Stability analysis of two-class retrial systems with constant retrial rates and general service times

TL;DR

This paper develops stability criteria for a two-class retrial system with Poisson arrivals, general service times, and class-dependent constant retrial rates, revealing partial stability phenomena through theoretical analysis and numerical experiments.

Contribution

It introduces new stability conditions for two-class retrial systems with general service times and class-dependent retrial rates, including the phenomenon of partial stability.

Findings

Established stability criteria for the system.

Identified partial stability where one orbit remains tight and the other diverges.

Validated results with numerical experiments.

Abstract

We establish stability criterion for a two-class retrial system with Poisson inputs, general class-dependent service times and class-dependent constant retrial rates. We also characterise an interesting phenomenon of partial stability when one orbit is tight but the other orbit goes to infinity in probability. All theoretical results are illustrated by numerical experiments.