Stochastic network equilibrium under stochastic demand

A generalisation of the conventional stochastic user equilibrium (SUE) model is developed in order to represent day-to-day variability in traffic flows due to stochastic variation in both a) the inter-zonal trip demand matrix, and b) the route choice proportions conditional on the demands. The equilibrated variables in this new problem are the link flow means and covariance matrix. A heuristic solution algorithm is proposed, based on the solution of a sequence of SUE subproblems. Numerical results are reported from the application of this technique to a realistic network, under the assumption of probit-based choice probabilities. In these tests, as the level of demand variability is increased (but the mean demand held fixed), the link flow variances predicted by the proposed model are seen to increase, but the effect on mean flows is relatively small. The increased variation in flows is, however, seen to have an inflationary effect on one of the prime indicators of network congestion, mean total travel cost.