Jiancheng Long

An Intersection-Movement-Based Dynamic User Optimal Route Choice Problem

In this paper a novel variational inequality (VI) formulation of the dynamic user optimal (DUO) route choice problem is proposed using the concept of approach proportion. An approach proportion represents the proportion of travelers that select a turning or through movement when leaving a node. Approach proportions contain travelers’ route information so that the realistic effects of physical queues can be captured in a formulation when a physical-queue traffic flow model is adopted, and so that route enumeration and path-set generation can be avoided in the solution procedure. In addition, the simple structure of the approach proportion representation allows us to decompose the constraint set for solving large-scale DUO route choice problems. This paper also discusses the existence and uniqueness of the solutions to the VI problem and develops a solution algorithm based on the extragradient method to solve the proposed VI problem. This solution algorithm makes use of the decomposition property of the constraint set and is convergent if the travel time functions are pseudomonotone and Lipschitz continuous. It is not necessary to know the Lipschitz constant of the travel time functions in advance. Finally, numerical examples are given to demonstrate the properties of the proposed model and the performance of the solution algorithm. Subject classifications: dynamic traffic assignment; dynamic user optimal; approach proportion; variational inequality;

A bi-objective turning restriction design problem in urban road networks

This paper introduces a bi-objective turning restriction design problem (BOTRDP), which aims to simultaneously improve network traffic efficiency and reduce environmental pollution by implementing turning restrictions at selected intersections. A bi-level programming model is proposed to formulate the BOTRDP. The upper level problem aims to minimize both the total system travel time (TSTT) and the cost of total vehicle emissions (CTVE) from the viewpoint of traffic managers, and the lower level problem depicts travelers’ route choice behavior based on stochastic user equilibrium (SUE) theory. The modified artificial bee colony (ABC) heuristic is developed to find Pareto optimal turning restriction strategies. Different from the traditional ABC heuristic, crossover operators are captured to enhance the performance of the heuristic. The computational experiments show that incorporating crossover operators into the ABC heuristic can indeed improve its performance and that the proposed heuristic significantly outperforms the non-dominated sorting genetic algorithm (NSGA) even if different operators are randomly chosen and used in the NSGA as in our proposed heuristic. The results also illustrate that a Pareto optimal turning restriction strategy can obviously reduce the TSTT and the CTVE when compared with those without implementing the strategy, and that the number of Pareto optimal turning restriction designs is smaller when the network is more congested but greater network efficiency and air quality improvement can be achieved. The results also demonstrate that traffic information provision does have an impact on the number of Pareto optimal turning restriction designs. These results should have important implications on traffic management.

A nonlinear equation system approach to the dynamic stochastic user equilibrium simultaneous route and departure time choice problem

In dynamic stochastic user equilibrium simultaneous route and departure time choice (DSUE-SRDTC) problems, route travel costs can be non-monotone even if route travel times are monotone with respect to route flows. As a result, the mapping function of the variational inequality (VI) problems for the DSUE-SRDTC problems can be non-monotone, and many existing solution algorithms developed for the DSUE-SRDTC problems do not guarantee convergence under this non-monotone condition. This paper formulates the DSUE-SRDTC problem with fixed demand as a system of nonlinear equations. The mapping function of the proposed system of nonlinear equations is defined by a dynamic route choice problem, which can also be formulated as a VI problem with a strictly monotone mapping function under some assumptions. This property enables that the solution algorithm for the DSUE-SRDTC problem can avoid the requirement of the monotonicity of the route travel cost functions for the convergence of the solution procedure. A backtracking inexact Broyden–Fletcher–Goldfarb–Shanno (BFGS) method is adopted to solve the system of nonlinear equations, and iterative methods are developed to generate an initial solution for the BFGS method and solve the dynamic route choice problem. Finally, numerical examples are set up to show that the proposed method outperforms many existing algorithms for solving the DSUE-SRDTC problem in terms of guaranteeing solution convergence.

An effective algorithm to simulate pedestrian flow using the heuristic force-based model

A heuristic method based on the concept of velocity obstacle has been included into the force-based model to describe the pedestrian dynamics. This paper has analysed the continuity and monotonicity of the heuristic function of finding the optimal direction of velocity, and proposed a heuristic detouring algorithm (HDA) to find approximate optimal solutions. In the cases of only one standing pedestrian in the vision field, the solutions calculated by the HDA are optimal; while in other cases, the solutions are near-optimal. To test the performances of HDA, numerical experiments are conducted by three other algorithms that are enumeration algorithm (EA), social force model (SFM), optimal reciprocal collision avoidance (ORCA). Results show that HDA is about 2 times faster than ORCA and 20 times faster than EA. HDA performs with higher efficiency than ORCA and EA, and the fundamental diagram obtained by HDA agrees with empirical data better than ORCA and SFM.

Multi-class dynamic traffic assignment with physical queues: intersection-movement-based formulation and paradox

ABSTRACT This paper proposes an intersection-movement-based variational inequality formulation for the multi-class dynamic traffic assignment (DTA) problem involving physical queues using the concept of approach proportion. An extragradient method that requires only pseudomonotonicity and Lipschitz continuity for convergence is developed to solve the problem. We also present a car–truck interaction paradox, which states that allowing trucks to travel or increasing the truck flow in a network can improve network performance for cars in terms of the total car travel time. Numerical examples are set up to illustrate the importance of considering multiple vehicle types and their interactions in a DTA model, the effects of various parameters on the occurrence of the paradox, and the performance of the solution algorithm.

A single-step-toll equilibrium for the bottleneck model with dropped capacity

The optimal time-varying tolling is cumbersome for practical implementation due to the incomplete knowledge of toll determination and high costs for toll collection. Alternatively, a step toll is easier to implement than an optimal time-varying toll and could have lower operation costs and has been developed to reduce queuing time. In this paper, it is assumed that some drivers are willing to brake, while other drivers may pass the bottleneck near the end of the tolling period, and the braking drivers queue on the lanes and can impede other drivers. Two novel single-step-toll equilibrium models are developed with consideration of dropped capacity due to lanes occupied by the brakers. We found that some existing step-toll models are special cases of the proposed models. The toll level is further optimised to minimise either the maximal queue length or the total social cost. Finally, a numerical example is developed to illustrate the effect of the optimised toll on system performance.

Dynamic traffic assignment in degradable networks: paradoxes and formulations with stochastic link transmission model

ABSTRACT This paper proposes a simultaneous route and departure time choice (SRDTC) problem with fixed demand in a degradable transport network. In this network, travelers face with stochastic travel times. Their selection of routes and departure times follows the UE principle in terms of the mean generalized route cost, which is defined as the probabilistic dynamic user optimal (PDUO) principle. The proposed PDUO-SRDTC problem is formulated as a variational inequality (VI) problem. As a special case of PDUO-SRDTC problem, the PDUO route choice (PDUO-RC) problem is also proposed and formulated as a VI problem. Network degradation is defined on the degradation of the outflow capacity of each link. A Monte Carlo-based stochastic link transmission model (MC-SLTM) is developed to capture the effect of physical queues and the random evolution of traffic states during flow propagation to estimate mean generalized route costs. Both the extragradient algorithm and the route-swapping method with a variable sample size scheme are developed to solve the proposed VI problems. Numerical examples are developed to illustrate the paradoxical phenomena of the problems and the effectiveness of the solution methods. Numerical results show that constructing a new road, enhancing link outflow capacity, or reducing outflow capacity degradation can lead to poor network performance and it is important to consider both network degradation and queue spillback when making transportation policies aimed at improving network performance. The results also demonstrate that the variable sample size scheme can give a quicker and better solution than the traditional fixed sample size scheme.

Phase transition in 2D partially asymmetric simple exclusion process with two species

The dynamics of two species of particles undergoing asymmetric simple exclusion process (ASEP) on the 2D lattice are investigated in this paper. A sharp transition from moving phase to jamming phase was shown under periodic boundary conditions. We have developed a mean field analysis for the moving phase by extending the method of [33] and this produces good agreement with simulation results. Two types of jamming phase were observed. In the first type of jamming phase, some particles at the border of the jamming cluster could move back and forth due to the ASEP rule. The first type of jamming phase reduces to the 1D ASEP with a barrier at the boundary of the lattice. We also have analyzed the average hops for the first type of jamming phase by analyzing the 1D ASEP model. The analytical results agree with the simulation results well. Under open boundary conditions, the system exhibits two phases when forward hopping probability q is larger than 0.5. The particles form a wall at the entrance when q is smaller than 0.5. The dependence of the average velocity, the density and the flow rate on the injection probability in the moving phase have also been obtained through mean field analysis.

Optimal official work start times in activity-based bottleneck models with staggered work hours

ABSTRACT This paper aims to optimize official work start times (OWSTs) in activity-based bottleneck models with staggered work hours (SWH). In the models, commuters’ departure time choice from home to work is assumed to follow user equilibrium principle in terms of total activity utility. An activity-based bottleneck model with a single OWST is firstly considered. According to the equilibrium flow pattern, the optimal single OWST is analytically derived with maximized total system activity utility (TSAU). Then, we find that there exist four possible equilibrium traffic flow patterns for the bottleneck model with double OWSTs. The optimal equilibrium traffic flow pattern and the optimal OWSTs with maximal TSAU are also derived. Besides, the optimal SWH scheme for the bottleneck model with double OWSTs is extended to the situation of the bottleneck model with multiple OWSTs. Finally, numerical examples are developed to illustrate the properties of the proposed models.