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 −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.
Domains
Probability [math.PR]
Origin : Files produced by the author(s)
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