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The waiting time distribution for the random order service \(M/M/1\) queue. (English) Zbl 0883.60086

Summary: The M/M/1 queue is considered in the case in which customers are served in random order. A formula is obtained for the distribution of the waiting time \(w\) in the stationary state. The formula is used to show that \(P(w> t)\sim\alpha t^{-5/6}\exp(-\beta t-\gamma t^{1/3})\) as \(t\to\infty\), with the constants \(\alpha\), \(\beta\), and \(\gamma\) expressed as functions of the traffic intensity \(\rho\). The distribution of \(w\) for the random order discipline is compared to that of the first in, first out discipline.

MSC:

60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
30C20 Conformal mappings of special domains
30D20 Entire functions of one complex variable (general theory)
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