Learning Marginal-Cost Pricing via Trial-and-Error Procedure with Day-to-Day Flow Dynamics

This paper investigates the convergence of the trial-and-error procedure to achieve system optimum by incorporating day-to-day evolution of traffic flows. The path flows are assumed to follow a so-called ‘excess travel cost dynamics’ and evolve from dis-equilibrium states to the equilibrium day by day. With this consideration, the observed link flow pattern during the trial-and-error procedure is in disequilibrium. With certain assumptions on the flow evolution dynamics, we prove that the trial-and-error procedure is capable of learning the system optimum link tolls without requirement of explicit knowledge on the demand functions and flow evolution mechanism. A methodology is developed for updating the toll charges and choosing the inter-trial periods to assure convergence of the iterative approach towards the system optimum. Some numerical examples are conducted to support the theoretical findings.