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.

single server queue;service in random order;heavy-tailed distribution;waiting time asymptotics;heavy-traffic limit theorem