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).