Excluded volume effect in queueing theory
Excluded volume effect in queueing theory
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DOI：
10.14495/jsiaml.2.61
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发表时间：
2010-01
期刊：
影响因子：
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通讯作者：
D. Yanagisawa;A. Tomoeda;R. Jiang;K. Nishinari
中科院分区：
文献类型：
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作者：
D. Yanagisawa;A. Tomoeda;R. Jiang;K. Nishinari
我们引入了排斥体积效应，这是一个重要的因素来模拟一个现实的行人排队，排队理论。精确地计算了行人排队人数和行人等待时间的概率分布。由于关闭队列所需的时间，行人的平均数量随着行人到达概率（λ）和离开概率（μ）的增加而增加，即使它们之间的比率（即，ρ = λ/μ）保持恒定。此外，在给定ρ的情况下，平均等待时间并不随服务时间单调增加（与μ成反比），而是可以达到最小值。
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 (λ) and leaving probability (μ) increase even if the ratio between them (i.e., ρ = λ/μ) remains constant. Furthermore, at a given ρ, the mean waiting time does not increase monotonically with the service time (which is inverse to μ), a minimum could be reached instead.