Starting-wave and Optimal Density in a Queue

Akiyasu Tomoeda (), Daichi Yanagisawa (), Takashi Imamura () and Katsuhiro Nishinari ()
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Akiyasu Tomoeda: Meiji University, Meiji Institute for Advanced Study of Mathematical Sciences
Daichi Yanagisawa: Ibaraki University, College of Science
Takashi Imamura: The University of Tokyo, Research Center for Advanced Science and Technology
Katsuhiro Nishinari: The University of Tokyo, Research Center for Advanced Science and Technology

A chapter in Pedestrian and Evacuation Dynamics 2012, 2014, pp 1375-1383 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-02447-9_114

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DOI: 10.1007/978-3-319-02447-9_114

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