TRAFFIC JAM INDUCED BY A CROSSCUT ROAD IN A TRAFFIC-FLOW MODEL

A deterministic cellular automaton model is presented to simulate the traffic jam induced by a crosscut road in a two-dimensional traffic flow. The effect of a crosscut road on the traffic flow is investigated by the use of a computer simulation. The traffic jam appears when a shock (discontinuous interface of different car densities) is formed. The condition for shock formation is derived for car densities p(y) and p(x) of the crosscut road and its crossing streets. The phase diagram and the dependence of the traffic flow on the car densities are shown. Also, we study the shock structure and the scaling of its width. The width DELTAw of the shock scales with the system size L as DELTAw almost-equal-to L1/2. We present a self-consistent mean-field theory for the traffic flow.