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Heavy traffic analysis for continuous polling models

Part of: Special processes Stochastic analysis Operations research and management science Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Dirk P. Kroese
Dirk P. Kroese*
Affiliation:
University of Twente
*
∗Postal address: Faculty of Applied Mathematics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands.
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Abstract

We consider a continuous polling system in heavy traffic. Using the relationship between such systems and age-dependent branching processes, we show that the steady-state number of waiting customers in heavy traffic has approximately a gamma distribution. Moreover, given their total number, the configuration of these customers is approximately deterministic.

Keywords

QUEUEING THEORYCONTINUOUS POLLING SYSTEMHEAVY TRAFFICQUEUE LENGTHAGE-DEPENDENT BRANCHING PROCESSEXPONENTIAL APPROXIMATIONGAMMA APPROXIMATIONRANDOM MEASUREGENERATING FUNCTION

MSC classification

Primary: 60K25: Queueing theory 90B22: Queues and service 60G55: Point processes
Secondary: 60G57: Random measures 60H05: Stochastic integrals
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 3 , September 1997 , pp. 720 - 732
Copyright
Copyright © Applied Probability Trust 1997 

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