A Fluid Limit for Processor-Sharing Queues Weighted by Functions of Remaining Amounts of Service

TL;DR

This paper derives a fluid limit for a single-server queue with a processor-sharing policy weighted by functions of remaining service times, providing a mathematical foundation for analyzing such systems.

Contribution

It introduces a fluid limit for measure-valued descriptors in processor-sharing queues weighted by remaining service functions, advancing theoretical understanding.

Findings

Established a fluid limit for the weighted processor-sharing queue

Provided a measure-valued system description under scaling

Enhanced analytical tools for queue performance analysis

Abstract

We study a single server queue under a processor-sharing type of scheduling policy, where the weights for determining the sharing are given by functions of each job's remaining service(processing) amount, and obtain a fluid limit for the scaled measure-valued system descriptors.