Sensitivity analysis of the probit-based stochastic user equilibrium model

The probit-based Stochastic User Equilibrium (SUE) model has the advantage of being able to represent perceptual differences in utility across the driver population, while taking proper account of the natural correlations in these utilities between overlapping routes within the network (which the simpler logit SUE is unable to do). Its main drawback is the potentially heavy computational demands, and this has previously been thought to preclude a consideration of the sensitivity analysis of probit-based SUE, whereby an approximation to changes in the equilibrium solution is deduced as its input parameters (specifically origin/destination flows and link cost-flow function parameters) are perturbed. In the present paper, an efficient computational method for performing such an analysis for general networks is described. This approach uses information on SUE path flows, but is not specific to any particular equilibrium solution algorithm. Problems inherent in the consideration of general network topologies are identified, and methods proposed for overcoming them. The paper concludes with an application of the method to a realistic network, and compares the approximate solutions with those obtained by direct estimation methods.