Revisiting Jiang’s dynamic continuum model for urban cities

Jiang et al. (Jiang, Y.Q., Wong, S.C., Ho, H.W., Zhang, P., Liu, R.X., Sumalee, A., 2011. A dynamic traffic assignment model for a continuum transportation system. Transportation Research Part B 45 (2), 343–363) proposed a predictive continuum dynamic user-optimaDUO-l to investigate the dynamic characteristics of traffic flow and the corresponding route-choice behavior of travelers. Their modeled region is a dense urban city that is arbitrary in shape and has a single central business district (CBD). However, we argue that the model is not well posed due to an inconsistency in the route-choice strategy under certain conditions. To overcome this inconsistency, we revisit the PDUO-C problem, and construct an improved path-choice strategy. The improved model consists of a conservation law to govern the density, in which the flow direction is determined by the improved path-choice strategy, and a Hamilton–Jacobi equation to compute the total travel cost. The simultaneous satisfaction of both equations can be treated as a fixed-point problem. A self-adaptive method of successive averages (MSA) is proposed to solve this fixed-point problem. This method can automatically determine the optimal MSA step size using the least squares approach. Numerical examples are used to demonstrate the effectiveness of the model and the solution algorithm.     

Dynamic system‐optimal traffic assignment for a city using the continuum modeling approach

This paper presents a continuum dynamic traffic assignment model for a city in which the total cost of the traffic system is minimized: the travelers in the system are organized to choose the route to their destinations that minimizes the total cost of the system. Combined with the objective function, which defines the total cost and constraints such as certain physical and boundary conditions, a continuum model can be formulated as an optimization scheme with a feasible region in the function space. To obtain an admissible locally optimal solution to this problem, we first reformulate the optimization in discrete form and then introduce a heuristic method to solve it. This method converges rapidly with attractive computational cost. Numerical examples are used to demonstrate the effectiveness of the method. Copyright © 2013 John Wiley & Sons, Ltd.     

A predictive dynamic traffic assignment model in congested capacity-constrained road networks

In this paper, a predictive dynamic traffic assignment model in congested capacity-constrained road networks is formulated. A traffic simulator is developed to incrementally load the traffic demand onto the network, and updates the traffic conditions dynamically. A time-dependent shortest path algorithm is also given to determine the paths with minimum actual travel time from an origin to all the destinations. The traffic simulator and time-dependent shortest path algorithm are employed in a method of successive averages to solve the dynamic equilibrium solution of the problem. A numerical example is given to illustrate the effectiveness of the proposed method.     

Multi-commodity traffic assignment by continuum approximation of network flow with variable demand

Consider a city with several highly compact central business districts (CBD), and the commuters’ destinations from each of them are dispersed over the whole city. Since at a particular location inside the city the traffic movements from different CBDs share the same space and do not cancel out each other as in conventional fluid flow problems albeit travelling in different directions, the traffic flows from a CBD to the destinations over the city are considered as one commodity. The interaction of the traffic flows among different commodities is governed by a cost–flow relationship. The case of variable demand is considered. The primal formulation of the continuum equilibrium model is given and proved to satisfy the user optimal conditions, and the dual formulation of the problem and its complementary conditions are also discussed. A finite element method is then employed to solve the continuum problem. A numerical example is given to illustrate the effectiveness of the proposed method.     

Decision tree method for modeling travel mode switching in a dynamic behavioral process

As road congestion is exacerbated in most metropolitan areas, many transportation policies and planning strategies try to nudge travelers to switch to other more sustainable modes of transportation. In order to better analyze these strategies, there is a need to accurately model travelers’ mode-switching behavior. In this paper, a popular artificial intelligence approach, the decision tree (DT), is used to explore the underlying rules of travelers’ switching decisions between two modes under a proposed framework of dynamic mode searching and switching. An effective and practical method for a mode-switching DT induction is proposed. A loss matrix is introduced to handle class imbalance issues. Important factors and their relative importance are analyzed through information gains and feature selections. Household Travel Survey data are used to implement and validate the proposed DT induction method. Through comparison with logit models, the improved prediction ability of the DT models is demonstrated.     

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.     

Roads in transition: Integrated modeling of a manufacturer-traveler-infrastructure system in a mixed autonomous/human driving environment

This paper develops an integrated model to characterize the market penetration of autonomous vehicles (AVs) in urban transportation networks. The model explicitly accounts for the interplay among the AV manufacturer, travelers with heterogeneous values of travel time (VOTT), and road infrastructure capacity. By making in-vehicle time use more leisurely or productive, AVs reduce travelers’ VOTT. In addition, AVs can move closer together than human-driven vehicles because of shorter safe reaction time, which leads to increased road capacity. On the other hand, the use of AV technologies means added manufacturing cost and higher price. Thus, traveler adoption of AVs will trade VOTT savings with additional out-of-pocket cost. The model is structured as a leader (AV manufacturer)-follower (traveler) game. Given the cost of producing AVs, the AV manufacturer sets AV price to maximize profit while anticipating AV market penetration. Given an AV price, the vehicle and routing choice of heterogeneous travelers are modeled by combining a multinomial logit model with multi-modal multi-class user equilibrium (UE). The overall problem is formulated as a mathematical program with complementarity constraints (MPCC), which is challenging to solve. We propose a solution approach based on piecewise linearization of the MPCC as a mixed-integer linear program (MILP) and solving the MILP to global optimality. Non-uniform distribution of breakpoints that delimit piecewise intervals and feasibility-based domain reduction are further employed to reduce the approximation error brought by linearization. The model is implemented in a simplified Singapore network with extensive sensitivity analyses and the Sioux Falls network. Computational results demonstrate the effectiveness and efficiency of the solution approach and yield valuable insights about transportation system performance in a mixed autonomous/human driving environment.     

A bi-level programming for bus lane network design

This paper proposes a bi-level programming model to solve the design problem for bus lane distribution in multi-modal transport networks. The upper level model aims at minimizing the average travel time of travelers, as well as minimizing the difference of passengers’ comfort among all the bus lines by optimizing bus frequencies. The lower level model is a multi-modal transport network equilibrium model for the joint modal split/traffic assignment problem. The column generation algorithm, the branch-and-bound algorithm and the method of successive averages are comprehensively applied in this paper for the solution of the bi-level model. A simple numerical test and an empirical test based on Dalian economic zone are employed to validate the proposed model. The results show that the bi-level model performs well with regard to the objective of reducing travel time costs for all travelers and balancing transit service level among all bus lines.     

Sequential optimization approach for the multi‐class user equilibrium problem in a continuous transportation system

We consider a city region with several facilities that are competing for customers of different classes. Within the city region, the road network is dense, and can be represented as a continuum. Customers are continuously distributed over space, and they choose a facility by considering both the transportation cost and market externalities. More importantly, the model takes into account the different transportation cost functions and market externalities to which different customer classes are subjected. A logit‐type distribution of demand is specified to model the decision‐making process of users' facility choice. We develop a sequential optimization approach to decompose the complex multi‐class and multi‐facility problem into a series of smaller single‐class and single‐facility sub‐problems. An efficient solution algorithm is then proposed to solve the resultant problem. A numerical example is given to demonstrate the effectiveness and potential applicability of the proposed methodology.     

Evaluation of exclusive bus lanes in a bi-modal degradable road network

In this paper, we proposed an evaluation method of exclusive bus lanes (EBLs) in a bi-modal degradable road network with car and bus transit modes. Link travel time with and without EBLs for two modes is analyzed with link stochastic degradation. Furthermore, route general travel costs are formulated with the uncertainty of link travel time for both modes and the uncertainty of waiting time at a bus stop and in-vehicle congestion costs for the bus mode. The uncertainty of bus waiting time is considered to be relevant to the degradation of the front links of the bus line. A bi-modal user equilibrium model incorporating travelers’ risk adverse behavior is proposed for evaluating EBLs. Finally, two numerical examples are used to illustrate how the road degradation level, travelers’ risk aversion level and the front link’s correlation level with the uncertainty of the bus waiting time affect the results of the user equilibrium model with and without EBLs and how the road degradation level affects the optimal EBLs setting scheme. A paradox of EBLs setting is also illustrated where adding one exclusive bus lane may decrease share of bus.     

Bayesian network-based formulation and analysis for toll road utilization supported by traffic information provision

Congestion pricing has been proposed and investigated as an effective means of optimizing traffic assignment, alleviating congestion, and enhancing traffic operation efficiencies. Meanwhile, advanced traffic information dissemination systems, such as Advanced Traveler Information System (ATIS), have been developed and deployed to provide real-time, accurate, and complete network-wide traffic information to facilitate travelers’ trip plans and routing selections. Recent advances in ATIS technologies, especially telecommunication technology, allow dynamic, personalized, and multimodal traffic information to be disseminated and impact travelers’ choices of departure times, alternative routes, and travel modes in the context of congestion pricing. However, few studies were conducted to determine the impact of traffic information dissemination on toll road utilizations. In this study, the effects of the provisions of traffic information on toll road usage are investigated and analyzed based on a stated preference survey conducted in Texas. A Bayesian Network (BN)-based approach is developed to discover travelers’ opinions and preferences for toll road utilization supported by network-wide traffic information provisions. The probabilistic interdependencies among various attributes, including routing choice, departure time, traffic information dissemination mode, content, coverage, commuter demographic information, and travel patterns, are identified and their impacts on toll road usage are quantified. The results indicate that the BN model performs reasonably well in travelers’ preference classifications for toll road utilization and knowledge extraction. The BN Most Probable Explanation (MPE) measurement, probability inference and variable influence analysis results illustrate travelers using highway advisory radio and internet as their primary mode of receiving traffic information are more likely to comply with routing recommendations and use toll roads. Traffic information regarding congested roads, road hazard warnings, and accident locations is of great interest to travelers, who tend to acquire such information and use toll roads more frequently. Travel time formation for home-based trips can considerably enhance travelers’ preferences for toll road usage. Female travelers tend to seek traffic information and utilize toll roads more frequently. As expected, the information provided at both pre-trip and en-route stages can positively influence travelers’ preferences for toll road usage. The proposed methodology and research findings advance our previous study and provide insight into travelers’ behavioral tendencies concerning toll road utilization in support of traffic information dissemination.     

A day-to-day and within-day dynamic stochastic assignment model

In this article a doubly dynamis assignment model for a general network is presented. It is assumed that users' choices are based on information about travel times and generalized transportation costs occurred in a finite number of previous days and, possibly, in previous periods of the same day. The information may be supplied and managed by an informative system. In this context, path and link flows vary for different subperiods of the same day (within-day dynamics) and for different days (day-to-day dynamics). The proposed model follows a nonequilibrium approach in which both within-day and day-to-day flow fluctuations are modelled as a stochastic process. A model of dynamic network loading for computing within-day variable arc flows from path flows is also presented. The model deals explicitly with queuing at oversaturated intersections and can be formulated as a fixed point problem. A solution scheme for the doubly dynamic assignment model is presented embedding a solution algorithm for the fixed-point problem.     

Stochastic Poisson game for an online decentralized and coordinated parking mechanism

This paper proposes a decentralized and coordinated online parking mechanism (DCPM), which seeks to reduce parking congestion at multiple parking facilities in a central business district (CBD) through guiding the parking decisions of a parking coordination group. To establish this DCPM, this study develops a stochastic Poisson game to model the competitions among parking vehicles en route at multiple parking facilities. The equilibrium condition for the proposed stochastic Poisson game is formulated through involving travelers’ parking choice behavior described by multinomial logit model. Furthermore, we prove that the stochastic Poisson game is a potential game with a unique equilibrium. A simultaneously updating distributed algorithm is developed to search the equilibrium solution of the DCPM. Its convergence is proved by both mathematical analysis and numerical experiments. The numerical experiments are conducted to test the efficiency of the DCPM, based on a real-world CBD covering Guicheng Community, Nanhai District at Foshan in China. The performance of the DCPM is compared to three greedy strategies following the nearest first, cheapest first, and least cruise first policies, respectively. The experimental results demonstrate that the DCPM significantly reduces cruise vehicles and average cruise distance per vehicle from all other three greedy strategies; the least cruise first strategy, which takes advantage of the real-time open spots information at parking facilities, performs better than the nearest first and the cheapest first strategies without the access to real-time information. The DCPM can further improve the benefit of the real-time information. Additionally, in terms of walking distance and parking cost, the DCPM provide a trade-off solution between the nearest first and the cheapest first strategies.     

Enhanced traffic information dissemination to facilitate toll road utilization: a nested logit model of a stated preference survey in Texas

This paper investigates the effects of the provision of traffic information on toll road usage based on a stated preference survey conducted in central Texas. Although many researchers have studied congestion pricing and traffic information dissemination extensively, most of them focused on the effects that these instruments individually produce on transportation system performance. Few studies have been conducted to elaborate on the impacts of traffic information dissemination on toll road utilization. In this study, 716 individuals completed a survey to measure representative public opinions and preferences for toll road usage in support of various traffic information dissemination classified by different modes, contents, and timeliness categories. A nested logit model was developed and estimated to identify the significant attributes of traffic information dissemination, traveler commuting patterns, routing behavior, and demographic characteristics, and analyze their impacts on toll road utilization. The results revealed that the travelers using dynamic message sign systems as their primary mode of receiving traffic information are more likely to choose toll roads. The potential toll road users also indicated their desire to obtain traffic information via internet. Information regarding accident locations, road hazard warnings, and congested roads is frequently sought by travelers. Furthermore, high-quality congested road information dissemination can significantly enhance travelers’ preferences of toll road usage. Specifically the study found that travelers anticipated an average travel time saving of about 11.3 min from better information; this is about 30 % of travelers’ average one-way commuting time. The mean value of the time savings was found to be about $11.82 per hour, close to ½ of the average Austin wage rate. The model specifications and result analyses provide in-depth insights in interpreting travelers’ behavioral tendencies of toll road utilization in support of traffic information. The results are also helpful to shape and develop future transportation toll system and transportation policy.     

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.     

Modeling intermodal equilibrium for bimodal transportation system design problems in a linear monocentric city

This paper investigates the intermodal equilibrium, road toll pricing, and bus system design issues in a congested highway corridor with two alternative modes - auto and bus - which share the same roadway along this corridor. On the basis of an in-depth analysis of the demand and supply sides of the bimodal transportation system, the mode choice equilibrium of travelers along the continuum corridor is first presented and formulated as an equivalent variational inequality problem. The solution properties of the bimodal continuum equilibrium formulation are analytically explored. Two models, which account for different infrastructure/system regulatory regimes (public and private), are then proposed. In the public regulatory model, the road toll location and charge level are simultaneously optimized together with the bus service fare and frequency. In the private regulatory model, the fare and frequency of bus services, which are operated by a profit-driven private operator, are optimized for exogenously given toll pricing schemes. Finally, an illustrative example is given to demonstrate the application of the proposed models. Sensitivity analysis of residential/household distribution along the corridor is carried out together with a comparison of four different toll pricing schemes (no toll, first best, distance based, and location based). Insightful findings are reported on the interrelationships among modal competition, market regulatory regimes, toll pricing schemes, and urban configurations as well as their implications in practice.     

Continuous price and flow dynamics of tradable mobility credits

This study examines the price and flow dynamics under a tradable credit scheme, when the credits can be traded in a free market. A continuous dynamic model in a finite time horizon is proposed to describe the travelers’ learning behavior and the evolution of network flows and credit price, and then the existence and uniqueness of the equilibria are established. The conditions for stability and convergence of the dynamic system as the time horizon extends to infinity and the impact of limited implementation time horizon on the system behavior are investigated.     

Model and a solution algorithm for the dynamic resource allocation problem for large-scale transportation network evacuation

Allocating movable resources dynamically enables evacuation management agencies to improve evacuation system performance in both the spatial and temporal dimensions. This study proposes a mixed integer linear program (MILP) model to address the dynamic resource allocation problem for transportation evacuation planning on large-scale networks. The proposed model is built on the earliest arrival flow formulation that significantly reduces problem size. A set of binary variables, specifically, the beginning and the ending time of resource allocation at a location, enable a strong formulation with tight constraints. A solution algorithm is developed to solve for an optimal solution on large-scale network applications by adopting Benders decomposition. In this algorithm, the MILP model is decomposed into two sub-problems. The first sub-problem, called the restricted master problem, identifies a feasible dynamic resource allocation plan. The second sub-problem, called the auxiliary problem, models dynamic traffic assignment in the evacuation network given a resource allocation plan. A numerical study is performed on the Dallas–Fort Worth network. The results show that the Benders decomposition algorithm can solve an optimal solution efficiently on a large-scale network.     

A combined activity/travel choice model for congested road networks with queues

This paper presents a combined activity/travel choice model and proposes a flow-swapping method for obtaining the model's dynamic user equilibrium solution on congested road network with queues. The activities of individuals are characterized by given temporal utility profiles. Three typical activities, which can be observed in morning peak period, namely at-home activity, non-work activity on the way from home to workplace and work-purpose activity, will be considered in the model. The former two activities always occur together with the third obligatory activity. These three activities constitute typical activity/travel patterns in time-space dimension. At the equilibrium, each combined activity/travel pattern, in terms of chosen location/route/departure time, should have identical generalized disutility (or utility) experienced actually. This equilibrium can be expressed as a discrete-time, finite-dimensional variational inequality formulation and then converted to an equivalent "zero-extreme value" minimization problem. An algorithm, which iteratively adjusts the non-work activity location, corresponding route and departure time choices to reach an extreme point of the minimization problem, is proposed. A numerical example with a capacity constrained network is used to illustrate the performance of the proposed model and solution algorithm.