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

Onno Boxma; Sergey Foss; Jean-Marc Lasgouttes; Rudesindo Núñez Queija

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arXiv · 1207.4449

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

Onno Boxma·Sergey Foss·Jean-Marc Lasgouttes·Rudesindo Núñez Queija

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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 -\nu, it is shown that the waiting time distribution is also regularly varying, with index 1 -\nu, 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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BibTeX RIS

Onno Boxma, Sergey Foss, Jean-Marc Lasgouttes, Rudesindo Núñez Queija. 2012-07-18. Waiting time asymptotics in the single server queue with service in random order. https://arxiv.org/abs/1207.4449

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