Continuous polling on graphs

E. G. Coffman, Aleksandr Stolyar

Research output: Contribution to journalArticle

Abstract

Past research on polling systems has been quite restricted in the form of the paths followed by the server. This paper formulates a general, continuous model of such paths that includes closed walks on graphs. Customers arrive by a Poisson process and have general service times. The distribution of arrivals over the path is governed by an absolutely continuous, but otherwise arbitrary, distribution. The main results include a characterization of the stationary state distribution and explicit formulas for expected waiting times. The formulas reveal an interesting decomposition of the system into two components: a fluid limit and an M/G/l queue.

Original languageEnglish (US)
Pages (from-to)209-226
Number of pages18
JournalProbability in the Engineering and Informational Sciences
Volume7
Issue number2
DOIs
StatePublished - Jan 1 1993
Externally publishedYes

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering

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