Heavy traffic limit for a processor sharing queue with soft deadlines

Details Heavy traffic limit for a processor sharing queue with soft deadlines Heavy traffic limit for a processor sharing queue with soft deadlines

2007-07-31

arxiv.org/abs/0707.4600v1

Annals of Applied Probability 2007, Vol. 17, No. 3, 1049-1101

Mathematics

Probability

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

Scientific paper

10.1214/105051607000000014

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.

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