Stability analysis of a constant time-headway driving strategy with driver memory effects modeled with distributed delays

Study of traffic flow dynamics has attracted considerable attention for decades. One way to thoroughly understand traffic flow is to study how each vehicle in traffic interacts with each other, through drivers’ acceleration/deceleration decisions. Such decisions are strongly influenced by reaction delays of drivers, which arise naturally due to drivers’ physiology, perception, and motor programming. In this article, we consider how the memory of drivers, modeled here with distributed delays, affects the decision making process in a car following scenario, in which each driver aims to keep a fixed time-headway with respect to the preceding vehicle. Taking a frequency domain analysis, we reveal the effects of the parameters of the driver memory model on the asymptotic stability features of the arising inter-vehicle spacing propagation dynamics.