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arXiv · 1001.4124

Excluded Volume Effect in Queueing Theory

Daichi Yanagisawa·Akiyasu Tomoeda·Rui Jiang·Katsuhiro Nishinari
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Abstract

We have introduced excluded volume effect, which is an important factor to model a realistic pedestrian queue, into queueing theory. The probability distributions of pedestrian number and pedestrian waiting time in a queue have been calculated exactly. Due to time needed to close up the queue, the mean number of pedestrians increases as pedestrian arrival probability ($\lambda$) and leaving probability ($\mu$) increase even if the ratio between them (i.e., $\rho=\lambda/\mu$) remains constant. Furthermore, at a given $\rho$, the mean waiting time does not increase monotonically with the service time (which is inverse to $\mu$), a minimum could be reached instead.

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Daichi Yanagisawa, Akiyasu Tomoeda, Rui Jiang, Katsuhiro Nishinari. 2010-01-23. Excluded Volume Effect in Queueing Theory. https://arxiv.org/abs/1001.4124

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