Bounding the Inefficiency of the Multiclass, Multicriteria C-Logit Stochastic User Equilibrium in a Transportation Network

We derive the exact inefficiency upper bounds of the multiclass C-Logit stochastic user equilibrium (CL-SUE) in a transportation network. All travelers are classified on the basis of different values of time (VOT) into M classes. The multiclass CL-SUE model gives a more realistic path choice probability in comparison with the logit-based stochastic user equilibrium model by considering the overlapping effects between paths. To find efficiency loss upper bounds of the multiclass CL-SUE, two equivalent variational inequalities for the multiclass CL-SUE model, i.e., time-based variational inequality (VI) and monetary-based VI, are formulated. We give four different methods to define the inefficiency of the multiclass CL-SUE, i.e., to compare multiclass CL-SUE with multiclass system optimum, or to compare multiclass CL-SUE with multiclass C-Logit stochastic system optimum (CL-SSO), under the time-based criterion and the monetary-based criterion, respectively. We further investigate the effects of various parameters which include the degree of path overlapping (the commonality factor), the network complexity, degree of traffic congestion, the VOT of user classes, the network familiarity, and the total demand on the inefficiency bounds.

Sensor Deployment Strategy and Traffic Demand Estimation with Multisource Data

Since traffic origin-destination (OD) demand is a fundamental input parameter of urban road network planning and traffic management, multisource data are adopted to study methods of integrated sensor deployment and traffic demand estimation. A sensor deployment model is built to determine the optimal quantity and locations of sensors based on the principle of maximum link and route flow coverage information. Minimum variance weighted average technology is used to fuse the observed multisource data from the deployed sensors. Then, the bilevel maximum likelihood traffic demand estimation model is presented, where the upper-level model uses the method of maximum likelihood to estimate the traffic demand, and the lower-level model adopts the stochastic user equilibrium (SUE) to derive the route choice proportion. The sequential identification of sensors and iterative algorithms are designed to solve the sensor deployment and maximum likelihood traffic demand estimation models, respectively. Numerical examples demonstrate that the proposed sensor deployment model can be used to determine the optimal scheme of refitting sensors. The values estimated by the multisource data fusion-based traffic demand estimation model are close to the real traffic demands, and the iterative algorithm can achieve an accuracy of 10−3 in 20 s. This research has significantly promoted the effects of applying multisource data to traffic demand estimation problems.

On Stochastic-User-Equilibrium-Based Day-to-Day Dynamics

Researchers have proposed many different concepts and models to study day-to-day dynamics. Some models explicitly model travelers’ perceiving and learning on travel costs, and some other models do not explicitly consider the travel cost perception but instead formulate the dynamics of flows as the functions of flows and measured travel costs (which are determined by flows). This paper investigates the interconnection between these two types of day-to-day models, in particular, those models whose fixed points are a stochastic user equilibrium. Specifically, a widely used day-to-day model that combines exponential-smoothing learning and logit stochastic network loading (called the logit-ESL model in this paper) is proved to be equivalent to a model based purely on flows, which is the logit-based extension of the first-in-first-out dynamic of Jin [Jin W (2007) A dynamical system model of the traffic assignment problem. Transportation Res. Part B Methodological 41(1):32–48]. Via this equivalent form, the logit-ESL model is proved to be globally stable under nonseparable and monotone travel cost functions. Moreover, the model of Cantarella and Cascetta is shown to be equivalent to a second-order dynamic incorporating purely flows and is proved to be globally stable under separable link cost functions [Cantarella GE, Cascetta E (1995) Dynamic processes and equilibrium in transportation networks: Towards a unifying theory. Transportation Sci. 29(4):305–329]. Further, other discrete choice models, such as C-logit, path-size logit, and weibit, are introduced into the logit-ESL model, leading to several new day-to-day models, which are also proved to be globally stable under different conditions.

A Multiclass Cumulative Prospect Theory-Based Stochastic User Equilibrium Model with Path Constraints in Degradable Transport Networks

The limited driving range and the unavailability or insufficiency of battery charging/swapping stations cause the so-called range anxiety issue for traffic assignment involving battery electric vehicle (BEV) users. In addition, expected utility theory-based stochastic user equilibrium (EUT-SUE) model generates the perfectly rational issue when the travellers make route choice decisions. To tackle these two problems, this article improves the cumulative prospect theory-based stochastic user equilibrium (CPT-SUE) model in a degradable transport network through incorporating the constraints of multiple user classes and distance limit. In this degradable network, the travellers experience stochastic travel times due to network link capacity degradations. For this improved CPT-SUE model, the equivalent variational inequality (VI) model and associated method of successive averages (MSA) based solution are provided. The improved CPT-SUE model is tested and compared with the EUT-SUE model with distance limit, with results showing that the improved CPT-SUE model can handle jointly the range anxiety issue and the perfectly rational issue.

Evaluating the Capacity Coordination in the Urban Multimodal Transport Network

The urban multimodal transport network is composed of multiple layers of networks; thus, coordinating the capacity equilibrium among different sub-transport networks plays a crucial role to keep the entire network running efficiently. To quantify and evaluate the passenger flow distribution in an urban multimodal transport network, this research proposes a method to evaluate the capacity coordination in an urban multimodal transport network on the basis of assignment results calculated by the Stochastic User Equilibrium (SUE) model considering the link and path impedance of different sub-transport networks. It suggests evaluation functions for the indicator level of service (LOS) of the multimodal transport network, Gini coefficient of transport network, and mode share of transport modes, and it shows how the functions were estimated. Then, it reports on results with the evaluation scheme collected in a multimodal example application for roadway network, transit networks (bus transit network and urban rail transit network), and connection network. The evaluation results under different assumed origin–destination (OD) demand show the coordination degree and can be used to recognize shortcomings of the network. Moreover, the OD demand interval of real network with good coordination can be deduced, which can also help transport planners to find the optimal strategy.

Traffic Control Scheme for Social Optimum Traffic Assignment with Dynamic Route Pricing for Automated Vehicles

In transportation modeling, after defining a road network and its origin-destination (OD) matrix, the next important question is how to assign traffic among OD-pairs. Nowadays, advanced traveler information systems (ATIS) make it possible to realize the user equilibrium solution. Simultaneously, with the advent of the Cooperative Intelligent Transport Systems (C-ITS), it is possible to solve the traffic assignment problem in a system optimum way. As a potential traffic assignment method in the future transportation system for automated cars, the deterministic system optimum (DSO) is modeled and simulated to investigate the potential changes it may bring to the existing traditional traffic system. In this paper, stochastic user equilibrium (SUE) is used to simulate the conventional traffic assignment method. This work concluded that DSO has considerable advantages in reducing trip duration, time loss, waiting time, and departure delay under the same travel demand. What is more, the SUE traffic assignment has a more dispersed vehicle density distribution. Moreover, DSO traffic assignment helps the maximum vehicle density of each alternative path arrive almost simultaneously. Furthermore, DSO can significantly reduce or avoid the occurrence of excessive congestion.

A Stochastic User Equilibrium Formulation for the Cumulative Prospect Theory-Based Cross-Nested Logit

The cumulative prospect theory provides a better description for route choice behavior of the travelers in an uncertain road network environment. In this study, we proposed a multiclass cumulative prospect value- (CPV-) based cross-nested logit (CNL) stochastic user equilibrium (SUE) model. For this model, an equivalent variational inequality (VI) model is provided, and the existence and equivalence of the model solutions are also proved. The method of successive averages (MSA), method of successive weighted averages (MSWA), and self-regulated averaging (SRA) method are designed and compared. In addition, the proposed multiclass CPV-based CNL SUE model is also compared with the multiclass utility value- (UV-) based CNL SUE model. The results show that the path flow assigned by the multiclass CPV-based CNL SUE model is more consistent with the actual situation. The impact of different model parameters on the cumulative prospect value (CPV) is investigated.

A Strategic Markovian Traffic Equilibrium Model for Capacitated Networks

In the realm of traffic assignment over a network involving rigid arc capacities, the aim of the present work is to generalize the model of Marcotte, Nguyen, and Schoeb [Marcotte P, Nguyen S, Schoeb A (2004) A strategic flow model of traffic assignment in static capacitated networks. Oper. Res. 52(2):191–212.] by casting it within a stochastic user equilibrium framework. The strength of the proposed model is to incorporate two sources of stochasticity stemming, respectively, from the users’ imperfect knowledge regarding arc costs (represented by a discrete choice model) and the probability of not accessing saturated arcs. Moreover, the arc-based formulation extends the Markovian traffic equilibrium model of Baillon and Cominetti [Baillon JB, Cominetti R ( 2008 ) Markovian traffic equilibrium. Math. Programming 111(1-2):33–56.] through the explicit consideration of capacities. This paper is restricted to the case of acyclic networks, for which we present solution algorithms and numerical experiments.