Traffic flow models with looking ahead-behind dynamics

TL;DR

This paper introduces a novel traffic flow model incorporating look ahead and behind dynamics, demonstrating improved dispersive and smoothing effects through numerical experiments, building upon previous models with relaxation dynamics.

Contribution

It proposes a new traffic flow model with combined look ahead relaxation and behind intensification, extending prior models with additional interaction dynamics.

Findings

Identifies finite time shock formation conditions.

Demonstrates enhanced dispersive effects.

Shows improved smoothing effects in simulations.

Abstract

Motivated by the traffic flow model with Arrhenius look-ahead relaxation dynamics introduced in [A. Sopasakis and M.A. Katsoulakis, SIAM J. Appl. Math., 66 (2006), p. 921--944], this paper proposes a traffic flow model with look ahead relaxation-behind intensification by inserting look behind intensification dynamics to the flux. Finite time shock formation conditions in the proposed model with various types of interaction potentials are identified. Several numerical experiments are performed in order to demonstrate the performance of the modified model. It is observed that, compare to other well-known traffic flow models, the model equipped with look ahead relaxation-behind intensification has both enhanced dispersive and smoothing effects