中国物理B ›› 2008, Vol. 17 ›› Issue (8): 2850-2858.doi: 10.1088/1674-1056/17/8/017

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

王俊峰1, 陈桂生2, 刘 进3   

  1. (1)College of Computer Science, Sichuan University, Chengdu 610065, China; (2)Institute of Electronic System Engineering, Beijing 100840, China; (3)State Key Laboratory of Software Engineering, Wuhan University, Wuhan 430007, China
  • 收稿日期:2007-11-23 修回日期:2008-02-22 出版日期:2008-08-20 发布日期:2008-08-20
  • 基金资助:
    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).

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)   

  1. 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
  • Received:2007-11-23 Revised:2008-02-22 Online:2008-08-20 Published:2008-08-20
  • Supported by:
    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).

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摘要： 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.

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.

Key words: cellular automaton, traffic flow model, speed distribution, discrete time Markov chain

中图分类号:  (Granular models of complex systems; traffic flow)

  • 45.70.Vn
89.40.Bb (Land transportation)