A self-consistent dynamic traffic flow model part I: modeling and analysis

Abstract

Traffic flow theory can provide real time prediction and evaluation of traffic management strategies. Lightwill, Whitham and Richards applied a fluid mechanism to traffic flow and proposed a dynamic model (LWR model) in 1955 first. However, the LWR model needs to couple with a specific speed-density relation to be solved. Sometimes the assumption of such a relationship is not consistent with the whole model. In this study, we develop a dynamic traffic flow model based on the continuity equation (LWR model) and second-order model. The assumptions of the system equations are consistent with each other. Therefore, a self-consistent system is proposed herein. The existence and uniqueness of the solution is also illustrated in this work. Numerical simulations are left for further studies.