A partially inexact trial method for the traffic restraint and road pricing problem

This study deals with a road pricing scheme that aims to restrict link traffic flows on a network within a predetermined upper-bound, such as road physical or environmental capacity. In our previous sequential experimental approach, the optimal link tolls are obtained, without resorting to both analytical travel cost and demand functions. In each trial, two steps are involved, prediction and correction, based on the observed link flows associated with a given link toll pattern. One key assumption made in the study is that the observed link flows are exactly in a deterministic equilibrium. This assumption is of course questionable in real applications, given the fact that travelers need sufficient time to learn and adjust their trip-making decisions in a new pricing environment. In this study, the exact prediction-correction method is modified to a partially inexact trial method, whose convergence is established theoretically. Numerical experiment shows that the partially inexact trial method is even more cost efficient in terms of the overall convergence rate. The extension thus obviates the requirement for observation of exact deterministic traffic equilibrium after each price experiment and makes the sequential experimental approach more robust in real applications.