Modeling non-equilibrium traffic dynamics in a Lagrangian framework

Abstract

In this paper, we propose a formulation for modeling macroscopic traffic flow using a modified speed–density relationship. The flow model consists of a nonlinear hyperbolic system of conservation laws. The proposed modification distinguishes between acceleration and deceleration by assuming a different equilibrium velocity for a given traffic density based on whether a platoon of vehicles is accelerating or decelerating. We examine the appropriateness of this modification to two prominent traffic flow models in a Lagrangian reference frame, which we solve computationally. We show that a Lagrangian coordinate system is ideal for the incorporation of the proposed modification due to its ability to track the behavior of moving vehicles. We see that the modification is particularly well suited to “second order” models.