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.
@article{1179839182,
author = {Gromoll, H. Christian and Kruk, \L ukasz},
title = {Heavy traffic limit for a processor sharing queue with soft deadlines},
journal = {Ann. Appl. Probab.},
volume = {17},
number = {1},
year = {2007},
pages = { 1049-1101},
language = {en},
url = {http://dml.mathdoc.fr/item/1179839182}
}
Gromoll, H. Christian; Kruk, Łukasz. Heavy traffic limit for a processor sharing queue with soft deadlines. Ann. Appl. Probab., Tome 17 (2007) no. 1, pp. 1049-1101. http://gdmltest.u-ga.fr/item/1179839182/