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Waiting time asymptotics in the single server queue with service in random order

Abstract : We consider the single server queue with service in random order. For a large class of heavy-tailed service time distributions, we determine the asymptotic behavior of the waiting time distribution. For the special case of Poisson arrivals and regularly varying service time distribution with index −ν, it is shown that the waiting time distribution is also regularly varying, with index 1 − ν, and the pre-factor is determined explicitly. Another contribution of the paper is the heavy-traffic analysis of the waiting time distribution in the M/G/1 case. We consider not only the case of finite service time variance, but also the case of regularly varying service time distribution with infinite variance.
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https://hal.inria.fr/hal-00719016
Contributor : Jean-Marc Lasgouttes <>
Submitted on : Wednesday, July 18, 2012 - 5:07:55 PM
Last modification on : Friday, May 25, 2018 - 12:02:03 PM
Long-term archiving on: : Friday, December 16, 2016 - 1:10:48 AM

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Onno Boxma, Serguei Foss, Jean-Marc Lasgouttes, Rudesindo Núñez Queija. Waiting time asymptotics in the single server queue with service in random order. Queueing Systems, Springer Verlag, 2004, 46 (1), pp.35-74. ⟨10.1023/B:QUES.0000021141.02821.6d⟩. ⟨hal-00719016⟩

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