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.
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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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Tomoeda, A., Yanagisawa, D., Imamura, T., Nishinari, K. (2014). Starting-wave and Optimal Density in a Queue. In: Weidmann, U., Kirsch, U., Schreckenberg, M. (eds) Pedestrian and Evacuation Dynamics 2012. Springer, Cham. https://doi.org/10.1007/978-3-319-02447-9_114
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DOI: https://doi.org/10.1007/978-3-319-02447-9_114
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