgh Beacon Bridge are the tolled bridges in New York State. Methodology for Calibration of Origin–Destination Demand for Dynamic Analysis Given static O-D demand information and time-dependent link measurements, the dynamic O-D demand estimation pro- cedure aims to find a consistent time-dependent O-D demand table that minimizes the deviation between (1) estimated link flows and observed link counts and (2) estimated demand and target demand (based on the static demand matrix). The induced network flow pattern can be expressed in terms of path flows and link flows. In a dynamic context, and especially in congested networks, elements of the mapping matrix between O-D demand and link flows are not constant and are, themselves, a function of the unknown O-D demand values. A bilevel dynamic O-D estimation formulation is adapted here in order to integrate the DTA constraint. Specifically, the upper-level problem seeks to estimate the dynamic O-D trip desires based on given link counts and flow proportions, subject to nonnegativity constraints for demand variables. The flow proportions are in turn generated from the dynamic traffic network loading problem at the lower level, which is solved by a DTA simulation program, with a dynamic O-D trip table calculated from the upper level. The mathematical formulations and solution algorithms for the time-dependent O-D estimation process are detailed in Appendix A. Application of the procedures to the New York regional network are also described. Recognizing some of the data limitations described earlier, it was still possible to develop and calibrate a reliable DTA tool that represents the dynamics of traffic in the study area to a reasonable degree and allows meaningful comparative analysis of alternative scenarios. To evaluate the performance of the procedure, the root mean squared error between observed link volumes and simulated link volumes are used as an overall measure of effectiveness. Validation against individual link counts was performed for selected links. Cumulative curves provide insight into the ability of the resulting assignment to capture the link flow volumes. The results are satisfactory in light of the available data, from the aggregate initial demand matrix to the link counts used, and provide encouraging indications for the ability of the DTA tool to support the intended analysis of traffic patterns under various scenarios. Figure 4.12 depicts an example of the results of the simulated link volumes compared with observed link volumes for a selected link. Figure 4.12. Sample of simulated link volumes versus observed link volumes.

106 Numerical Experiments Scenario Definition The planning horizon is the morning period from 6:00 to 10:00 a.m. The departure time interval is 15 minutes. Figure 4.13 shows the time-dependent pattern of person trip departures in this study. Link toll information is obtained based on the existing pricing schemes implemented in the New York region. Six of the 297 tolled links are dynamic toll roads for peak periods (weekdays, 6:00–9:00 a.m. and 4:00–7:00 p.m.; Saturday and Sunday, noon–8:00 p.m.). The price distribution applied for tolled links is given in Figure 4.14, and the road type distribu- tion is shown in Figure 4.15. The experimental set-ups for the MDUE model were established with the aim of validating the performance of the gap-based selection technique in the bicriterion time-dependent shortest-path calculation and evaluating the solutions with different settings of VOT step sizes (D). Three experiments were set up as presented in Table 4.1. Figure 4.13. Time-dependent person trip departures. Figure 4.14. Price distributions for tolled links in the New York network.

107 Convergence Pattern of the Integrated Model The convergence of the algorithm is examined by the objective function of formulation described in Appendix A, specifically in Equation A.16, for the dynamic mode choice problem. This expression is a gap measure of the total square of the differ- ence between assigned mode flows ymwt and expected mode flows qwt × pmwt(y) calculated by the mode choice model under the prevailing trip times and network attributes obtained with those assigned flows ymwt. This measure is an extension of the convergence criterion defined in Zhang et al. (2008) for a generalized dynamic SUE problem. Figure 4.16 shows the convergence pattern in terms of this average gap measure. The smaller this quantity is, the closer the agreement will be between the demand values corresponding to the travel time attributes (by the mode choice equation) and the assigned flows that have produced these network attributes. In other words, smaller values reflect consistency between the demand models and network performance simulation, thereby cor- responding to an equilibrium solution that satisfies the TDMSUE conditions defined in the previous section. The convergence pattern exhibited in Figure 4.16 suggests success- ful equilibration and a very efficient overall iterative scheme. Convergence Pattern of Multicriterion Dynamic Use Equilibrium Model From a methodological perspective, the convergence pat- terns of the proposed MDUE solution algorithm together with different implementation techniques are examined on the New York metropolitan regional network. The objective function Gap(r) = gR(x, aI) [where gR(x, aI) is as defined in Equation A.41 in Appendix A] is calculated based on vehicle- experienced generalized cost at each iteration. Another measure Figure 4.15. Road-type distributions for tolled links in the New York network. Table 4.1. Experimental Set-up for MDUE Model Gap- Based Technique VOT Step Size (D) Outer Loop Inner Loop Experiment 1 No 0.3 5 Iterations 1 Iteration Experiment 2 Yes 0.3 5 Iterations 1 Iteration Experiment 3 Yes 0.5 5 Iterations 1 Iteration Figure 4.16. Convergence pattern of TDMSUE solution.

108 of effectiveness is collected in all conducted experiments, in addition to the objective function Gap(r). The additional measure is the average gap over all the vehicles in the network for a given path flow pattern r: , , (4.10) AGap r x GC x x K k wtm i k wtm i wtm i ikmtw wtm i imtw  ∑∑∑∑∑ ∑∑∑∑ [ ] ) ) ) ) )( ( ( ( (= α × α −pi α α AGap(r) is used as a surrogate of the gap function Gap(r) and is calculated based on the vehicle-experienced path generalized cost in this study. The lower bound of the AGap(r) is zero. Essentially, the smaller the average gap, the closer the solution is to an MDUE, as differences in generalized cost across paths used at equilibrium between a given O-D pair at a given time become very small. To get a better illustration of the solution quality, AGap(r) is calculated with and without considering travel time reliability in the path generalized cost function and is reported separately, as shown in Figure 4.17. As shown in Figure 4.17 (top), the MDUE algorithm can effectively reduce the average gap measures (with travel time reliability) in all three experiments, although the convergence patterns are not strictly monotonically decreasing. As for solution quality, the final average gap values at least iteration reduced 63.56%, 64.93%, and 62.25% of the initial gap values, respectively, for the three experiments. Additional convergence criteria based on average gap without travel time reliability, as shown in Figure 4.17 (bottom), exhibit similar convergence trends, with relatively lower average gap values obtained at each iteration as an additional term is left out in the path general- ized cost. Recognizing the complexity of the problem and the scale of the network, the convergence patterns indicate that the MDUE algorithm can find a sufficiently close-to-MDUE solution for the New York metropolitan regional network. Computational Time Analysis of Multicriterion Dynamic Use Equilibrium Model From a practical application standpoint, the effectiveness of the implementation techniques is investigated in this section. As discussed above, the most intensive computational opera- tion in MDUE solution algorithm is PAM, which calculates the time-dependent least-generalized cost TDLGC path tree and partitions the entire feasible range for each destination. The computational time required by MNDL in DYNASMART and RMDUE (inner loop) only depends on the total number of vehicles loaded on the network; therefore it remains constant at any iteration in all experiments. Actual times depend on the specific hardware configuration used, although the former is in the order of 2 hours and the latter 2 minutes on medium- end workstations. To examine the effectiveness of the implementation tech- niques, the relative computational times required by PAM in three experiments are demonstrated in Figure 4.18. Relative Figure 4.17. Convergence patterns in terms of average gap ( top) with travel time reliability and ( bottom) without travel time reliability.

109 computational time is defined as the average time required by one operation in PAM for a root node (destination) of a TDLGC path tree relative to the average time in E1; this measure is used to explore the magnitude of the improvement. The amount of time required in PAM depends on the number of destinations and VOT step size. The full run of PAM with 0.3 for VOT step size in E1 requires a large number of com- putations and takes the most computational time. In E2, a gap-based selection technique was implemented that reduced the number of TDLGC path trees in PAM by a factor of 1/k at each iteration. There was an approximately 50% reduction of total time in E2 compared with E1. The improvement was the most significant in E3, in which both a gap-based selection technique and adjustment of VOT step size to a greater value (0.5) were implemented, because the number of computations involved was lower relative to other experiments. It was also observed that the marginal contribution (by gap-based selection technique) of reduction on computational time diminishes as the number of iterations increases, as those destinations left in PAM are the most sensitive to VOT value and thus require time to partition VOT ranges. Both E2 and E3 attained com- parable levels of solution quality (see Figure 4.17), but PAM in E3 was faster (i.e., only 72% of the total time required in E2). Therefore, the combined implementation techniques provide the most reduction in computational time for the MDUE solution algorithm. Analysis of Mode Choice Results According to the NYBPM model and the latest calibrated nested logit mode choice model, there are 13 modes in this study, as depicted in Figure 4.3. This study specified three income categories: low (average income is $7,182), middle (average income is $41,065), and high (average income is $129,795); this stratification is based on the 1990 PUMS data. In addition, there are eight trip purposes including work with low income, work with middle income, work with high income, school, university, maintenance, discretionary, and at-work. The mode share pattern was analyzed by time period, trip purpose, and income level. Figure 4.19 shows a time-dependent mode share pattern of travelers in which travelers are inclined to drive alone in the early morning. That is, 6:00–7:30 a.m. is the peak period for SOV travelers; travelers will choose ride- sharing after 7:30 a.m. The share of toll road users does not change very much in this case study, partly because the num- ber of toll links is very small in the network. The shares of transit and rail modes increase slightly from 6:00–10:00 a.m. Figure 4.20 shows mode shares by trip purpose. It can be seen that more than 40% of high-income travelers will drive alone to work, which is also confirmed by Figure 4.21, which shows mode share by income group. Similarly, low-income travelers tend to use transit modes to go to work. Figure 4.22 shows the time-dependent vehicle patterns by occupancy level (drive alone, HOV2, HOV3, and HOV4+). From this figure, it can be seen that the time-dependent pattern is consistent with the time-dependent mode share pattern in Figure 4.19, which confirms the correct integration of dynamic mode choice and route choice model in this study. Impact of Implementation Techniques and Continuously Distributed Value of Time of Multicriterion Dynamic Use Equilibrium Model An important additional consideration is whether using the implementation techniques would lead to large differences in Figure 4.18. Computational time required by PAM (parametric bicriterion path-finding procedure).

110 Figure 4.19. Time-dependent mode share. Figure 4.20. Mode share by trip purpose.

111 Figure 4.21. Mode share by income group. Figure 4.22. Time-dependent vehicle share by occupancy level.

112 prediction of the flow patterns on the network. To address this concern and investigate the impact of continuously distributed VOT across the entire population, numerical results regarding the toll road usage are presented in this section. Toll road usage is examined from three perspectives: total revenue, total number of vehicles passing through toll links, and to reflect heterogeneity, grouped toll road users in different VOT segments. It is observed in Figure 4.23 that the stability of toll road usage (both in terms of total revenue collected and total number of vehicles passing through the toll links) is attained in all experiments and stays at approximately the same level. Figure 4.24 provides the toll road usage of trip makers in different VOT segments over the planning horizon predicted in all experiments. Note that the partition of the feasible range of VOT distribution ([amin, amax]) is independent of the step size selected in the MDUE algorithm. As illustrated in Figure 4.24, trip makers with different VOT react differently to a given road pricing scheme; thus significant discrepancies are obtained under the conventional assumption of homo­ geneous (constant VOT) users. Toll road usage is lower for those trip makers in the low VOT segment, but higher for high VOT users. Again, all experiments predict similar proportions of toll road users in all VOT segments. Supported by those results, it can be concluded that the MDUE algorithm can capture greater realism in path choice behavior, and the proposed Figure 4.23. Toll road usage for ( left) total revenue and (right) total number of tolled vehicles. Figure 4.24. Grouped toll road users in different VOT segments.

113 implementation techniques do not compromise the accuracy of flow pattern prediction. Summary of Network Modeling procedures The proposed integrated model framework is a demonstration of a trip-based integration of a well-calibrated mode choice model in practice and a simulation-based dynamic traffic microassignment model. However, the framework is sufficiently flexible to incorporate other dimensions (e.g., destination choice and departure time choice) in addition to the mode choice dimension from the demand side. In addition, the framework can be readily extended to an activity-based integration of demand models and an activity-based dynamic traffic microassignment model. The basic methodological challenges inherent in such integration problems have been substantially addressed and demonstrated in the present study. Extension and generalization would require additional investment in time and effort, as well as considerable detail in implementation that would be specific to the activity demand structure developed in a particular area, albeit using and building on components demonstrated in the present study. Accordingly, this study provides an essential foundation and direction toward an evolution that provides a conceptually, theoretically, and methodologically complete and sound approach to address heterogeneous user responses to con- gestion, pricing, and reliability in large-scale regional multi- modal transportation networks. The principal contributions of the integration effort presented in this chapter include the following: 1. Integrating additional dimensions of user choice in a net- work simulation assignment platform; 2. Consistently solving a complex realistic stochastic mode choice model equilibration problem in connection with a large-scale network assignment process; 3. Incorporating multiple attributes in the route choice process, particularly price and travel time reliability, in addition to mean travel time; 4. Recognizing user heterogeneity in terms of preferences, especially with regard to VOT in response to pricing schemes and other congestion-related measures; 5. Calibrating a route choice model with a distributed VOT following a lognormal distribution; 6. Devising and testing path-finding procedures that recog- nize multiple criteria and developing efficient implementa- tions for large-scale networks; 7. Incorporating travel time reliability in the route choice process and devising a robust and efficient traffic-theoretic procedure to generate reliability attributes for path-level choices; and 8. Demonstrating the integrated procedure on the actual network of the New York metropolitan region, which is the largest application of DTA equilibration procedures reported to date. In the application to the New York region, the team presented dynamic mode share and toll road usage results of the proposed integrated model for the region’s networks. These results demonstrated the applicability of the model and procedures developed in this work to practical large-scale networks. The team also examined the convergence of the proposed algorithms, establishing successful attainment of the desired equilibrium conditions at all levels of the procedure in con- nection with both route and mode choices. The convergence process revealed a relatively efficient iterative process, further supporting the practical applicability of the integrated pro- cedures developed in this work. The proposed model and the implementation techniques uniquely address the needs of metropolitan areas and agencies for prediction of mode and path choices and the resulting network flow patterns and pro- vide the capability for evaluating a wide range of road-pricing scenarios on large-scale networks.

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 Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand
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TRB’s second Strategic Highway Research Program (SHRP 2) Report S2-C04-RW-1: Improving Our Understanding of How Highway Congestion and Pricing Affect Travel Demand includes mathematical descriptions of the full range of highway user behavioral responses to congestion, travel time reliability, and pricing. The descriptions included in the report were achieved by mining existing data sets. The report estimates a series of nine utility equations, progressively adding variables of interest.

The report explores the effect on demand and route choice of demographic characteristics, car occupancy, value of travel time, value of travel time reliability, situational variability, and an observed toll aversion bias.

An unabridged, unedited version of Chapter 3: Demand Model Specifications and Estimation Results is available electronically.

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