A dynamic traffic assignment formulation that encapsulates the cell-transmission model

This study develops an analytical dynamic traffic assignment (DTA) formulation based on a dynamic extension of Wardrop's Principle, referred to as dynamic user optimal (DUO) (Ran and Boyce, 1996). We develop a gap function for the corresponding nonlinear complementarity prolem (NCP) and prove 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-back and dynamic traffic phenomena such as shock-wave. Instead, traffic in this formulation is modeled after the Cell-Transmission Model (CTM) (Daganzo, 1994, 1995a). CTM provides a convergent approximation to the Lighthill and Whitham (1955) and Richards (1956) (LWR) model and covers the full range of the fundamental diagram. This study transforms CTM in its entirely 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 developed herein, dynamic signal control, and possibly other applications.