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May 1997 The waiting time distribution for the random order service $M/M/1$ queue
L. Flatto
Ann. Appl. Probab. 7(2): 382-409 (May 1997). DOI: 10.1214/aoap/1034625337


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 $P9w > t) \sim \alpha t^{-5/6} \exp (-\beta t - \gamma t^{1/3})$ 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.


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L. Flatto. "The waiting time distribution for the random order service $M/M/1$ queue." Ann. Appl. Probab. 7 (2) 382 - 409, May 1997.


Published: May 1997
First available in Project Euclid: 14 October 2002

zbMATH: 0883.60086
MathSciNet: MR1442319
Digital Object Identifier: 10.1214/aoap/1034625337

Primary: 60K25 , 90B22
Secondary: 30C20 , 30D20 , 44R10

Keywords: $M/M/1$ queue , Little's law , random order service discipline , waiting time distribution

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.7 • No. 2 • May 1997
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