Conditions for stability and instability of retrial queueing systems with general retrial times

TL;DR

This paper investigates the stability conditions of single server retrial queueing systems with general retrial time distributions, analyzing three main policies using renovating events and convergence methods.

Contribution

It provides new sufficient stability and instability conditions for retrial queues with general retrial times under various policies, extending existing theoretical frameworks.

Findings

Derived stability conditions for classical, constant, and control retrial policies.

Established instability criteria via convergence to improper limits.

Applied renovating events approach for analyzing queue dynamics.

Abstract

We study the stability of single server retrial queues under general distribution for retrial times and stationary ergodic service times, for three main retrial policies studied in the literature: classical linear, constant and control policies. The approach used is the renovating events approach to obtain sufficient stability conditions by strong coupling convergence of the process modeling the dynamics of the system to a unique stationary ergodic regime. We also obtain instability conditions by convergence in distribution to improper limiting sequences.