Excluded Volume Effect in Queueing Theory

Details Excluded Volume Effect in Queueing Theory Excluded Volume Effect in Queueing Theory

2010-01-23

arxiv.org/abs/1001.4124v1

JSIAM Letters, 2, pp. 61-64, 2010

Physics

Physics and Society

4 pages, 6 figures, Submitted to JSIAM Letters

Scientific paper

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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