Product Forms for FCFS Queueing Models with Arbitrary Server-Job Compatibilities: An Overview

TL;DR

This paper surveys product form results for FCFS queueing models with arbitrary server-job compatibilities, highlighting their derivation from order independent queues and applications to steady-state response time distributions.

Contribution

It provides a comprehensive overview of product form models with arbitrary compatibilities and connects these results to order independent queues, enhancing understanding of their steady-state behavior.

Findings

Many models have product form stationary distributions under Markov assumptions.

Results for these models are often corollaries of order independent queue results.

Product form solutions facilitate the analysis of steady-state response times.

Abstract

In recent years a number of models involving different compatibilities between jobs and servers in queueing systems, or between agents and resources in matching systems, have been studied, and, under Markov assumptions and appropriate stability conditions, the stationary distributions have been shown to have product forms. We survey these results and show how, under an appropriate detailed description of the state, many are corollaries of similar results for the Order Independent Queue. We also discuss how to use the product form results to determine distributions for steady-state response times.