A new continuum model with driver’s continuous sensory memory and preceding vehicle’s taillight

Abstract

Car taillights are ubiquitous during the deceleration process in real traffic, while drivers have a memory for historical information. The collective effect may greatly affect driving behavior and traffic flow performance. In this paper, we propose a continuum model with the driver’s memory time and the preceding vehicle’s taillight. To better reflect reality, the continuous driving process is also considered. To this end, we first develop a unique version of a car-following model. By converting micro variables into macro variables with a macro conversion method, the micro car-following model is transformed into a new continuum model. Based on a linear stability analysis, the stability conditions of the new continuum model are obtained. We proceed to deduce the modified KdV-Burgers equation of the model in a nonlinear stability analysis, where the solution can be used to describe the propagation and evolution characteristics of the density wave near the neutral stability curve. The results show that memory time has a negative impact on the stability of traffic flow, whereas the provision of the preceding vehicle’s taillight contributes to mitigating traffic congestion and reducing energy consumption.