A Second Order Stochastic Network Equilibrium Model, II: Solution Method and Numerical Experiments

Real traffic networks typically exhibit considerable day-to-day variations in traffic flows and travel times, yet these variations are commonly neglected in network performance models. Recently, two alternative theoretical approaches were proposed for incorporating stochastic flow variation in the equilibration of route choices: the stochastic process (SP) approach (Cantarella and Cascetta 1995) and the second order generalized stochastic user equilibrium (GSUE(2)) model (Watling 2002). The theoretical basis of the two approaches is contrasted, and the paper goes on to present a heuristic solution method for the GSUE(2) model, and two alternative simulation methods for the SP model, each applicable to the realistic case of probit-based choice probabilities. These solution methods are then applied to two realistic networks. Factors affecting convergence and reproducibility are first identified, followed by comparisons of the GSUE(2) and SP predictions. It is seen that a quasi-periodic behaviour commonly arises in the SP model, with the predictions radically different from the GSUE(2) model. However, by modifying the link performance functions in the overcapacity regime, the nature of the SP solution changes, and for a memory filter based on a large number of days' experience, its moments are seen to be approximated by those of the GSUE(2) model. Implications for the application of these models are discussed.