Stochastic Networks and Traffic Assignment

Abstract

This paper explores the use of some stochastic models for traffic assignment in the case of homogeneous traffic and simple networks. For non-dynamic routing we obtain asymptotic results in the form of paths representing time dependent evolution of traffic over routes. A functional limit theorem gives integral equations for the limiting fluid path which converges to an assignment satisfying Wardrop's first principle as time goes to infinity. For linear cost functions we are able to use the theory of large deviations to examine the way in which rare network overload events occur. In the case of dynamic assignment, we discuss the use of heavy traffic limits and Brownian models to examine the efficiency of network capacity usage when drivers choose routes according to conditions obtaining on entrance to the network. In particular we discuss the phenomenon of resource pooling.

Citation

Evans, S.P. (1998), "Stochastic Networks and Traffic Assignment", Griffiths, J.D. (Ed.) Mathematics in Transport Planning and Control, Emerald Group Publishing Limited, Leeds, pp. 109-118. https://doi.org/10.1108/9780585474182-011