Whilst User Equilibrium (UE) assignment methods have been applied with success to congested urban networks, and pure stochastic methods to lightly congested inter-urban networks, both have their weaknesses. UE methods are deterministic and assume that drivers have perfect and complete knowledge of network conditions and that all drivers perceive these conditions identically. Stochastic methods, on the other hand, allow for variations in knowledge and perceptions between drivers, but do not incorporate capacity restraint. Stochastic User Equilibrium (SUE) has for some time been a recognised goal. This paper describes a new SUE method, formed by incorporating capacity restraint (in the form of link-based restraint (in the form of link-based cost-flow functions) into a stochastic loading method, which is profit-based (unlike dial) and numerical (unlike the Monte Carlo method of Burrell). The nature of the SUE algorithm is similar to the Frank-Wolfe method which is commonly used for the solution of the UE problem. A technique is described for overcoming the "deadlock" problem, thus permitting the method to be applied to networks of any configuration. The new model is demonstrated by applying it to the Sioux Falls network. The progress of the iterative process is shown by (1) the steady reduction in an objective function and (2) by a convergence statistic which measures the "distance" between the current and auxiliary solutions. It is shown how, as the variability parameter (representing the between-driver variation in perceptions of link cost) decreases, so the SUE solutions tend to the UE solution. Finally, the paper discusses possible extensions of the model to allow for multiple user classes, elastic demand and junction modelling. (A)
Abstract