Multiple Traffic Jams in Full Velocity Difference Model with Reaction-time Delay

A full velocity difference model for traffic flow, including driver’s reaction time delay is considered. The uniform flow and traffic jams are interpreted through stability and bifurcation analysis. Specifically, the uniform flow is represented by the equilibrium of the model. Linear stability reveals that when the equilibrium loses its stability, local bifurcation turn up through Hopf bifurcations. To analyse the behaviour of the model after bifurcating, numerical continuation techniques are employed. Branches of oscillating solutions and the corresponding stabilities are obtained. It is shown that bifurcating oscillations can coexist and correspond to different traffic patterns. To visualize the spatial patterns, numerical simulations are performed, which are presented by velocity time histories and spatio-temporal diagrams. Analysing the characteristic features, these oscillating solutions are classified into three types, and further correspond to three types of traffic jams: almost traffic jams, width-equal traffic jam and width-alternated traffic jam. The obtained results provide an explanation of how multiple jams induced by driver’s reaction time delay occur. (Received, processed and accepted by the Chinese Representative Office.)