A queueing model has J≥2 heterogeneous service stations, each consisting of many independent servers with identical capabilities. Customers of I≥2 classes can be served at these stations at different rates, that depend on both the class and the station. A system administrator dynamically controls scheduling and routing. We study this model in the central limit theorem (or heavy traffic) regime proposed by Halfin and Whitt. We derive a diffusion model on ℝI with a singular control term that describes the scaling limit of the queueing model. The singular term may be used to constrain the diffusion to lie in certain subsets of ℝI at all times t>0. We say that the diffusion is null-controllable if it can be constrained to $\mathbb {X}_{-}$ , the minimal closed subset of ℝI containing all states of the prelimit queueing model for which all queues are empty. We give sufficient conditions for null controllability of the diffusion. Under these conditions we also show that an analogous, asymptotic result holds for the queueing model, by constructing control policies under which, for any given 0<ɛ
Publié le : 2006-11-14
Classification:
Multiclass queueing systems,
heavy traffic,
scheduling and routing,
singular control of diffusions,
null controllability,
60K25,
68M20,
90B22,
90B36,
60F05,
49N25
@article{1169065207,
author = {Atar, Rami and Mandelbaum, Avi and Shaikhet, Gennady},
title = {Queueing systems with many servers: Null controllability in heavy traffic},
journal = {Ann. Appl. Probab.},
volume = {16},
number = {1},
year = {2006},
pages = { 1764-1804},
language = {en},
url = {http://dml.mathdoc.fr/item/1169065207}
}
Atar, Rami; Mandelbaum, Avi; Shaikhet, Gennady. Queueing systems with many servers: Null controllability in heavy traffic. Ann. Appl. Probab., Tome 16 (2006) no. 1, pp. 1764-1804. http://gdmltest.u-ga.fr/item/1169065207/