Unified analysis of BMAP/G/1 cyclic polling models

Zsolt Saffer, Miklós Telek

Research output: Contribution to journalArticle

15 Citations (Scopus)


In this paper we present a unified analysis of the BMAP/G/1 cyclic polling model and its application to the gated and exhaustive service disciplines as examples. The applied methodology is based on the separation of the analysis into service discipline independent and dependent parts. New expressions are derived for the vector-generating function of the stationary number of customers and for its mean in terms of vector quantities depending on the service discipline. They are valid for a broad class of service disciplines and both for zero- and nonzero-switchover-times polling models. We present the service discipline specific solution for the nonzero-switchover-times model with gated and exhaustive service disciplines. We set up the governing equations of the system by using Kronecker product notation. They can be numerically solved by means of a system of linear equations. The resulting vectors are used to compute the service discipline specific vector quantities.

Original languageEnglish
Pages (from-to)69-102
Number of pages34
JournalQueueing Systems
Issue number1
Publication statusPublished - Jan 1 2010


  • BMAP
  • Polling model
  • Queueing theory
  • Service discipline
  • Stationary relationship

ASJC Scopus subject areas

  • Statistics and Probability
  • Computer Science Applications
  • Management Science and Operations Research
  • Computational Theory and Mathematics

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