Some observations on stochastic user equilibrium and system optimum of traffic assignment

Traffic assignment models can be classified according to the behavioral ass umption governing route choice. The deterministic user equilibrium (UE), st ochastic user equilibrium (SUE) and system optimum (SO) models have been st udied extensively in the literature. The relationship between the UE soluti on and the SO solution for a given network is well known, as is the relatio nship between UE and SUE. The question that arises concerns the relationshi p between SUE and (deterministic) SO. The flow pattern obtained from the SO solution serves as a yardstick for comparison with the flow patterns obtai ned from the UE and SUE solutions. The investigation examines whether the s tochastic equilibriums "closer" than the deterministic user equilibrium to the system optimum. This paper compares the performance of the different so lutions for simple networks. The comparison is made by evaluating the relat ive difference in total system times for UE and SUE solutions with respect to the SO solution. This paper also presents an extension of previous resul ts to show that the Braess' paradox can occur for certain ranges of demand volumes in the case of stochastic equilibrium and non-linear cost functions . (C) 2000 Elsevier Science Ltd. All rights reserved.