Finding equilibrium in two-stage traffic assignment model

Abstract

Authors describe a two-stage traffic assignment model. It contains of two blocks. The first block consists of model for calculating correspondence (demand) matrix, whereas the second block is a traffic assignment model. The first model calculates a matrix of correspondences using a matrix of transport costs. It characterizes the required volumes of movement from one area to another. The second model describes how exactly the needs for displacement, specified by the correspondence matrix, are distributed along the possible paths. It works on the basis of the Nash--Wardrop equilibrium (each driver chooses the shortest path). Knowing the ways of distribute flows along the paths, it is possible to calculate the cost matrix. Equilibrium in a two-stage model is a fixed point in the sequence of these two models. The article proposes a method of reducing the problem of finding the equilibrium to the problem of the convex non-smooth optimization. Also a numerical method for solving the obtained optimization problem is proposed. Numerical experiments were carried out for the small towns.

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