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 -\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.
Keywords
Cite
@article{arxiv.1207.4449,
title = {Waiting time asymptotics in the single server queue with service in random order},
author = {Onno Boxma and Sergey Foss and Jean-Marc Lasgouttes and Rudesindo Núñez Queija},
journal= {arXiv preprint arXiv:1207.4449},
year = {2017}
}
Comments
single server queue;service in random order;heavy-tailed distribution;waiting time asymptotics;heavy-traffic limit theorem