A retrial system with two input streams and two orbit queues

TL;DR

This paper analyzes a complex queueing system with two input streams, orbit queues, and a shared buffer, deriving stability conditions and performance metrics using advanced probabilistic methods.

Contribution

It introduces a novel model of a two-stream retrial system with dependent queues and provides a comprehensive stability analysis and performance evaluation.

Findings

Derived necessary and sufficient stability conditions.

Calculated various performance measures.

Presented numerical results illustrating system behavior.

Abstract

Two independent Poisson streams of jobs flow into a single-server service system having a limited common buffer that can hold at most one job. If a type-i job (i=1,2) finds the server busy, it is blocked and routed to a separate type-i retrial (orbit) queue that attempts to re-dispatch its jobs at its specific Poisson rate. This creates a system with three dependent queues. Such a queueing system serves as a model for two competing job streams in a carrier sensing multiple access system. We study the queueing system using multi-dimensional probability generating functions, and derive its necessary and sufficient stability conditions while solving a boundary value problem. Various performance measures are calculated and numerical results are presented.