Steady state speed distribution analysis for a combined cellular automaton traffic model
Wang Jun-Feng(王俊峰)a)†, Chen Gui-Sheng(陈桂生)b), and Liu Jin(刘进)c)
a College of Computer Science, Sichuan University, Chengdu 610065, China; b Institute of Electronic System Engineering, Beijing 100840, China; c State Key Laboratory of Software Engineering, Wuhan University, Wuhan 430007, China
Abstract Cellular Automaton (CA) based traffic flow models have been extensively studied due to their effectiveness and simplicity in recent years. This paper develops a discrete time Markov chain (DTMC) analytical framework for a Nagel--Schreckenberg and Fukui--Ishibashi combined CA model (W$^2$H traffic flow model) from microscopic point of view to capture the macroscopic steady state speed distributions. The inter-vehicle spacing Markov chain and the steady state speed Markov chain are proved to be irreducible and ergodic. The theoretical speed probability distributions depending on the traffic density and stochastic delay probability are in good accordance with numerical simulations. The derived fundamental diagram of the average speed from theoretical speed distributions is equivalent to the results in the previous work.
Received: 23 November 2007
Revised: 22 February 2008
Accepted manuscript online:
PACS:
45.70.Vn
(Granular models of complex systems; traffic flow)
Fund: Project supported by the National
Basic Research Program of China (Grant No 2007CB310800), the
National Natural Science Foundation of China (Grant Nos 60772150 and
60703018), the National High Technology Research and Development
Program of China (Grant No 2008AA01Z208).
Cite this article:
Wang Jun-Feng(王俊峰), Chen Gui-Sheng(陈桂生), and Liu Jin(刘进) Steady state speed distribution analysis for a combined cellular automaton traffic model 2008 Chin. Phys. B 17 2850
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