Weakly nonlinear analysis for car-following model with consideration of cooperation and time delays

TL;DR

This paper analyzes how cooperation and time delays influence traffic flow stability in car-following models, deriving equations and solutions that reveal the complex effects of these factors on traffic wave formation and stability.

Contribution

It introduces a comprehensive analysis of linear stability and weak nonlinear dynamics considering cooperation and delays in general car-following models, including derivation of Burgers and KdV equations.

Findings

Delays and cooperation effects are model-dependent.

Cooperative behavior can inhibit traffic flow stabilization.

Certain delays can trigger or relieve traffic waves.

Abstract

In traffic systems, cooperative driving has attracted the researchers attentions. A lot of works attempt to understand the effects of cooperative driving behavior and/or time delays on traffic flow dynamics for specific traffic flow model. This paper is a new attempt to investigate analyses of linear stability and weak nonlinear for the general car-following model with consideration of cooperation and time delays. We derive linear stability condition and study that how the combinations of cooperation and time delays affect the stability of traffic flow. Burgers equation and Korteweg de Vries (KdV) equation for car-following model considering cooperation and time delays are derived. Their solitary wave solutions and constraint conditions are concluded. We investigate the property of cooperative optimal velocity(OV) model which estimates the combinations of cooperation and time delays about the evolution of traffic waves using both analytic and numerical methods. The results indicate that delays and cooperation are model-dependent, and cooperative behavior could inhibit the stabilization of traffic flow. Moreover, delays of sensing to relative motion are easy to trigger the traffic waves; delays of sensing to host vehicle are beneficial to relieve the instability effect a certain extent.