English

Heavy traffic limit for a processor sharing queue with soft deadlines

Probability 2009-09-29 v1

Abstract

This paper considers a GI/GI/1 processor sharing queue in which jobs have soft deadlines. At each point in time, the collection of residual service times and deadlines is modeled using a random counting measure on the right half-plane. The limit of this measure valued process is obtained under diffusion scaling and heavy traffic conditions and is characterized as a deterministic function of the limiting queue length process. As special cases, one obtains diffusion approximations for the lead time profile and the profile of times in queue. One also obtains a snapshot principle for sojourn times.

Keywords

Cite

@article{arxiv.0707.4600,
  title  = {Heavy traffic limit for a processor sharing queue with soft deadlines},
  author = {H. Christian Gromoll and Łukasz Kruk},
  journal= {arXiv preprint arXiv:0707.4600},
  year   = {2009}
}

Comments

Published at http://dx.doi.org/10.1214/105051607000000014 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

R2 v1 2026-06-21T09:03:25.591Z