Steady state speed distribution analysis for a combined cellular automaton traffic model

Cellular Automaton (CA) based traffic flow models have beenextensively studied due to their effectiveness and simplicity inrecent years. This paper develops a discrete time Markov chain(DTMC) analytical framework for a Nagel--Schreckenberg andFukui--Ishibashi combined CA model (W$^2$H traffic flow model) frommicroscopic point of view to capture the macroscopic steady statespeed distributions. The inter-vehicle spacing Markov chain and thesteady state speed Markov chain are proved to be irreducible andergodic. The theoretical speed probability distributions dependingon the traffic density and stochastic delay probability are in goodaccordance with numerical simulations. The derived fundamentaldiagram of the average speed from theoretical speed distributions isequivalent to the results in the previous work.