Analysis of a Car-Following Model with Driver Memory Effect

A nonlinear car-following model considering memory effect of human drivers is studied by means of theoretical analysis and numerical simulation. We model the memory effect of the response of drivers to the traffic situation for a car-following model by introducing a system variable related to velocity. The memory effect of the drivers is a kind of state-dependent delay. The stability of the car-following model with two kinds of time delay is studied. The hysteresis loop of traffic flow from different initial states is compared. The effect of the maximum time delay on the stability is discussed.