Variational Inequality Models of Dynamic Departure Time/Route Choice Problems

Abstract

In this chapter, we consider an ideal situation where all travelers are equipped with navigation devices and fully comply with the dynamic user-optimal criterion when choosing routes, departure times and modes. We first present a dynamic, user-optimal departure time/route choice model for a general network with multiple origin-destination pairs. We model this choice problem by specifying that a given number of travelers are ready for departure between each origin-destination pair at time 0. However, their departure times may be delayed to reduce their overall travel costs. A route-based variational inequality model for joint departure time/route choice is presented in Section 14.1. In a parallel fashion, a link-based variational inequality model is proposed in Section 14.2. The relationship between the variational inequality models and the optimization models is discussed in Section 14.3.