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May 1998 State-dependent stochastic networks. Part I. Approximations and applications with continuous diffusion limits
Avi Mandelbaum, Gennady Pats
Ann. Appl. Probab. 8(2): 569-646 (May 1998). DOI: 10.1214/aoap/1028903539

Abstract

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.

Citation

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Avi Mandelbaum. Gennady Pats. "State-dependent stochastic networks. Part I. Approximations and applications with continuous diffusion limits." Ann. Appl. Probab. 8 (2) 569 - 646, May 1998. https://doi.org/10.1214/aoap/1028903539

Information

Published: May 1998
First available in Project Euclid: 9 August 2002

zbMATH: 0945.60025
MathSciNet: MR1624965
Digital Object Identifier: 10.1214/aoap/1028903539

Subjects:
Primary: 60F17 , 60G17 , 60J70 , 60K25 , 60K30
Secondary: 68M20 , 90B10 , 90B22 , 90B30 , 90C33

Keywords: birth and death process , congestion-dependent routing , fluid and diffusion approximations , large finite buffers , learning systems , multiserver systems , state- and time-dependent oblique reflection , state-dependent networks , transient analysis , weak convergence

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.8 • No. 2 • May 1998
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