Tail Asymptotics for a Retrial Queue with Bernoulli Schedule

TL;DR

This paper analyzes the tail behavior of customer numbers in a steady-state M/G/1 retrial queue with Bernoulli scheduling, focusing on cases where service times have regularly varying tails, providing detailed asymptotic results.

Contribution

It offers new tail asymptotic results for the queue's customer count distributions under regularly varying service times, extending previous analyses.

Findings

Derived asymptotic tail probabilities for queue, orbit, and system

Identified conditions under which tail behavior follows regular variation

Provided detailed asymptotic formulas for various queue states

Abstract

In this paper, we study 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. Detailed tail asymptotic properties are obtained for the (conditional and unconditional) probability of the number of customers in the (priority) queue, orbit and system, respectively.