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Queueing Systems 46, 1 (2004) 35-74
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Waiting time asymptotics in the single server queue with service in random order
Onno Boxma1, 2, Serguei Foss3, Jean-Marc Lasgouttes4, Rudesindo Núñez Queija2

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.
1 :  Department of mathematics and computing science [Eindhoven]
2 :  CWI - Centrum voor Wiskunde en Informatica
3 :  Department of Actuarial Mathematics and Statistics [Edinburgh]
4 :  INRIA Rocquencourt - PREVAL