Tail Asymptotics for a Retrial Queue with Bernoulli Schedule

TLDR: In this article , the authors studied the asymptotic behavior of the tail probability of the number of customers in the steady-state M/G/1 retrial queue with Bernoulli schedule, under the assumption that the service time distribution has a regularly varying tail.

Abstract: In this paper, we study the asymptotic behaviour of the tail probability of the number of customers in the steady-state M/G/1 retrial queue with Bernoulli schedule, under the assumption that the service time distribution has a regularly varying tail. Detailed tail asymptotic properties are obtained for the conditional probability of the number of customers in the (priority) queue and orbit, respectively, in terms of the recently proposed exhaustive stochastic decomposition approach. Numerical examples are presented to show the impacts of system parameters on the tail asymptotic probabilities.