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A polling model with reneging at polling instants

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  • M. Boon

Abstract

In this paper we consider a single-server, cyclic polling system with switch-over times and Poisson arrivals. The service disciplines that are discussed, are exhaustive and gated service. The novel contribution of the present paper is that we consider the reneging of customers at polling instants. In more detail, whenever the server starts or ends a visit to a queue, some of the customers waiting in each queue leave the system before having received service. The probability that a certain customer leaves the queue, depends on the queue in which the customer is waiting, and on the location of the server. We show that this system can be analysed by introducing customer subtypes, depending on their arrival periods, and keeping track of the moment when they abandon the system. In order to determine waiting time distributions, we regard the system as a polling model with varying arrival rates, and apply a generalised version of the distributional form of Little’s law. The marginal queue length distribution can be found by conditioning on the state of the system (position of the server, and whether it is serving or switching). Copyright The Author(s) 2012

Suggested Citation

  • M. Boon, 2012. "A polling model with reneging at polling instants," Annals of Operations Research, Springer, vol. 198(1), pages 5-23, September.
    • Handle: RePEc:spr:annopr:v:198:y:2012:i:1:p:5-23:10.1007/s10479-010-0758-2
    DOI: 10.1007/s10479-010-0758-2
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    References listed on IDEAS

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    1. Martin Eisenberg, 1972. "Queues with Periodic Service and Changeover Time," Operations Research, INFORMS, vol. 20(2), pages 440-451, April.
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    3. David Assaf & Moshe Haviv, 1990. "Reneging from Processor Sharing Systems and Random Queues," Mathematics of Operations Research, INFORMS, vol. 15(1), pages 129-138, February.
    4. S. W. Fuhrmann & Robert B. Cooper, 1985. "Stochastic Decompositions in the M / G /1 Queue with Generalized Vacations," Operations Research, INFORMS, vol. 33(5), pages 1117-1129, October.
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    Cited by:

    1. Vladimir Vishnevsky & Olga Semenova, 2021. "Polling Systems and Their Application to Telecommunication Networks," Mathematics, MDPI, vol. 9(2), pages 1-30, January.
    2. Kevin Granville & Steve Drekic, 2019. "On a 2-class polling model with reneging and $$k_i$$ k i -limited service," Annals of Operations Research, Springer, vol. 274(1), pages 267-290, March.
    3. Ravi Suman & Ananth Krishnamurthy, 2020. "Analysis of tandem polling queues with finite buffers," Annals of Operations Research, Springer, vol. 293(1), pages 343-369, October.

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