The diffusion approximation of the Multiclass Processor Sharing queue

TL;DR

This paper develops a diffusion approximation for a complex multiclass processor-sharing queue with feedback, providing insights into its behavior under heavy traffic with general service time distributions.

Contribution

It introduces a novel diffusion approximation for a measure-valued process in a multiclass queue with feedback, extending prior models to more general settings.

Findings

Diffusion approximation accurately models the queue under heavy traffic.

The approach handles general service time distributions.

Provides a foundation for analyzing complex queueing systems.

Abstract

This paper considers a multiclass processor-sharing queue with feedback. Jobs arrive according to renewal processes, and service times follow general distributions. Upon service completion, jobs may either depart the system or re-enter as a different class according to a probabilistic, Jackson-like routing mechanism. Under heavy-traffic conditions, we establish a diffusion approximation for a measure-valued process tracking the residual service times of jobs.