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Random Fluid Limit of an Overloaded Polling Model

Part of: Limit theorems Special processes Operations research and management science

Published online by Cambridge University Press:  22 February 2016

Maria Remerova ,
Sergey Foss  and
Bert Zwart
Maria Remerova*
Affiliation:
CWI
Sergey Foss*
Affiliation:
Heriot-Watt University and Sobolev Institute of Mathematics
Bert Zwart*
Affiliation:
CWI, EURANDOM, VU University Amsterdam and Georgia Institute of Technology
*
∗ Current address: Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands. Email address: m.remerova@tue.nl
∗∗ Postal address: Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh EH14 4AS, UK.
∗ Current address: Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands. Email address: m.remerova@tue.nl
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Abstract

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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.

Keywords

Cyclic pollingoverloadrandom fluid limitbranching processmulti-stage gated disciplinebusy period moment

MSC classification

Primary: 60K25: Queueing theory 60F17: Functional limit theorems; invariance principles
Secondary: 90B15: Network models, stochastic 90B22: Queues and service
Type
Research Article
Information
Advances in Applied Probability , Volume 46 , Issue 1 , March 2014 , pp. 76 - 101
Copyright
© Applied Probability Trust 

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