JSIAM Letters
Online ISSN : 1883-0617
Print ISSN : 1883-0609
Articles
Excluded volume effect in queueing theory
Daichi YanagisawaAkiyasu TomoedaRui JiangKatsuhiro Nishinari
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Volume 2 (2010) Pages 61-64

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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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© 2010 The Japan Society for Industrial and Applied Mathematics
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