Closed-Form Waiting Time Approximations for Polling Systems

TL;DR

This paper introduces simple closed-form approximations for mean waiting times in polling systems with renewal arrivals, applicable across all workloads, aiding system design and optimization in various industries.

Contribution

It presents the first closed-form approximations for polling systems with general renewal arrivals, based on heavy and light traffic limits.

Findings

Perform well across all workloads

Applicable to diverse application areas

First to provide such approximations for renewal arrivals

Abstract

A typical polling system consists of a number of queues, attended by a single server in a fixed order. The vast majority of papers on polling systems focusses on Poisson arrivals, whereas very few results are available for general arrivals. The current study is the first one presenting simple closed-form approximations for the mean waiting times in polling systems with renewal arrival processes, performing well for ALL workloads. The approximations are constructed using heavy traffic limits and newly developed light traffic limits. The closed-form approximations may prove to be extremely useful for system design and optimisation in application areas as diverse as telecommunication, maintenance, manufacturing and transportation.