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 JAMP  Vol.2 No.7 , June 2014
Analytical Solutions of Fukui-Ishibashi (FI) Model and Quick-Start (QS) Model
Abstract: Through straightforward deduction procedure, we explicitly show analytical solutions for both Fukui-Ishibashi (FI) model and Quick-Start (QS) model, which are fundamental deterministic Cellular Automaton (CA), applied to traffic flow.
Cite this paper: Kukida, S. , Tanimoto, J. , Ikegaya, N. and Hagishimaors, A. (2014) Analytical Solutions of Fukui-Ishibashi (FI) Model and Quick-Start (QS) Model. Journal of Applied Mathematics and Physics, 2, 691-697. doi: 10.4236/jamp.2014.27076.
References

[1]   Wolfram, S. (1986) Theory and Applications of Cellular Automata. World Scientific, Singapore.

[2]   Fukui, M. and Ishibashi, Y. (1996) Traffic Flow in 1D Cellular Automaton Model including Cars Moving with High Speed. Journal of the Physical Society of Japan, 65, 1868-1870.
http://dx.doi.org/10.1143/JPSJ.65.1868

[3]   Nagel, K. and Schreckenberg, M. (1992) A Cellular Automaton Model for Freeway Traffic. Journal de Physique I, 2, 2221. http://dx.doi.org/10.1051/jp1:1992277

[4]   Barlovic, R., Santen, L., Schadschneider, A. and Schreckenberg, M. (1998) Metastable State in Cellular Automata for Traffic Flow. European Physical Journal B, 5, 793-800.
http://dx.doi.org/10.1007/s100510050504

[5]   Nishinari, K. and Takahashi, D. (2000) Multi-Value Cellular Automaton Model for Freeway Traffic. Journal of Physics A, 33, 7709. http://dx.doi.org/10.1088/0305-4470/33/43/304

[6]   Sakai, S., Nishinari, K. and Iida, S. (2006) A New Stochastic Cellular Automaton Model on Traffic Flow and Its Jamming Phase Transition. Journal of Physics A: Mathematical and General, 39, 15327.
http://dx.doi.org/10.1088/0305-4470/39/50/002

[7]   Kokubo, S., Tanimoto, J. and Hagishima, A. (2011) A New Cellular Automata Model Including a Decelerating Damping Effect to Reproduce Kerner’s Three-Phase Theory. Physica A: Statistical Mechanics and Its Applications, 390, 561-568. http://dx.doi.org/10.1016/j.physa.2010.10.027

[8]   Kerner, B.S. and Klenov, S.L. (2009) Phase Transitions in Traffic Flow on Multilane Roads. Physical Review E, 80, Article ID: 056101. http://dx.doi.org/10.1103/PhysRevE.80.056101

[9]   Derrida, B., Evans, M.R., Hakim, V. and Pasquier, V. (1993) Exact Solution of a1D Asymmetric Exclusion Model Using a Matrix Formulation. Journal of Physics A: Mathematical and General, 26, 1493.
http://dx.doi.org/10.1088/0305-4470/26/7/011

[10]   O’Loan, O.J., Evans, M.R. and Cates, M.E. (1998) Jamming Transition in a Homogeneous One-Dimensional Systems: The Bus Route Model. Physical Review E, 58, 1404.
http://dx.doi.org/10.1103/PhysRevE.58.1404

[11]   Schadschneider, A. and Schreckenberg, M. (1993) Cellular Automaton Models and Traffic Flow, Journal of Physics A: Mathematical and General, 26, L679. http://dx.doi.org/10.1088/0305-4470/26/15/011

[12]   Klauck, K. and Shadshneider, A. (1999) On the Ubiquity of Matrix-Product States in One-Dimensional Stochastic Processes with Boundary Interactions. Physica A, 271, 102-117.
http://dx.doi.org/10.1016/S0378-4371(99)00176-4

 
 
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