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arXiv · 2502.12824

The diffusion approximation of the Multiclass Processor Sharing queue

Mohamed Ghazali·Abdelghani Ben Tahar·Amal Ezzidani
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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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Mohamed Ghazali, Abdelghani Ben Tahar, Amal Ezzidani. 2025-02-18. The diffusion approximation of the Multiclass Processor Sharing queue. https://arxiv.org/abs/2502.12824

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