User Equilibrium, System Optimum, and Externalities in Time-Dependent Road Networks

This paper develops a comprehensive framework for analyzing and calculating equilibrium and system optimizing flows and externalities in time-dependent road networks. Under dynamic equilibrium, travelers are assigned such that for each origin-destination pair in the network, the total travel costs experienced by travelers, no matter which combination of travel routes and departure times they choose, are equal and minimal. The system optimal flow is determined by solving a state-dependent optimal control problem, which assigns traffic such that the total system cost of the network system is minimized. The externalities are derived by using a novel sensitivity analysis of traffic models. The analyses developed in this paper can work with general travel time models and cost functions. Deterministic queue is predominantly used in dynamic network models. The analysis in this paper is more general. Numerical examples are provided for illustration and discussion. Finally, some concluding remarks are given.