The Day-to-Day Departure Time Choice of Heterogeneous Commuters Under an Anonymous Toll Charge for System Optimum

We consider a bottleneck system in a state of disequilibrium, in which commuters are heterogeneous in the values of travel time and schedule delays. Three representative dynamical systems are used to formulate the day-to-day departure time choice of commuters, and a Walrasian toll charge scheme is utilized to control the evolutionary process of traffic flows. The toll charge scheme is anonymous; that is, toll charges are identical for all user classes, and the scheme’s implementation does not need to resort to information on the values of travel time and schedule delays. We find that the system optimum (SO) flow pattern can be achieved at the stationary state under the implementation of the toll charge scheme. The equivalence between the stationary state and the SO, the existence of the toll charge for achieving the SO, and the convergence of day-to-day traffic flows to the SO under the implementation of the toll charge scheme are theoretically proved. The distributions of traffic flows and toll charges at the SO state during morning rush hour are analytically shown. The application of the toll charge scheme to a network with multiple trip origins is presented. The effectiveness of the toll charge scheme for achieving the SO is also examined by numerical analyses. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72171007, 71890972/71890970, and 72021001]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.1191 .