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

Traffic assignment models can be classified according to the behavioral assumption governing route choice. The deterministic user equilibrium (UE), stochastic user equlibrium (SUE) and system optimum (SO) models have been studied extensively in the literature. The relationship between the UE solution and the SO solution for a given network is well known, as is the relationship between UE and SUE. The question that arises concerns the relationship between SUE and (deterministic) SO. The flow pattern obtained from the SO solution serves as a yardstick for comparison with the flow patterns obtained from the UE and SUE solutions. The investigation examines whether the stochastic equilibrium is ‘closer’ than the deterministic user equilibrium to the system optimum. This paper compares the performance of the different solutions for simple networks. The comparison is made by evaluating the relative difference in total system times for UE and SUE solutions with respect to the SO solution. This paper also presents an extension of previous results 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.