Car-following model of multispecies systems of road traffic

Abstract

A speed-adjustment car-following model is extended to systems of traffic where there is a variety of vehicle response times and speed-headway relationships. This is proposed as a model of the interactions between cars and trucks on single-lane roads where there is no overtaking, and some of its properties are derived. First, we make a distinction between temporal stability on a circular road and spatial stability on a straight road and go on to derive criteria for linear stability in each case. The propagation and dispersion of a linear disturbance wave is studied, and we also compare the nonlinear evolution of both single- and multiple-species systems on circuitous and straight roads. When the speed-headway relationship of all vehicles is given by the nonlinear law proposed by Bando et al. [Phys. Rev. E 51, 2 (1995)], we find that for models of car-truck systems, as for systems consisting of one type of vehicle only, there is a range of equilibrium headways for which the system is linearly unstable. The size of this range increases with the proportion of the more unreactive vehicle type, trucks, in the population of vehicles. Computer simulations verify the analytical results and show the nonlinear development of disturbances when the system is linearly unstable. It is demonstrated that slow vehicles in a platoon moving at close to their top speed can damp nonlinear congestion waves.