Abstract: In this paper, Fukui Ishibashi one dimensional traffic flow cellular automaton model for high speed vehicles (v_max=M>1) with stochastic delay is studied from the point of view of inter-car spacings. Starting from the basic equation describing the time evolution of the number of empty sites in front of each car, the concepts of inter-car spacing longer (shorter) than M are defined, the occurrence probabilities of longer spacing and shorter spacing are calculated respectively. For the situation of high density (d ≥ 1/M), it is proved that the inter-car spacing longer than M will be shorten, any initial configuration will approach to the steady state for which all the inter-car spacing belong to shorter type. Hence it is proved strictly that for general Fukui -Ishibashi traffic flow model with stochastic delay, when the car density is high, the fundamental diagram for the traffic flow asymptotic steady state does not change as the delay probability.

Key words: fundamental diagram, mean field equation, traffic flow, cellular automaton