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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

Abstract

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)αt5/6exp(βtγt1/3) as t, with the constants α,β, and γ expressed as functions of the traffic intensity ρ. The distribution of w for the random order discipline is compared to that of the first in, first out discipline.

Citation

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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. https://doi.org/10.1214/aoap/1034625337

Information

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

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

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

Keywords: 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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