Flatto, L. The waiting time distribution for the random order service \(M/M/1\) queue. (English) Zbl 0883.60086 Ann. Appl. Probab. 7, No. 2, 382-409 (1997). 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. Cited in 1 ReviewCited in 21 Documents 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) Keywords:queue; random order service discipline; waiting time distribution; Little’s law PDFBibTeX XMLCite \textit{L. Flatto}, Ann. Appl. Probab. 7, No. 2, 382--409 (1997; Zbl 0883.60086) Full Text: DOI