A polling model with an autonomous server

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Abstract

Polling models are used as an analytical performance tool in several application areas. In these models, the focus often is on controlling the operation of the server as to optimize some performance measure. For several applications, controlling the server is not an issue as the server moves independently in the system. We present the analysis for such a polling model with a so-called autonomous server. In this model, the server remains for an exogenous random time at a queue, which also implies that service is preemptive. Moreover, in contrast to most of the previous research on polling models, the server does not immediately switch to a next queue when the current queue becomes empty, but rather remains for an exponentially distributed time at a queue. The analysis is based on considering imbedded Markov chains at specific instants. A system of equations for the queue-length distributions at these instant is given and solved for. Besides, we study to which extent the queues in the polling model are independent and identify parameter settings for which this is indeed the case. These results may be used to approximate performance measures for complex multi-queue models by analyzing a simple single-queue model.
Original languageUndefined
Place of PublicationEnschede
PublisherStochastic Operations Research (SOR)
Number of pages22
Publication statusPublished - Jul 2007

Publication series

NameMemorandum / Department of Applied Mathematics
PublisherUniversity of Twente, Department of Applied Mathematics
No.128/1845
ISSN (Print)1874-4850
ISSN (Electronic)1874-4850

Keywords

  • IR-64166
  • METIS-241761
  • EWI-10428

Cite this

de Haan, R., Boucherie, R. J., & van Ommeren, J. C. W. (2007). A polling model with an autonomous server. (Memorandum / Department of Applied Mathematics; No. 128/1845). Enschede: Stochastic Operations Research (SOR).
de Haan, Roland ; Boucherie, Richardus J. ; van Ommeren, Jan C.W. / A polling model with an autonomous server. Enschede : Stochastic Operations Research (SOR), 2007. 22 p. (Memorandum / Department of Applied Mathematics; 128/1845).
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de Haan, R, Boucherie, RJ & van Ommeren, JCW 2007, A polling model with an autonomous server. Memorandum / Department of Applied Mathematics, no. 128/1845, Stochastic Operations Research (SOR), Enschede.

A polling model with an autonomous server. / de Haan, Roland; Boucherie, Richardus J.; van Ommeren, Jan C.W.

Enschede : Stochastic Operations Research (SOR), 2007. 22 p. (Memorandum / Department of Applied Mathematics; No. 128/1845).

Research output: Book/ReportReportProfessional

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AB - Polling models are used as an analytical performance tool in several application areas. In these models, the focus often is on controlling the operation of the server as to optimize some performance measure. For several applications, controlling the server is not an issue as the server moves independently in the system. We present the analysis for such a polling model with a so-called autonomous server. In this model, the server remains for an exogenous random time at a queue, which also implies that service is preemptive. Moreover, in contrast to most of the previous research on polling models, the server does not immediately switch to a next queue when the current queue becomes empty, but rather remains for an exponentially distributed time at a queue. The analysis is based on considering imbedded Markov chains at specific instants. A system of equations for the queue-length distributions at these instant is given and solved for. Besides, we study to which extent the queues in the polling model are independent and identify parameter settings for which this is indeed the case. These results may be used to approximate performance measures for complex multi-queue models by analyzing a simple single-queue model.

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de Haan R, Boucherie RJ, van Ommeren JCW. A polling model with an autonomous server. Enschede: Stochastic Operations Research (SOR), 2007. 22 p. (Memorandum / Department of Applied Mathematics; 128/1845).