Cluster effect in initially homogeneous traffic flow

It is shown that, in an initially homogeneous traffic flow, a region of high density and low average velocity of cars can spontaneously appear, if the density of cars in the flow exceeds some critical value. This region—a cluster of cars—can move with constant velocity in the opposite direction or in the direction of the flow, depending on the selected parameters and the initial conditions of the traffic flow. Based on numerical simulations, the kinetics of cluster formation and the shape of stationary moving clusters are found. The results presented can explain the appearance of a ‘‘phantom traffic jam,’’ which is observed in real traffic flow.