ASYMMETRIC PROBLEMS AND STOCHASTIC-PROCESS MODELS OF TRAFFIC ASSIGNMENT

There is a spectrum of asymmetric assignment problems to which existin g results on uniqueness of equilibrium do not apply. Moreover, multipl e equilibria may be seen to exist in a number of simple examples of re al-life phenomena, including interactions at priority junctions, respo nsive traffic signals, multiple user classes, and multi-modal choices. In contrast, recent asymptotic results on the stochastic process appr oach to traffic assignment establish the existence of a unique, statio nary, joint probability distribution of flows under mild conditions, t hat include problems with multiple equilibria. In studying the simple examples mentioned above, this approach is seen to be a powerful tool in suggesting the relative, asymptotic attractiveness of alternative e quilibrium solutions. It is seen that the stationary distribution may have multiple peaks, approximated by the stable equilibria, or a unimo dal shape in cases where one of the equilibria dominates. It is seen, however, that the convergence to stationarity may be extremely slow. I n Monte Carlo simulations of the process, this gives rise to different types of pseudo-stable behaviour (flows varying in an apparently stab le manner, with a mean close to one of the equilibria) for a given pro blem, and this may prevail for long periods. The starting conditions a nd random number seed are seen to affect the type of pseudo-stable beh aviour over long, but finite, time horizons. The frequency of transiti ons between these types of behaviour (equivalently, the average sojour n in a locally attractive, pseudo-stable set of states) is seen to be affected by behavioural parameters of the model. Recommendations are g iven for the application of stochastic process models, in the light of these issues. Copyright (C) 1996 Elsevier Science Ltd