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February 2001 Heavy Traffic Limits for Some Queueing Networks
Maury Bramson, J.G. Dai
Ann. Appl. Probab. 11(1): 49-90 (February 2001). DOI: 10.1214/aoap/998926987

Abstract

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.

Citation

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Maury Bramson. J.G. Dai. "Heavy Traffic Limits for Some Queueing Networks." Ann. Appl. Probab. 11 (1) 49 - 90, February 2001. https://doi.org/10.1214/aoap/998926987

Information

Published: February 2001
First available in Project Euclid: 27 August 2001

zbMATH: 1016.60084
MathSciNet: MR1825460
Digital Object Identifier: 10.1214/aoap/998926987

Subjects:
Primary: 60F17 , 60G17 , 60K25
Secondary: 60J15 , 68M20 , 90B22

Keywords: Brownian model , diffusion approximation , heavy traffic , Multiclass queueing network , Reflecting Brownian motion

Rights: Copyright © 2001 Institute of Mathematical Statistics

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Vol.11 • No. 1 • February 2001
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