A two-class queueing system with constant retrial policy and general class dependent service times

TL;DR

This paper analyzes a two-class retrial queueing system with general class-dependent service times, deriving the stationary distribution's generating function and explicit delay expressions, and illustrating system performance through a numerical example.

Contribution

It introduces a novel analysis of a two-class retrial queue with class-dependent service times, deriving explicit formulas and solving a boundary value problem.

Findings

Derived the generating function of the stationary distribution.

Obtained explicit delay expressions for symmetrical systems.

Provided a numerical example illustrating system performance.

Abstract

A single server retrial queueing system with two-classes of orbiting customers, and general class dependent service times is considered. If an arriving customer finds the server unavailable, it enters a virtual queue, called the orbit, according to its type. The customers from the orbits retry independently to access the server according to the constant retrial policy. We derive the generating function of the stationary distribution of the number of orbiting customers at service completion epochs in terms of the solution of a Riemann boundary value problem. For the symmetrical system we also derived explicit expressions for the expected delay in an orbit without solving a boundary value problem. A simple numerical example is obtained to illustrate the system's performance.