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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Boxma, O., Foss, S., Lasgouttes, JM. et al. Waiting Time Asymptotics in the Single Server Queue with Service in Random Order. Queueing Systems 46, 35–73 (2004). https://doi.org/10.1023/B:QUES.0000021141.02821.6d
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DOI: https://doi.org/10.1023/B:QUES.0000021141.02821.6d