The diffusion approximation of the Multiclass Processor Sharing queue

2025/02/18 by Ghazali, Mohamed, Tahar, Abdelghani Ben, Ezzidani, Amal
#60K25 #68M20 #90B22 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2502.12824

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.

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