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March 2014 Random fluid limit of an overloaded polling model
Maria Remerova, Sergey Foss, Bert Zwart
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Adv. in Appl. Probab. 46(1): 76-101 (March 2014). DOI: 10.1239/aap/1396360104

Abstract

In the present paper, we study the evolution of an overloaded cyclic polling model that starts empty. Exploiting a connection with multitype branching processes, we derive fluid asymptotics for the joint queue length process. Under passage to the fluid dynamics, the server switches between the queues infinitely many times in any finite time interval causing frequent oscillatory behavior of the fluid limit in the neighborhood of zero. Moreover, the fluid limit is random. In addition, we suggest a method that establishes finiteness of moments of the busy period in an M/G/1 queue.

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Maria Remerova. Sergey Foss. Bert Zwart. "Random fluid limit of an overloaded polling model." Adv. in Appl. Probab. 46 (1) 76 - 101, March 2014. https://doi.org/10.1239/aap/1396360104

Information

Published: March 2014
First available in Project Euclid: 1 April 2014

zbMATH: 1292.60093
MathSciNet: MR3189049
Digital Object Identifier: 10.1239/aap/1396360104

Subjects:
Primary: 60F17 , 60K25
Secondary: 90B15 , 90B22

Keywords: branching process , busy period moment , Cyclic polling , multi-stage gated discipline , overload , random fluid limit

Rights: Copyright © 2014 Applied Probability Trust

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Vol.46 • No. 1 • March 2014
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