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The user equilibrium traffic assignment principle is very important in the traffic assignment problem. Mathematical programming models are designed to solve the user equilibrium problem in traditional algorithms. Recently, the Physarum shows the ability to address the user equilibrium and system optimization traffic assignment problems. However, the Physarum model are not efficient in real traffic networks with two-way traffic characteristics and multiple origin-destination pairs. In this article, a modified Physarum-inspired model for the user equilibrium problem is proposed. By decomposing traffic flux based on origin nodes, the traffic flux from different origin-destination pairs can be distinguished in the proposed model. The Physarum can obtain the equilibrium traffic flux when no shorter path can be discovered between each origin-destination pair. Finally, numerical examples use the Sioux Falls network to demonstrate the rationality and convergence properties of the proposed model.

The user equilibrium traffic assignment principle is very important in the traffic assignment problem. Mathematical programming models are designed to solve the user equilibrium problem in traditional algorithms. Recently, the Physarum shows the ability to address the user equilibrium and system optimization traffic assignment problems. However, the Physarum model are not efficient in real traffic networks with two-way traffic characteristics and multiple origin-destination pairs. In this article, a modified Physarum-inspired model for the user equilibrium problem is proposed. By decomposing traffic flux based on origin nodes, the traffic flux from different origin-destination pairs can be distinguished in the proposed model. The Physarum can obtain the equilibrium traffic flux when no shorter path can be discovered between each origin-destination pair. Finally, numerical examples use the Sioux Falls network to demonstrate the rationality and convergence properties of the proposed model.

The paper investigates the application of some large scale solution techniques to the so called traffic assignment problem, or multicommodity flow problem. As this is a network problem, there are two equivalent formulations. The first is based on the node-arc incidence matrix and is the usual approach. The second is based on an arc-chain matrix and the formulation is an extension of Ford and Fulkerson's multi-commodity work. Decomposition techniques are applied to the first formulation and a minimum chain network approach applied to the second. Then an extension of the arc-chain formulation shows it is equivalent to decomposition theory being applied to a slightly different node- arc formulation.

This paper presents a method for solving a stochastic version of the dynamic traffic assignment problem. It shows that a globally optimal solution may be obtained by a sequence of linear optimizations. A decomposition algorithm for this procedure is presented that efficiently solves large-scale problems. Solution examples with up to sixty-six thousand variables are described. Keywords: Stochastic programming; Traffic assignment; Multi-Stage problems.

Journal of Research of the National Bureau of Standards

Journal of Research of the National Bureau of Standards