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

In traffic systems, cooperative driving has attracted the researchers’ attention. 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 models. This paper is a new attempt to investigate analyses of linear stability and weak nonlinearity for the general car-following model with consideration of cooperation and time delays. We derive linear stability condition and study 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 relative motion are easy to trigger the traffic waves; delays of sensing host vehicle are beneficial to relieve the instability effect to a certain extent.