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PreprintCC BY 4.0arXiv

Fluid and Diffusion Approximation of a Multiclass Proportional Processor Sharing Queue with Reneging and General Distributions

  • Eva Loeser
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Abstract

In this paper, we resolve the long open problem of the diffusion approximation for a generally distributed processor sharing queue with reneging. In particular, we first extend the known fluid limit for a single class processor sharing queue with reneging to the multiclass proportional processor sharing queue with reneging. We prove uniqueness of fluid model solutions and convergence of fluid scaled models to fluid model solutions. Next, we show that, under diffusion-scaling, the models are tight, and that subsequential limits can be uniquely characterized by a certain system of SDEs driven by a Gaussian sheet on R+2 with a nontrivial covariation structure.

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Cite

BibTeXRIS
BibTeX
@misc{loeser2026fluid,
  title = {{Fluid and Diffusion Approximation of a Multiclass Proportional Processor Sharing Queue with Reneging and General Distributions}},
  author = {Eva Loeser},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.06616},
  eprint = {2609.06616},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06616},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Fluid and Diffusion Approximation of a Multiclass Proportional Processor Sharing Queue with Reneging and General Distributions
AU  - Eva Loeser
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.06616
UR  - https://arxiv.org/abs/2609.06616
AB  - In this paper, we resolve the long open problem of the diffusion approximation for a generally distributed processor sharing queue with reneging. In particular, we first extend the known fluid limit for a single class processor sharing queue with reneging to the multiclass proportional processor sharing queue with reneging. We prove uniqueness of fluid model solutions and convergence of fluid scaled models to fluid model solutions. Next, we show that, under diffusion-scaling, the models are tight, and that subsequential limits can be uniquely characterized by a certain system of SDEs driven by a Gaussian sheet on R_+^2 with a nontrivial covariation structure.
ER  -