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Starting-wave and Optimal Density in a Queue

  • Akiyasu Tomoeda
  • Daichi Yanagisawa
  • Takashi Imamura
  • Katsuhiro Nishinari
Conference paper

Abstract

We have investigated the fundamental relation between the density and the propagation speed of starting-wave, which is a wave of people’s successive reaction in a relaxation process of a queue, by both our mathematical model built on the stochastic cellular automata and experimental measurements. The analysis of our mathematical model implies that the relation is well approximated by power law a = αρ β (β ≠ 1) and the experimental results verify this feature. Moreover, when the starting-wave is characterized by power law (β ≠ 1), we have revealed the existence of optimal density, where the required time which is sum of the waiting time until the starting-wave reaches and the travel time of last pedestrians in a queue to pass the head position of the initial queue is minimized. This optimal density inevitably plays a significant role to achieve a smooth movement of crowds and vehicles in a queue.

Keywords

Jamology Stochastic cellular automaton Queuing system Starting-wave Optimization problem 

Notes

Acknowledgments

We thank Kozo Keikaku Engineering Inc. in Japan and the members of the Meiji University Global COE Program “Formation and Development of Mathematical Sciences Based on Modeling and Analysis” for the assistance of the experiments, which is described in Sect. 3. We also acknowledge the support of Japan Society for the Promotion of Science and Japan Science and Technology Agency.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Akiyasu Tomoeda
    • 1
    • 2
  • Daichi Yanagisawa
    • 3
  • Takashi Imamura
    • 4
  • Katsuhiro Nishinari
    • 4
    • 5
  1. 1.Meiji Institute for Advanced Study of Mathematical SciencesMeiji UniversityKawasakiJapan
  2. 2.JST CRESTKawasakiJapan
  3. 3.College of ScienceIbaraki UniversityMitoJapan
  4. 4.Research Center for Advanced Science and TechnologyThe University of TokyoMeguro-kuJapan
  5. 5.Department of Aeronautics and Astronautics, School of EngineeringThe University of TokyoBunkyo-kuJapan

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