A new approach to analysis of polling systems

Tetsuji Hirayama, Sung Jo Hong, Marwan M. Krunz

Research output: Contribution to journalArticle

15 Scopus citations

Abstract

In this paper, we consider polling systems with J stations with Poisson arrivals and general service distributions attended by a cyclic server. The service discipline at each station is either exhaustive or gated. We propose a new approach to analysis of the mean waiting times in the polling systems. The outline of our method is as follows. We first define the stochastic process Q that represents an evolution of the system state, and define three types of the performance measures Wi,Hi and Fi, which are the expected waiting times conditioned on the system state. Then from the analysis of customers at polling instants, we find their linear functional expressions. The steady state average waiting times can be derived from the performance measures by simple limiting procedures. Their actual values can be obtained by solving J(J+1) linear equations.

Original languageEnglish (US)
Pages (from-to)135-158
Number of pages24
JournalQueueing Systems
Volume48
Issue number1-2
DOIs
StatePublished - Sep 1 2004

Keywords

  • a new approach
  • linear functional expressions
  • mean waiting times
  • polling systems

ASJC Scopus subject areas

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

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