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

This study develops an analytical dynamic traffic assignment (DTA) formulat ion based on a dynamic extension of Wardrop's Principle, referred to as dyn amic user optimal (DUO) (Ran and Boyce, 1996). We develop a gap function fo r the corresponding nonlinear complementarity prolem (NCP) and prove that m inimizing the gap function produces a solution that fulfills the ideal DUO conditions. Existing analytical DTA formulations mostly use macroscopic lin k travel time functions to model traffic. In general it is difficult for su ch 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 th e full range of the fundamental diagram. This study transforms CTM in its e ntirely 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 proble ms, such as the DUO formulation developed herein, dynamic signal control, a nd possibly other applications.