A Public Conveyance Model and Analysis on Clustering of Vehicles

  • Akiyasu Tomoeda
  • Katsuhiro Nishinari
  • Debashish Chowdhury
  • Andreas Schadschneider
Conference paper


A new Public Conveyance Model (PCM) applicable to buses and trains is proposed in this study by using stochastic cellular automaton. We apply our PCM to the bus system and measure the efficiency of the system. By using mean field analysis, we estimate the average velocity and the waiting passengers in the low density limit. We have obtained the theoretical results which are in good agreement with numerical simulations. It is also observed clustering of vehicles which is caused by the time delay effect of passengers when they get on a vehicle. We have found that the big cluster of vehicles is divided into small clusters, by incorporating information of the number of vehicles between successive stops.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    B. Schmittmann and R.K.P. Zia, in: Phase Transition and Critical Phenomena, Vol. 17, eds. C. Domb and J.L. Lebowitz (Academic Press 1995). Google Scholar
  2. 2.
    B. Derrida, Phys. Rep. 301, 65 (1998). CrossRefMathSciNetGoogle Scholar
  3. 3.
    G.M. Schütz, in Phase Transitions and Critical Phenomena, vol. 19 (Acad. Press, 2001). Google Scholar
  4. 4.
    D. Chowdhury, L. Santen and A. Schadschneider, Phys. Rep. 329, 199 (2000). CrossRefMathSciNetGoogle Scholar
  5. 5.
    D. Helbing, Rev. Mod. Phys. 73, 1067 (2001). CrossRefGoogle Scholar
  6. 6.
    A. Schadschneider, Physica A 313, 153 (2002). zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    T. Nagatani, Rep. Prog. Phys. 65, 1331 (2002). CrossRefGoogle Scholar
  8. 8.
    D. Chowdhury, K. Nishinari, L. Santen and A. Schadschneider, Stochastic Transport in Complex Systems, Elsevier (2008). Google Scholar
  9. 9.
    O.J. O’Loan, M.R. Evans and M.E. Cates, Phys. Rev. E 58, 1404 (1998). CrossRefGoogle Scholar
  10. 10.
    R. Jiang, B. Jia and Q.S. Wu, J. Phys. A: Math. Gen. 37, 2063 (2004). zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    A. Tomoeda, K. Nishinari, D. Chowdhury and A. Schadschneider, Physica A 384, 600 (2007). CrossRefGoogle Scholar
  12. 12.
    D. Chowdhury, V. Guttal, K. Nishinari and A. Schadschneider, J. Phys. A: Math. Gen. 35, L573 (2002). zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    A. Kunwar, A. John, K. Nishinari, A. Schadschneider and D. Chowdhury, J. Phys. Soc. Jpn. 73, 2979 (2004). zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Akiyasu Tomoeda
    • 1
  • Katsuhiro Nishinari
    • 1
  • Debashish Chowdhury
    • 2
  • Andreas Schadschneider
    • 3
  1. 1.Department of Aeronautics and AstronauticsUniversity of TokyoBunkyoJapan
  2. 2.Department of PhysicsIndian Institute of TechnologyKanpurIndia
  3. 3.Institut für Theoretische PhysikUniversität zu KölnKölnGermany

Personalised recommendations