Instantaneous Dynamic User-Optimal Route Choice Models

In this chapter, we discuss optimal control models for instantaneous dynamic user-optimal route choice problems. Using a network with two parallel routes, we first present an example to illustrate the instantaneous dynamic user-optimal concept in Section 5.1. The general definition of instantaneous dynamic useroptimal state is given in Section 5.2. Then, we present three instantaneous dynamic user-optimal route choice models. Model 1 is described in Section 5.3. In Section 5.4, the equivalence of Model 1 with DUO route choice is demonstrated by proving the equivalence of the first order necessary conditions of the model with the instantaneous DUO route choice conditions. In Section 5.5, the second DUO model employing a different link travel time function assumption is formulated, and the equivalence of Model 2 with the instantaneous DUO route choice conditions is also demonstrated. In Section 5.6, the third instantaneous DUO model employing a simpler link travel time function assumption is formulated, and its equivalence with the instantaneous DUO conditions is also demonstrated. Finally, we present a discrete-time numerical example indicating that this class of models yields realistic results.