The diffusion approximation of the Multiclass Processor Sharing queue
Probability
2025-04-30 v2
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.
Cite
@article{arxiv.2502.12824,
title = {The diffusion approximation of the Multiclass Processor Sharing queue},
author = {Mohamed Ghazali and Abdelghani Ben Tahar and Amal Ezzidani},
journal= {arXiv preprint arXiv:2502.12824},
year = {2025}
}