User Equilibrium Assignment Problem Research Articles

A bi-level programming approach for trip matrix estimation and traffic control problems with stochastic user equilibrium link flows

This paper deals with two mathematically similar problems in transport network analysis: trip matrix estimation and traffic signal optimisation on congested road networks. These two problems are formulated as bi-level programming problems with stochastic user equilibrium assignment as the second-level programming problem. We differentiate two types of solutions in the combined matrix estimation and stochastic user equilibrium assignment problem (or the combined signal optimisation and stochastic user equilibrium assignment problem): one is the solution to the bi-level programming problem and the other the mutually consistent solution where the two sub-problems in the combined problem are solved simultaneously. In this paper, we shall concentrate on the bi-level programming approach, although we shall also consider mutually consistent solutions so as to contrast the two types of solutions. The purpose of the paper is to present a solution algorithm for the two bi-level programming problems and to test the algorithm on several networks.

A combined trip distribution and assignment model for multiple user classes

This paper presents a combined trip distribution and assignment model with multiple user classes, in which the trip productions at origins and trip attractions at destinations for each mode are available. In this model, the entropy-type (or gravity-type) trip distribution submodel is incorporated with the user equilibrium assignment problem for multiclass-user transportation networks. The original unsymmetrical link cost functions can be converted to symmetric forms by a ‘normalization’ procedure, and hence an equivalent convex mathematical programming model is formulated. Two different algorithms based on the Frank-Wolfe's and Evans', respectively are developed and their computational results on test networks are reported. This model is appropriate to be used on congested and multi-modal road networks in which the link travel time is similar for all traffic.

Estimating departure times from traffic counts using dynamic assignment

Dynamic traffic assignment and observed traffic counts are used to estimate the distribution of departure times in an urban area trip matrix. The objective is to find the maximum entropy distribution of departure times by origin zone subject to observed traffic counts on a subset of network links. The procedure results in the estimated number of trip departures from each origin in 10–15 minute time intervals of the full analysis period. Such an analysis period will typically range from one to three hours long. We first review the dynamic user-equilibrium assignment problem (DUE) and the dynamic traffic assignment algorithm (DTA) from a previous paper, and then describe its use with traffic counts to estimate departure times in a trip matrix. We present an application to a Pittsburgh network in which trip departures are estimated for each 10 minute interval of a peak-hour survey trip matrix. Dynamic assignment and departure time estimation based on traffic counts can be used to examine the impacts of alternative transportation management strategies such as work hour changes and ramp metering. Computational advances such as parallel computing will enable the procedure to be run on large networks while counts are being monitored. Such an application may provide near real-time detection of temporal trip departure profiles by origin zone in emergency evacuations or other special events.

Dynamic traffic assignment for urban road networks

This paper presents a nonlinear programming formulation of the dynamic user-equilibrium assignment problem (DUE) for urban road networks with multiple trip origins and destinations. DUE is a temporal generalization of the static user-equilibrium assignment problem (SUE) with additional constraints to insure temporally continuous paths of flow. In DUE, the full assignment period of several hours is discretized into shorter time intervals of 10–15 minutes each for which trip departure matrices are assumed to be known. This formulation of DUE includes SUE as a special case in which there is only one time interval for the full assignment period. The assumption of steady-state flows allows SUE to have all linear constraints, but DUE requires nonlinear flow continuity constraints. Whereas SUE is typically solved by methods of linear combinations, these methods create temporally discontinuous flows if applied to DUE. A dynamic traffic assignment heuristic (DTA) is presented that generates approximate solutions to DUE in an efficient manner for large networks. DTA is not a convergent solution algorithm for DUE, but was designed instead to produce assignments that approximate the DUE optimality conditions. An overview of alternative dynamic assignment approaches is given, including the limitations of other optimization and simulation approaches. Test results presented in this paper show that DTA generates both static and dynamic assignments that approximately satisfy the user-equilibrium conditions of these problems.