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Simulation of bi-direction pedestrian movement using a cellular automata model. (English) Zbl 1011.90011
Summary: A cellular automata model is presented to simulate the bi-direction pedestrian movement. The pedestrian movement is more complex than vehicular flow for the reason that people are more flexible than cars. Some special technique is introduced considering simple human judgment to make the rules more reasonable. Also the custom in the countries where the pedestrian prefer to walk on the right-hand side of the road are highlighted. By using the model to simulate the bi-direction pedestrian movement, the phase transition phenomena in pedestrian counter flow is presented. Furthermore, the introduction of back stepping breaks the deadlock at the relatively low pedestrian density. By studying the critical density of changing from freely moving state to jammed state with different system sizes and different probabilities of back stepping, we find the critical density increases as the probability of back stepping increases at the same system size. And with the increasing system size, the critical density decreases at the same probability of back stepping according to the scope of system size studied in this paper.

90B20Traffic problems
82C32Neural nets (statistical mechanics)
Full Text: DOI
[1] D.E. Wolf, M. Schreckenberg, A. Bachem (Eds.), Traffic and Granular Flow, World Scientific, Singapore, 1996.
[2] Helbing, D.: Verkehrsdynamik. (1997)
[3] M. Schreckenberg, D.E. Wolf (Eds.), Traffic and Granular Flow ’97, Springer, Berlin, 1998.
[4] D. Helbing, H.J. Herrmann, M. Schreckenberg, D.E. Wolf (Eds.), Traffic and Granular Flow ’99, Springer, Berlin, 2000. · Zbl 0942.00072
[5] Schreckenberg, M.; Schadschneider, A.; Nagatani, T.; Ito, N.: Phys. rev. E. 51, 2939 (1995)
[6] Wolf, D. E.: Physica A. 263, 438 (1999)
[7] Schadschneider, A.: Physica A. 285, 101 (2000)
[8] Kerner, B. S.; Rehborn, H.: Phys. rev. E. 53, R1297 (1996)
[9] Kerner, B. S.; Rehborn, H.: Phys. rev. E. 53, R4275 (1996)
[10] B.S. Kerner, in: M. Schreckenberg, D.E. Wolf (Eds.), Traffic and Granular Flow ’97, Springer, Singapore, 1998.
[11] Wolfram, S.: Theory and applications of cellular automata. (1986) · Zbl 0609.68043
[12] Wolfram, S.: Cellular automata and complexity. (1994) · Zbl 0823.68003
[13] Kai, N.; Michael, S.: J. phys. I. 2, No. 12, 2221 (1992)
[14] Fukui, M.; Ishibashi, Y.: J. phys. Soc. Japan. 65, No. 6, 1868 (1996)
[15] Biham, O.; Middelton, A. A.; Levine, D. A.: Phys. rev. A. 46, R6124 (1992)
[16] Cuesta, J. A.; Matinez, F. C.; Molera, J. M.; Sanchez, A.: Phys. rev. E. 48, 4175 (1993)
[17] Nagatani, T.: Phys. rev. E. 48, 3290 (1993)
[18] Chung, K. H.; Hui, P. M.; Gu, G. Q.: Phys. rev. E. 51, 772 (1995)
[19] Burstedde, C.; Klauck, K.; Schadschneider, A.; Zittartz, J.: Physica A. 295, 507 (2001) · Zbl 0978.90018
[20] Helbing, D.; Farkas, L.; Vicsek, T.: Nature. 407, No. 28, 487 (2000)
[21] Blue, V. J.; Adler, J. L.: Transp. res. Part B. 35, 293 (2001)
[22] Muramatsu, M.; Irie, T.; Nagatani, T.: Physica A. 267, 487 (1999)
[23] Muramatsu, M.; Nagatani, T.: Physica A. 275, 281 (2000) · Zbl 1052.90530
[24] Muramatsu, M.; Nagatani, T.: Physica A. 286, 377 (2000) · Zbl 1052.90530
[25] Tajima, Y.; Nagatani, T.: Physica A. 292, 545 (2000)
[26] Tajima, Y.; Takimoto, K.; Nagatani, T.: Physica A. 294, 257 (2000) · Zbl 0978.90016