Car-following model with explicit reaction-time delay: linear stability analysis of a uniform solution on a ring

Abstract

A microscopic car-following model with an explicit reaction-time delay is considered. The acceleration of every vehicle depends on its actual speed, the predecessor speed, and the distance between them. The acceleration function explicitly includes the driver’s reaction-time delay. On the one hand, this is an undoubted advantage of the model, and on the other hand, it significantly complicates the mathematical analysis. The subject of the study is the stability analysis of the uniform solutions on a ring. Using the linear stability analysis, we obtained the conditions on the model parameters including the driver’s reaction time, for which perturbations around the uniform solution decay. The calculations show that there are values for the model parameters, which satisfy the obtained conditions and at the same time provide a realistic dynamic of the vehicles. An important result is the fact that this model is able to reproduce such phenomenon as propagation of stop-and-go waves, which are widely known in traffic flow theory and are observed in practice. The latter is another advantage of the proposed car-following model.