Time-dependent congestion pricing system for large networks: Integrating departure time choice,dynamic traffic assignment and regional travel surveys in the Greater Toronto Area

Congestion pricing is one of the widely contemplated methods to manage traffic congestion. The purpose of congestion pricing is to manage traffic demand generation and supply allocation by charging fees (i.e., tolling) for the use of certain roads in order to distribute traffic demand more evenly over time and space. This study presents a framework for large-scale variable congestion pricing policy determination and evaluation. The proposed framework integrates departure time choice and route choice models within a regional dynamic traffic assignment (DTA) simulation environment. The framework addresses the impact of tolling on: (1) road traffic congestion (supply side), and (2) travelers’ choice dimensions including departure time and route choices (demand side). The framework is applied to a simulation-based case study of tolling a major freeway in Toronto while capturing the regional effects across the Greater Toronto Area (GTA). The models are developed and calibrated using regional household travel survey data that reflect the heterogeneity of travelers’ attributes. The DTA model is calibrated using actual traffic counts from the Ontario Ministry of Transportation and the City of Toronto. The case study examined two tolling scenarios: flat and variable tolling. The results indicate that: (1) more benefits are attained from variable pricing, that mirrors temporal congestion patterns, due to departure time rescheduling as opposed to predominantly re-routing only in the case of flat tolling, (2) widespread spatial and temporal re-distributions of traffic demand are observed across the regional network in response to tolling a significant, yet relatively short, expressway serving Downtown Toronto, and (3) flat tolling causes major and counterproductive rerouting patterns during peak hours, which was observed to block access to the tolled facility itself.     

On the variance of recurrent traffic flow for statistical traffic assignment

This paper generalizes and extends classical traffic assignment models to characterize the statistical features of Origin-Destination (O-D) demands, link/path flow and link/path costs, all of which vary from day to day. The generalized statistical traffic assignment (GESTA) model has a clear multi-level variance structure. Flow variance is analytically decomposed into three sources, O-D demands, route choices and measurement errors. Consequently, optimal decisions on roadway design, maintenance, operations and planning can be made using estimated probability distributions of link/path flow and system performance. The statistical equilibrium in GESTA is mathematically defined. Its multi-level statistical structure well fits large-scale data mining techniques. The embedded route choice model is consistent with the settings of O-D demands considering link costs that vary from day to day. We propose a Method of Successive Averages (MSA) based solution algorithm to solve for GESTA. Its convergence and computational complexity are analyzed. Three example networks including a large-scale network are solved to provide insights for decision making and to demonstrate computational efficiency.     

An alternative formulation of the simultaneous route and departure-time choice equilibrium problem

Traditional (static) network equilibrium models have always been formulated in a route-based fashion rather than a vehicle-based fashion. That is, the decision variables have been the number of vehicles using each route rather than the route choices of each vehicle. Given the success of this approach, it is not surprising that recent “dynamic” network equilibrium models have been formulated in a similar way. That is, the decision variables in these models are usually the route-specific departure rates over time. In this paper, we develop a vehicle-based equilibrium model of simultaneous route and departure-time choice and discuss the possible advantages of this approach. We then describe a heuristic for solving this model and demonstrate its effectiveness on several small examples.     

Learning-based framework for transit assignment modeling under information provision

The modeling of service dynamics has been the focus of recent developments in the field of transit assignment modeling. The emerging focus on dynamic service modeling requires a corresponding shift in transit demand modeling to represent appropriately the dynamic behaviour of passengers and their responses to Intelligent Transportation Systems technologies. This paper presents the theoretical development of a departure time and transit path choice model based on the Markovian Decision Process. This model is the core of the MIcrosimulation Learning-based Approach to TRansit Assignment. Passengers, while traveling, move to different locations in the transit network at different points in time (e.g. at stop, on board), representing a stochastic process. This stochastic process is partly dependent on the transit service performance and partly controlled by the transit rider’s trip choices. This can be analyzed as a Markovian Decision Process, in which actions are rewarded and hence passengers’ optimal policies for maximizing the trip utility can be estimated. The proposed model is classified as a bounded rational model, with a constant utility term and a stochastic choice rule. The model is appropriate for modeling information provision since it distinguishes between individual’s experience with the service performance and information provided about system dynamics.     

Transit Users’ Route‐Choice Modelling in Transit Assignment: A Review

Abstract

This paper reviews the main studies on transit users’ route choice in the context of transit assignment. The studies are categorized into three groups: static transit assignment, within‐day dynamic transit assignment, and emerging approaches. The motivations and behavioural assumptions of these approaches are re‐examined. The first group includes shortest‐path heuristics in all‐or‐nothing assignment, random utility maximization route‐choice models in stochastic assignment, and user equilibrium based assignment. The second group covers within‐day dynamics in transit users’ route choice, transit network formulations, and dynamic transit assignment. The third group introduces the emerging studies on behavioural complexities, day‐to‐day dynamics, and real‐time dynamics in transit users’ route choice. Future research directions are also discussed.     

A latent class joint mode and departure time choice model for the Greater Toronto and Hamilton Area

This paper presents a closed-form Latent Class Model (LCM) of joint mode and departure time choices. The proposed LCM offers compound substitution patterns between the two choices. The class-specific choice models are of two opposing nesting structures, each of which provides expected maximum utility feedback to the corresponding class membership model. Such feedback allows switching class membership in response to the changes in choice contexts. The model is used for an empirical investigation of commuting mode and departure time choices in the Greater Toronto and Hamilton Area (GTHA) by using a large sample household travel survey dataset. The empirical model reveals that overall 38% of the commuters in the GTHA are more likely to switch modes than departure times and 62% of them are more likely to do the reverse. The empirical model also reveals that the average Subjective Value of Travel Time Savings (SVTTS) of the commuters in the GTHA can be as low as 3 dollars if a single choice pattern of departure time choices nested within mode choices is considered. It can also be as high as 67 dollars if the opposite nesting structure is assumed. However, the LCM estimates the average SVTTS to be around 27 dollars in the GTHA. An empirical scenario analysis by using the estimated model indicates that a 50% increase in morning peak period car travel time does not sway more than 4% of commuters from the morning peak period.

     

Park-and-ride lot choice model using random utility maximization and random regret minimization

This research aims to understand the park-and-ride (PNR) lot choice behaviour of users i.e., why PNR user choose one PNR lot versus another. Multinomial logit models are developed, the first based on the random utility maximization (RUM) concept where users are assumed to choose alternatives that have maximum utility, and the second based on the random regret minimization (RRM) concept where users are assumed to make decisions such that they minimize the regret in comparison to other foregone alternatives. A PNR trip is completed in two networks, the auto network and the transit network. The travel time of users for both the auto network and the transit network are used to create variables in the model. For the auto network, travel time is obtained using information from the strategic transport network using EMME/4 software, whereas travel time for the transit network is calculated using Google’s general transit feed specification data using a backward time-dependent shortest path algorithm. The involvement of two different networks in a PNR trip causes a trade-off relation within the PNR lot choice mechanism, and it is anticipated that an RRM model that captures this compromise effect may outperform typical RUM models. We use two forms of RRM models; the classical RRM and µRRM. Our results not only confirm a decade-old understanding that the RRM model may be an alternative concept to model transport choices, but also strengthen this understanding by exploring differences between two models in terms of model fit and out-of-sample predictive abilities. Further, our work is one of the few that estimates an RRM model on revealed preference data.

     

A nested recursive logit model for route choice analysis

We propose a route choice model that relaxes the independence from irrelevant alternatives property of the logit model by allowing scale parameters to be link specific. Similar to the recursive logit (RL) model proposed by Fosgerau et al. (2013), the choice of path is modeled as a sequence of link choices and the model does not require any sampling of choice sets. Furthermore, the model can be consistently estimated and efficiently used for prediction.A key challenge lies in the computation of the value functions, i.e. the expected maximum utility from any position in the network to a destination. The value functions are the solution to a system of non-linear equations. We propose an iterative method with dynamic accuracy that allows to efficiently solve these systems.We report estimation results and a cross-validation study for a real network. The results show that the NRL model yields sensible parameter estimates and the fit is significantly better than the RL model. Moreover, the NRL model outperforms the RL model in terms of prediction.     

A network equilibrium approach for modelling activity-travel pattern scheduling problems in multi-modal transit networks with uncertainty

An understanding of the interaction between individuals’ activities and travel choice behaviour plays an important role in long-term transit service planning. In this paper, an activity-based network equilibrium model for scheduling daily activity-travel patterns (DATPs) in multi-modal transit networks under uncertainty is presented. In the proposed model, the DATP choice problem is transformed into a static traffic assignment problem by constructing a new super-network platform. With the use of the new super-network platform, individuals’ activity and travel choices such as time and space coordination, activity location, activity sequence and duration, and route/mode choices, can be simultaneously considered. In order to capture the stochastic characteristics of different activities, activity utilities are assumed in this study to be time-dependent and stochastic in relation to the activity types. A concept of DATP budget utility is proposed for modelling the uncertainty of activity utility. An efficient solution algorithm without prior enumeration of DATPs is developed for solving the DATP scheduling problem in multi-modal transit networks. Numerical examples are used to illustrate the application of the proposed model and the solution algorithm.     

A utility-based travel impedance measure for public transit network accessibility

A utility-based travel impedance measure is developed for public transit modes that is capable of capturing the passengers’ behaviour and their subjective perceptions of impedance when travelling in the transit networks. The proposed measure is time-dependent and it estimates the realisation of the travel impedance by the community of passengers for travelling between an origin–destination (OD) pair.The main advantage of the developed measure, as compared to the existing transit impedance measures, relates to its capability in capturing the diversity benefit that the transit systems may offer the society of travellers with different traveling preferences. To clarify the necessity of such capability, we demonstrate the randomness (subjectivity) of travel impedance perceived by transit passengers, through evidence from the observed path choices made in the transit network of the greater Brisbane metropolitan region in Australia.The proposed impedance measure is basically a nested logit “logsum” composition over a generated set of reasonable path options whose systematic utilities are evaluated based on a discrete choice model previously developed and calibrated for the greater Brisbane transit passengers. As a case study, the proposed impedance measure is calculated for all the origin blocks in the Brisbane area, during the morning commutes to the Central Business District (CBD). The results are presented and discussed, and intuitive and important advantages are demonstrated for the proposed measure.     

Activity-based market equilibrium for capacitated multimodal transport systems

Empirical studies have shown that demand for multimodal transport systems is highly correlated with activity schedules of individuals. Nonetheless, existing analytical equilibrium models of multimodal systems have only considered trip-based demand. We propose a new market equilibrium model that is sensitive to traveler activity schedules and system capacities. The model is based on a constrained mixed logit model of activity schedule choice, where each schedule in the choice set is generated with a multimodal extension of the household activity pattern problem. The extension explicitly accounts for both passenger choices of activity participation and multimodal choices like public transit, walking, and vehicle parking. The market equilibrium is achieved with Lagrangian relaxation to determine the optimal dual price of the capacity constraint, and a method of successive averages with column generation finds an efficient choice set of activity schedules to assign flows over the dynamic network load capacities. An example illustrates the model and algorithm, effects similar to Vickrey’s morning commute model can be observed as a special case. A case study of the Oakville Go Transit station access “last mile” problem in the Greater Toronto Area is conducted with 166 survey samples reflecting 3680 individuals. Results suggest that a $10 fixed parking fee at Oakville station would lead to a reduction of access auto share from 54.8% to 49.5%, an increase in access transit share from 20.7% to 25.9%, and a disutility increase of 11% for the of single-activity residents of Oakville.     

An activity-based approach for scheduling multimodal transit services

This paper proposes a new activity-based transit assignment model for investigating the scheduling (or timetabling) problem of transit services in multi-modal transit networks. The proposed model can be used to generate the short-term and long-term timetables of multimodal transit lines for transit operations and service planning purposes. The interaction between transit timetables and passenger activity-travel scheduling behaviors is captured by the proposed model, as the activity and travel choices of transit passengers are considered explicitly in terms of departure time choice, activity/trip chain choices, activity duration choice, transit line and mode choices. A heuristic solution algorithm which combines the Hooke–Jeeves method and an iterative supply–demand equilibrium approach is developed to solve the proposed model. Two numerical examples are presented to illustrate the differences between the activity-based approach and the traditional trip-based method, together with comparison on the effects of optimal timetables with even and uneven headways. It is shown that the passenger travel scheduling pattern derived from the activity-based approach is significantly different from that obtained by the trip-based method, and that a demand-sensitive (with uneven headway) timetable is more efficient than an even-headway timetable.     

Incorporating Driver Behaviors in Network Design Problems: Challenges and Opportunities

The goal of a network design problem (NDP) is to make optimal decisions to achieve a certain objective such as minimizing total travel time or maximizing tolls collected in the network. A critical component to NDP is how travelers make their route choices. Researchers in transportation have adopted human decision theories to describe more accurate route choice behaviors. In this paper, we review the NDP with various route choice models: the random utility model (RUM), random regret-minimization (RRM) model, bounded rationality (BR), cumulative prospect theory (CPT), the fuzzy logic model (FLM) and dynamic learning models. Moreover, we identify challenges in applying behavioral route choice models to NDP and opportunities for future research.     

Continuity of the path delay operator for dynamic network loading with spillback

This paper establishes the continuity of the path delay operators for dynamic network loading (DNL) problems based on the Lighthill–Whitham–Richards model, which explicitly capture vehicle spillback. The DNL describes and predicts the spatial-temporal evolution of traffic flow and congestion on a network that is consistent with established route and departure time choices of travelers. The LWR-based DNL model is first formulated as a system of partial differential algebraic equations. We then investigate the continuous dependence of merge and diverge junction models with respect to their initial/boundary conditions, which leads to the continuity of the path delay operator through the wave-front tracking methodology and the generalized tangent vector technique. As part of our analysis leading up to the main continuity result, we also provide an estimation of the minimum network supply without resort to any numerical computation. In particular, it is shown that gridlock can never occur in a finite time horizon in the DNL model.     

Dynamic stochastic transit assignment with explicit seat allocation model

This paper proposes a stochastic dynamic transit assignment model with an explicit seat allocation process. The model is applicable to a general transit network. A seat allocation model is proposed to estimate the probability of a passenger waiting at a station or on-board to get a seat. The explicit seating model allows a better differentiation of in-vehicle discomfort experienced by sitting and standing passengers. The paper proposes simulation procedures for calculating the sitting probability of each type of passengers. A heuristic solution algorithm for finding an equilibrium solution of the proposed model is developed and tested. The numerical tests show significant influences of the seat allocation model on equilibrium departure time and route choices of passengers. The proposed model is also applied to evaluate the effects of an advanced public transport information system (APTIS) on travellers’ decision-making.     

Cognitive cost in route choice with real-time information: An exploratory analysis

Real-time traffic information is increasingly available to support route choice decisions by reducing the travel time uncertainty. However it is likely that a traveler cannot assess all available information on all alternative routes due to time constraints and limited cognitive capacity. This paper presents a model that is consistent with a general network topology and can potentially be estimated based on revealed preference data. It explicitly takes into account the information acquisition and the subsequent path choice. The decision to acquire information is assumed to be based on the cognitive cost involved in the search and the expected benefit defined as the expected increase in utility after the search. A latent class model is proposed, where the decision to search or not to search and the depth of the search are latent and only the final path choices are observed. A synthetic data set is used for the purpose of validation and ease of illustration. The data are generated from the postulated cognitive-cost model, and estimation results show that the true values of the parameters can be recovered with enough variability in the data. Two other models with simplifying assumptions of no information and full information are also estimated with the same set of data with significantly biased path choice utility parameters. Prediction results show that a smaller cognitive cost encourages information search on risky and fast routes and thus higher shares on those routes. As a result, the expected average travel time decreases and the variability increases. The no-information and full-information models are extreme cases of the more general cognitive-cost model in some cases, but not generally so, and thus the increasing ease of information acquisition does not necessarily warrant a full-information model.     

Validating the results of a route choice simulator

This paper describes the validation of a route choice simulator known as VLADIMIR (Variable Legend Assessment Device for Interactive Measurement of Individual Route choice). VLADIMIR is an interactive computer-based tool designed to study drivers’ route choice behaviour. It has been extensively used to obtain data on route choice in the presence of information sources such as Variable Message Signs or In-Car Navigation devices. The simulator uses a sequence of digitized photographs to portray a real network with junctions, links, landmarks and road signs. Subject drivers are invited to make journeys between specified origins and destinations under a range of travel scenarios, during which the simulator automatically records their route choices. This paper describes validation experiments carried out during the period Summer 1994 to Autumn 1995 and reports on the results obtained. Each experiment involved a comparison of routes selected in real life with those driven under simulated conditions in VLADIMIR. The analysis included investigation of the subjects’ own assessment of the realism of the VLADIMIR routes they had chosen, a comparison of models based on the real life routes with models based on VLADIMIR routes, and a statistical comparison of the two sets of routes. After an extensive series of data collection exercises and analyses, we have concluded that a well designed simulator is able to replicate real life route choices with a very high degree of detail and accuracy. Not only was VLADIMIR able to precisely replicate the route choices of drivers who were familiar with the network but it also appears capable of representing the kind of errors made and route choice strategies adopted by less familiar drivers. Furthermore, evidence is presented to suggest that it can accurately replicate route choice responses to roadside VMS information.     

Hierarchical ordering of nests in a joint mode and destination choice model

This paper seeks to explore the relationship between mode and destination choice in an integrated nested choice model. A fundamental argument can be made that in certain circumstances, the ordering of choices should be reversed from the usual sequence of destination choice preceding mode choice. This results in a travel demand model where travelers are more likely to change destinations than to change transportation modes. For small and medium size urban areas, particularly in the United States, with less well developed public transit systems that draw few choice riders, this assumption makes much more sense than the traditional modeling assumptions. The models used in the new travel modeling system developed for Knoxville, Tennessee utilize this reversed ordering, with generally good results, which required no external tinkering in the logsum parameters.     

Capturing correlation with a mixed recursive logit model for activity-travel scheduling

Representing activity-travel scheduling decisions as path choices in a time–space network is an emerging approach in the literature. In this paper, we model choices of activity, location, timing and transport mode using such an approach and seek to estimate utility parameters of recursive logit models. Relaxing the independence from irrelevant alternatives (IIA) property of the logit model in this setting raises a number of challenges. First, overlap in the network may not fully characterize perceptual correlation between paths, due to their interpretation as activity schedules. Second, the large number of states that are needed to represent all possible locations, times and activity combinations imposes major computational challenges to estimate the model. We combine recent methodological developments to build on previous work by Blom Västberg et al. (2016) and allow to model complex and realistic correlation patterns in this type of network. We use sampled choices sets in order to estimate a mixed recursive logit model in reasonable time for large-scale, dense time-space networks. Importantly, the model retains the advantage of fast predictions without sampling choice sets. In addition to estimation results, we present an extensive empirical analysis which highlights the different substitution patterns when the IIA property is relaxed, and a cross-validation study which confirms improved out-of-sample fit.