Using a slight modification of the framework of Bramson [7] and Williams [54], we prove heavy traffic limit theorems for six families of multiclass queueing networks. The first three families are single-station systems operating under first-in-first-out (FIFO), generalized-head-of-the-line proportional processor sharing (GHLPPS) and static buffer priority (SBP) service disciplines. The next two families are reentrant lines that operate under first-buffer-first-serve (FBFS) and last-buffer-first-serve (LBFS) service disciplines; the last family consists of certain two-station, five-class networks operating under an SBP service discipline. Some of these heavy traffic limits have appeared earlier in the literature; our new proofs demonstrate the significant simplifications that can be achieved in the present setting.
@article{998926987,
author = {Bramson, Maury and Dai, J.G.},
title = {Heavy Traffic Limits for Some Queueing Networks},
journal = {Ann. Appl. Probab.},
volume = {11},
number = {2},
year = {2001},
pages = { 49-90},
language = {en},
url = {http://dml.mathdoc.fr/item/998926987}
}
Bramson, Maury; Dai, J.G. Heavy Traffic Limits for Some Queueing Networks. Ann. Appl. Probab., Tome 11 (2001) no. 2, pp. 49-90. http://gdmltest.u-ga.fr/item/998926987/