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August, 1993 Parallel and Tandem Fluid Networks with Dependent Levy Inputs
Offer Kella
Ann. Appl. Probab. 3(3): 682-695 (August, 1993). DOI: 10.1214/aoap/1177005358

Abstract

A group of stations in parallel is considered, where the input processes to the various stations are stochastically dependent nondecreasing Levy processes and the release rates are deterministic linear flows. It is shown that the model of a tandem fluid network, with dependent or independent Levy inputs to the stations, can be seen as a special case of this construction. In addition to other natural applications, the joint stochastic structure of the workload processes of the different classes in a preemptive resume priority M/G/1 queue can be viewed as a special case of the model considered. Using martingale and regenerative arguments, certain steady state characteristics are studied.

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Offer Kella. "Parallel and Tandem Fluid Networks with Dependent Levy Inputs." Ann. Appl. Probab. 3 (3) 682 - 695, August, 1993. https://doi.org/10.1214/aoap/1177005358

Information

Published: August, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0780.60072
MathSciNet: MR1233620
Digital Object Identifier: 10.1214/aoap/1177005358

Subjects:
Primary: 60J30
Secondary: 60K25 , 60K30

Keywords: fluid models , generalized Pollaczek-Khinchine formula , Levy process , M/G/1 queue , martingale , multi-dimensional Levy process , Queueing networks , queues , reflected Levy process , storage networks

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.3 • No. 3 • August, 1993
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