A reliability‐based traffic assignment model for multi‐modal transport network under demand uncertainty

In densely populated and congested urban areas, the travel times in congested multi‐modal transport networks are generally varied and stochastic in practice. These stochastic travel times may be raised from day‐to‐day demand fluctuations and would affect travelers' route and mode choice behaviors according to their different expectations of on‐time arrival. In view of these, this paper presents a reliability‐based user equilibrium traffic assignment model for congested multi‐modal transport networks under demand uncertainty. The stochastic bus frequency due to the unstable travel time of bus route is explicitly considered. By the proposed model, travelers' route and mode choice behaviors are intensively explored. In addition, a stochastic state‐augmented multi‐modal transport network is adopted in this paper to effectively model probable transfers and non‐linear fare structures. A numerical example is given to illustrate the merits of the proposed model. Copyright © 2012 John Wiley & Sons, Ltd.     

The existence, uniqueness and computation of an arc-based dynamic network user equilibrium formulation

In this paper, a dynamic user equilibrium traffic assignment model with simultaneous departure time/route choices and elastic demands is formulated as an arc-based nonlinear complementarity problem on congested traffic networks. The four objectives of this paper are (1) to develop an arc-based formulation which obviates the use of path-specific variables, (2) to establish existence of a dynamic user equilibrium solution to the model using Brouwer's fixed-point theorem, (3) to show that the vectors of total arc inflows and associated minimum unit travel costs are unique by imposing strict monotonicity conditions on the arc travel cost and demand functions along with a smoothness condition on the equilibria, and (4) to develop a heuristic algorithm that requires neither a path enumeration nor a storage of path-specific flow and cost information. Computational results are presented for a simple test network with 4 arcs, 3 nodes, and 2 origin–destination pairs over the time interval of 120 periods.     

New technology and the modeling of risk-taking behavior in congested road networks

Intelligent transport systems provide various means to improve traffic congestion in road networks. Evaluation of the benefits of these improvements requires consideration of commuters’ response to reliability and/or uncertainty of travel time under various circumstances. Various disruptions cause recurrent or non-recurrent congestion on road networks, which make road travel times intrinsically fluctuating and unpredictable. Confronted with such uncertain traffic conditions, commuters are known to develop some simple decision-making process to adjust their travel choices. This paper represents the decision-making process involved in departure-time and route choices as risk-taking behavior under uncertainty. An expected travel disutility function associated with commuters’ departure-time and route choices is formulated with taking into account the travel delay (due the recurrent congestion), the uncertainty of travel times (due to incident-induced congestion) and the consequent early or late arrival penalty. Commuters are assumed to make decision on the departure-time and route choices on the basis of the minimal expected travel disutility. Thus the network will achieve a simultaneous route and departure-time user equilibrium, in which no commuter can decrease his or her expected disutility by unilaterally changing the route or departure-time. The equilibrium is further formulated as an equivalent nonlinear complementarity problem and is then converted into an unconstrained minimization problem with the use of a gap function suggested recently. Two algorithms based on the Nelder–Mead multidimensional simplex method and the heuristic route/time-swapping approach, are adapted to solve the problem. Finally, numerical example is given to illustrate the application of the proposed model and algorithms.     

A specialized equilibrium assignment algorithm for air quality modeling

A multiple user class equilibrium assignment algorithm is formulated to determine vehicle trips and the vehicle miles of travel (VMT) in various operating modes on highway links. A heuristic solution algorithm based on the Frank–Wolfe decomposition of the equilibrium assignment problem is presented. The treatment of intrazonal trips, which are very important for emission studies is also discussed. The solution algorithm is implemented in a traffic assignment program for emission studies, referred to as TAPES. The use of the algorithm is demonstrated through a TAPES model case study on a Charlotte, NC network database for 1990 AM peak period. The operating mode mix of VMT in cold transient, hot transient and hot stabilized modes, also known as the mix of cold-starts, hot-starts and stabilized mode trips, is derived on a link by link basis. The results are aggregated by facility type and the location of link segments. It is observed that the operating mode fractions in transient and stabilized modes could vary widely across different facility types geographic locations. The aggregated operating mode fractions derived from the assignment analysis indicates that a lesser proportion of VMT operates in cold and hot transient modes when compared to the operating mode mix derived from the Federal Test Procedure (FTP).     

A path-based flow formulation for the traffic assignment problem

In order to improve cooperation between traffic management and travelers, traffic assignment is the key component to achieve the objectives of both traffic management and route choice decisions for travelers. Traffic assignment can be classified into two models based on the behavioral assumptions governing route choices: User Equilibrium (UE) and System Optimum (SO) traffic assignment. According to UE and SO traffic assignment, travelers usually compete to choose the least cost routes to minimize their own travel costs, while SO traffic assignment requires travelers to work cooperatively to minimize overall cost in the road network. Thus, the paradox of benefits between UE and SO indicates that both are not practical. Thus, a solution technique needs to be proposed to balance UE and SO models, which can compromise both sides and give more feasible traffic assignments. In this paper, Stackelberg game theory is introduced to the traffic assignment problem, which can achieve the trade-off process between traffic management and travelers. Since traditional traffic assignments have low convergence rates, the gradient projection algorithm is proposed to improve efficiency.     

Route Choice Models Used in the Stochastic User Equilibrium Problem: A Review

Several route choice models are reviewed in the context of the stochastic user equilibrium problem. The traffic assignment problem has been extensively studied in the literature. Several models were developed focusing mainly on the solution of the link flow pattern for congested urban areas. The behavioural assumption governing route choice, which is the essential part of any traffic assignment model, received relatively much less attention. The core of any traffic assignment method is the route choice model. In the wellknown deterministic case, a simple choice model is assumed in which drivers choose their best route. The assumption of perfect knowledge of travel costs has been long considered inadequate to explain travel behaviour. Consequently, probabilistic route choice models were developed in which drivers were assumed to minimize their perceived costs given a set of routes. The objective of the paper is to review the different route choice models used to solve the traffic assignment problem. Focus is on the different model structures. The paper connects some of the route choice models proposed long ago, such as the logit and probit models, with recently developed models. It discusses several extensions to the simple logit model, as well as the choice set generation problem and the incorporation of the models in the assignment problem.     

Should subsidies to urban passenger transport be increased? A spatial CGE analysis for a German metropolitan area

In many countries passenger transport is significantly subsidized in a variety of ways for various reasons. The objective of this paper is to examine efficiency, distributional, environmental (CO₂ emissions) and spatial effects of increasing different kinds of passenger transport subsidies discriminating between household types, travel purposes and travel modes. The effects are calculated by applying a numerical spatial general equilibrium approach calibrated to an average German metropolitan area. In extension to most studies focusing on only one kind of subsidy, we compare the effects of different transport subsidies within the same unified framework that allows to account for two features not yet considered simultaneously in studies on transport subsidies: endogenous labor supply and location decisions. Furthermore, congestion, travel mode choice, travel related CO₂ emissions and institutional details regarding the tax system in Germany are taken into account. The results suggest that optimal subsidy levels are either small or even zero. While subsidizing public transport is welfare enhancing, subsidies to urban road traffic reduce aggregate urban welfare. Concerning the latter it is shown that making investments in urban road infrastructure capacity or reducing gasoline taxes may even be harmful to residents using predominantly automobile. In contrast, pure commuting subsidies hardly affect aggregate urban welfare, but distributional effects are substantial. All policies cause suburbanization of city residents and (except for subsidizing public transport) contribute to urban sprawl by raising the spatial imbalance of residences and jobs but the effect is relatively small. In addition, the policies induce a very differentiated pattern regarding distributional effects, benefits of landowners and environmental effects.     

Network equilibrium for congested multi‐mode networks with elastic demand

This paper proposes an elastic demand network equilibrium model for networks with transit and walking modes. In Hong Kong, the multi‐mode transit system services over 90% of the total journeys and the demand on it is continuously increasing. Transit and walking modes are related to each other as transit passengers have to walk to and from transit stops. In this paper, the multi‐mode elastic‐demand network equilibrium problem is formulated as a variational inequality problem where the combined mode and route choices are modeled in a hierarchical logit structures and the total travel demand for each origin‐destination pair is explicitly given by an elastic demand function. In addition, the capacity constraint for transit vehicles and the effects of bi‐directional flows on walkways are considered in the proposed model. All these congestion effects are taken into account for modeling the travel choices. A solution algorithm is developed to solve the multi‐mode elastic‐demand network equilibrium model. It is based on a Block Gauss‐Seidel decomposition approach coupled with the method of successive averages. A numerical example is used to illustrate the application of the proposed model and solution algorithm.     

Optimization method of alternate traffic restriction scheme based on elastic demand and mode choice behavior

As a countermeasure to urban traffic congestion, alternate traffic restriction (ATR) involves a certain proportion of automobiles being prohibited from entering pre-determined ATR districts during specific time periods. The present study introduces an optimization method for ATR schemes in terms of both their restriction districts and the proportion of restricted automobiles. As a Stackelberg game between traffic policy makers and road users, the ATR scheme optimization problem is established using a bi-level programming model, with the upper-level examining an ATR scheme aimed at consumers’ surplus maximization under the condition of overload flow minimization, and the lower-level synthetically optimizing elastic demand, mode choice (private car, public transit and park-and-ride) and multi-class user equilibrium assignment. A genetic algorithm based on the graph theory is also proposed to solve the bi-level programming model with a gradient project algorithm for solving the lower-level model. To our knowledge, this study represents the first attempt to theoretically optimize an ATR scheme using a systematic approach with mathematical model specification.     

Transportation serviceability analysis for metropolitan commuting corridors based on modal choice modeling

Major commuting corridors in metropolitan areas generally comprise multiple transportation modes for commuters, such as transit (subways or buses), private vehicles, or park-and-ride combinations. During the morning peak hour, the commuters would choose one of the available transportation modes to travel through the corridors from rural/suburban living areas to urban working areas. This paper introduces a concept of transportation serviceability to evaluate a transportation mode’s service status in a specific link, route, road, or network during a certain period. The serviceability can be measured by the possibility that travelers choose a specific type of transportation service at a certain travel cost. The commuters’ modal-choice possibilities are calculated using a stochastic equilibrium model based on general travel cost. The modeling results illustrate how transportation serviceability is influenced by background traffic flow in a corridor, value of comfort for railway mode, and parking fee distribution.     

On the distribution of urban road space for multimodal congested networks

Transport systems in real cities are complex with many modes of transport sharing and competing for limited road space. This work intends to understand how space distributions for modes and interactions among modes affect network traffic performance. While the connection between performance of transport systems and general land allocation is the subject of extensive research, space allocation for interacting modes of transport is an open research question. Quantifying the impact of road space distribution on the performance of a congested multimodal transport system with a dynamic aggregated model remains a challenge. In this paper, a multimodal macroscopic fundamental diagram (MFD) is developed to represent the traffic dynamics of a multimodal transport system. Optimization is performed with the objective of minimizing the total passenger hours traveled (PHT) to serve the total demand by redistributing road space among modes. Pricing strategies are also investigated to provide a higher demand shift to more efficient modes. We find by an application to a bi-modal two-region city that (i) the proposed model captures the operational characteristics of each mode, and (ii) optimal dynamic space distribution strategies can be developed. In practice, the approach can serve as a physical dynamic model to inform space distribution strategies for policy makers with different goals of mobility.     

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.     

Comparative analysis of transit assignment: evidence from urban railway system in the Tokyo Metropolitan Area

This paper empirically compares the performance of six traffic assignment methods using the same empirical dataset of route choice. Multinomial logit (MNL), structured multinomial probit (SMNP), user equilibrium (UE), logit-based stochastic user equilibrium (SUE), probit-based SUE, and all-or-nothing (AON) assignment methods are applied to the comparative analysis. The investigated methods include those with three types of error components in their cost functions and two types of flow dependencies. Four methods of generating the route choice set are also compared for use as stochastic traffic assignment methods. The revealed preference data of urban rail route choice in the Tokyo Metropolitan Area are used for the case analysis. The empirical case analysis shows that probit-based SUE provides the best accuracy but requires the longest computation time. It also shows that the heuristics used to generate the choice set influence the method’s accuracy, while the incorporation of route commonality and in-vehicle congestion significantly improves its accuracy. Finally, the implications for practical rail planning are discussed on the basis of the analysis results.     

Improvement of the volume-delay function by incorporating the impact of trucks on traffic flow

In current transportation modelling, travel time is the most important factor in decisions regarding transport modes, destinations and routes. The calculation of travel time is deployed by volume-delay functions (VDFs), a sub-model of route assignment procedure, using the correlation between increasing numbers of vehicles on a road and the road's restrictive capacity. By investigating existing VDFs, a clear gap is seen, demonstrating that current functions are not suited to reflect the empirically known large impact of trucks on passenger car travel times. This issue becomes crucial when transport models are used to reflect future scenarios where goods transportation is expected to increase greatly, and when transport models combine passenger and commercial traffic. This paper presents a new VDF which successfully includes trucks’ impact on traffic flow in the case of Germany and, with slight deviations, for North America. The function is developed using ideal-type data for German motorways. The differences between German and US data and their implications for VDFs are also discussed.     

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 methodology to control urban traffic noise under the constraint of environmental capacity: A case study of a double-decision optimization model

This paper presents a novel methodology to control urban traffic noise under the constraint of environmental capacity. Considering the upper limits of noise control zones as the major bottleneck to control the maximum traffic flow is a new idea. The urban road network traffic is the mutual or joint behavior of public self-selection and management decisions, so is a typical double decision optimization problem.The proposed methodology incorporates theoretically model specifications. Traffic noise calculation model and traffic assignment model for O–D matrix are integrated based on bi-level programming method which follows an iterated process to obtain the optimal solution. The upper level resolves the question of how to sustain the maximum traffic flow with noise capacity threshold in a feasible road network. The user equilibrium method is adopted in the lower layer to resolve the O–D traffic assignment.The methodology has been applied to study area of QingDao, China. In this illustrative case, the noise pollution level values of optimal solution could satisfy the urban environmental noise capacity constraints. Moreover, the optimal solution was intelligently adjusted rather than simply reducing the value below a certain threshold. The results indicate that the proposed methodology is feasible and effective, and it can provide a reference for a sustainable development and noise control management of the urban traffic.     

Maximum car ownership under constraints of road capacity and parking space

This paper presents a model for determining the maximum number of cars by zones in view of the capacity of the road network and the number of parking spaces available. In other words, the proposed model is to examine whether existing road network and parking supply is capable of accommodating future zonal car ownership growth (or the reserve capacity in each zone); i.e. the potential maximum zonal car ownership growth that generates the road traffic within the network capacity and parking space constraints. In the proposed model, the vehicular trip production and attraction are dependent on the car ownership, available parking spaces and the accessibility measures by traffic zones. The model is formulated as a bi-level programming problem. The lower-level problem is an equilibrium trip distribution/assignment problem, while the upper-level problem is to maximize the sum of zonal car ownership by considering travellers’ route and destination choice behaviour and satisfying the network capacity and parking space constraints. A sensitivity analysis based heuristic algorithm is developed to solve the proposed bi-level car ownership problem and is illustrated with a numerical example.     

A systematic analysis of multimodal transport systems with road space distribution and responsive bus service

A smart design of transport systems involves efficient use and allocation of the limited urban road capacity in the multimodal environment. This paper intends to understand the system-wide effect of dividing the road space to the private and public transport modes and how the public transport service provider responds to the space changes. To this end, the bimodal dynamic user equilibrium is formulated for separated road space. The Macroscopic Fundamental Diagram (MFD) model is employed to depict the dynamics of the automobile traffic for its state-dependent feature, its inclusion of hypercongestion, and its advantage of capturing network topology. The delay of a bus trip depends on the running speed which is in turn affected by bus lane capacity and ridership. Within the proposed bimodal framework, the steady-state equilibrium traffic characteristics and the optimal bus fare and service frequency are analytically derived. The counter-intuitive properties of traffic condition, modal split, and behavior of bus operator in the hypercongestion are identified. To understand the interaction between the transport authority (for system benefit maximization) and the bus operator (for its own benefit maximization), we examine how the bus operator responds to space changes and how the system benefit is influenced with the road space allocation. With responsive bus service, the condition, under which expanding bus lane capacity is beneficial to the system as a whole, has been analytically established. Then the model is applied to the dynamic framework where the space allocation changes with varying demand and demand-responsive bus service. We compare the optimal bus services under different economic objectives, evaluate the system performance of the bimodal network, and explore the dynamic space allocation strategy for the sake of social welfare maximization.     

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.     

Tollroads are only part of the overall trip: the error of our ways in past willingness to pay studies

With rare exception, actual tollroad traffic in many countries has failed to reproduce forecast traffic levels, regardless of whether the assessment is made after an initial year of operation or as long as 10 years after opening. Pundits have offered many reasons for this divergence, including optimism bias, strategic misrepresentation, the promise to equity investors of early returns on investment, errors in land use forecasts, and specific assumptions underlying the traffic assignment models used to develop traffic forecasts. One such assumption is the selection of a behaviourally meaningful value of travel time savings (VTTS) for use in a generalised cost or generalised time user benefit expression that is the main behavioural feature of the traffic assignment (route choice) model. Numerous empirical studies using stated choice experiments have designed choice sets of alternatives as if users choose a tolled route or a free route under the (implied) assumption that the tolled route is tolled for the entire trip. Reality is often very different, with a high incidence of use of a non-tolled road leading into and connecting out of a tolled link. In this paper we recognise this feature of route choice and redesign the stated choice experiment to account for it. Furthermore, this study is a follow up to a previous study undertaken before a new toll road was in place, and it benefits from real exposure to the new toll road. We find that the VTTS is noticeably reduced, and if the VTTS is a significant contributing influence on errors on traffic forecasts, then the lower estimates make sense behaviourally.