A DYNAMIC TRAFFIC ASSIGNMENT FORMULATION THAT ENCAPSULATES THE CELL-TRANSMISSION MODEL

An analytical dynamic traffic assignment (DTA) formulation is developed based on a dynamic extension of Wardrop's Principle. It is referred to as dynamic user optimal (DUO). A gap function for the corresponding nonlinear complementarity problem is developed and it is proven that minimizing the gap function produces a solution that fulfills the ideal DUO conditions. Existing analytical DTA formulations mostly use macroscopic link travel time functions to model traffic. In general, it is difficult for such functions to capture traffic interactions across multiple links such as queue spill-backs and dynamic traffic phenomena such as shock waves. Instead, traffic in this formulation is modeled after the Cell Transmission Model (CTM), which provides a convergent approximation to the Lighthill and Whitham and Richards (LWR) model and covers the full range of the fundamental diagram. This study transforms CTM in its entirety to a set of mixed-integer constraints. The significance of this is that it opens up CTM to a wide range of dynamic traffic optimization problems, such as the DUO formulation and dynamic signal control.