Excluded volume effect in a pedestrian queue

  • Authors:

  • Daichi Yanagisawa;Yuki Tanaka;Rui Jiang;Akiyasu Tomoeda;Kazumichi Ohtsuka;Yushi Suma;Katsuhiro Nishinari

  • Affiliations:

  • School of Engineering, The University of Tokyo, Japan and JSPS Research Fellow, Japan;School of Engineering, The University of Tokyo, Japan;School of Engineering Science, Univ. of Science and Technology of China, China;Meiji Institute for Advanced Study of Mathematical Sciences, Meiji Univ., Japan;Research Center for Advanced Science and Technology, Univ. of Tokyo, Japan;School of Engineering, The University of Tokyo, Japan;Research Center for Advanced Science and Technology, Univ. of Tokyo, Japan and PRESTO, Japan Science and Technology Agency, Japan and School of Engineering, The University of Tokyo, Japan

  • Venue:
  • ACRI'10 Proceedings of the 9th international conference on Cellular automata for research and industry
  • Year:
  • 2010

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Abstract

We have introduced excluded volume effect, which is a significant factor to model a realistic pedestrian queue, into queueing theory. The model has been exactly solved. Concretely, probability distributions and means of the number of waiting pedestrians, length of a queue, and waiting time have been derived. Due to the excluded volume effect, the process of closing up is included in our new model, so that the mean number of pedestrians increases as pedestrian arrival probability (λ) and leaving probability (µ) increase even if the ratio between them (i.e., ρ = λ/µ) remains constant. Moreover, interval distance between pedestrians is included in our model because of the excluded volume effect, thus, length of a queue is considered more realistically than previous model. A queueing experiment is also performed to verify the validity of our model.