UPPER-BOUNDS FOR THE CRITICAL CAR DENSITIES IN TRAFFIC FLOW PROBLEMS

Zn most models of traffic flow, the car density p is the only free parameter in determining the average car velocity [upsilon]. The critical car density p(c), which is defined to be the car density separating the jamming phase (with [upsilon]=0) and the moving phase (with [upsilon]>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 that p(c) less than or equal to 11/12 in 2 dimension and p(c) less than or equal to 1-((D-1)/2D)(D) in D(D>2) dimensions.