In a state-dependent queueing network, arrival and service rates, as
well as routing probabilities, depend on the vector of queue lengths. For
properly normalized such networks, we derive functional laws of large numbers
(FLLNs) and functional central limit theorems (FCLTs). The former support fluid
approximations and the latter support diffusion refinements.
¶ The fluid limit in FLLN is the unique solution to a multidimensional
autonomous ordinary differential equation with state-dependent reflection. The
diffusion limit in FCLT is the unique strong solution to a stochastic
differential equation with time-dependent reflection.
¶ Examples are provided that demonstrate how such approximations
facilitate the design, analysis and optimization of various manufacturing,
service, communication and other systems.
Publié le : 1998-05-14
Classification:
Birth and death process,
state-dependent networks,
fluid and diffusion approximations,
weak convergence,
state- and time-dependent oblique reflection,
congestion-dependent routing,
learning systems,
multiserver systems,
large finite buffers,
transient analysis,
60F17,
60G17,
60J70,
60K25,
60K30,
68M20,
90B10,
90B22,
90B30,
90C33
@article{1028903539,
author = {Mandelbaum, Avi and Pats, Gennady},
title = {State-dependent stochastic networks. Part I. Approximations and
applications with continuous diffusion limits},
journal = {Ann. Appl. Probab.},
volume = {8},
number = {1},
year = {1998},
pages = { 569-646},
language = {en},
url = {http://dml.mathdoc.fr/item/1028903539}
}
Mandelbaum, Avi; Pats, Gennady. State-dependent stochastic networks. Part I. Approximations and
applications with continuous diffusion limits. Ann. Appl. Probab., Tome 8 (1998) no. 1, pp. 569-646. http://gdmltest.u-ga.fr/item/1028903539/