THE ASYMPTOTIC STEADY STATE BEHAVIOR OF DETERMINISTIC GRADUAL ACCELERATION TRAFFIC FLOW MODEL

Abstract

In this paper, the fundamental diagram of the average traffic flow speed in the asymptotic steady state as a function of vehicle density for deterministic Nagel-Schreckenberg(NS) traffic flow cellular automaton model of high speed car without stochastic delay has been studied. It is proved that due to self organization of traffic flow, the fundamental diagram in steady state of deterministic NS model is exactly the same as the of deterministic Fukui-Ishibashi(FI) traffic flow model. The result shows if the abrupt acceleration scenario(where the speed of a car may be accelerated to the velocity limit M or the maximum velocity permitted by the spacing ahead in only one time step) is changed to the gradual acceleration scenario (where the speed of a car can increase one unit at most in one time step), the traffic flow behavior in asymptotic steady state will not be changed by self organization car interactions).