Waiting Time Asymptotics in the Single Server Queue with Service in Random Order

Authors:
O. J. Boxma;S. G. Foss;J. -M. Lasgouttes;R. Queija
Affiliations:
Department of Mathematics & Computer Science and EURANDOM, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands, and CWI, P.O. Box 94079, 1090 GB Amsterdam, The ...;Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS UK;INRIA, Domaine de Voluceau, Rocquencourt, B.P. 105, 78153 Le Chesnay Cedex, France;Department of Mathematics & Computer Science and EURANDOM, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands, and CWI, P.O. Box 94079, 1090 GB Amsterdam, The ...
Venue:
Queueing Systems: Theory and Applications
Year:
2004

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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.