Upper bounds for the critical car densities in traffic flow problems

Abstract

In most models of traffic flow, the car density p is the only free parameter in determining the average car velocity 〈v〉. The critical car density p c, which is defined to be the car density separating the jamming phase (with 〈v〉=0) and the moving phase (with 〈v〉>0), is an important physical quantity to investigate. By means of simple statistical argument, we show that p c< 1 for the Biham-Middleton-Levine model of traffic flow in two or higher spatial dimensions. In particular, we show thatp c < 11/12 in 2 dimension andp c≤ 1 -((D- 1)/2D) D in D(D>2) dimensions.