Two-queue polling systems with switching policy based on the queue that is not being served

Efrat Perel*, Uri Yechiali

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We study a system of two non-identical and separate M/M/1/• queues with capacities (buffers) C 1 < ∞ and C 2 = ∞, respectively, served by a single server that alternates between the queues. The server’s switching policy is threshold-based, and, in contrast to other threshold models, is determined by the state of the queue that is not being served. That is, when neither queue is empty while the server attends Qi (i = 1, 2), the server switches to the other queue as soon as the latter reaches its threshold. When a served queue becomes empty we consider two switching scenarios: (i) Work-Conserving, and (ii) Non-Work-Conserving. We analyze the two scenarios using Matrix Geometric methods and obtain explicitly the rate matrix R, where its entries are given in terms of the roots of the determinants of two underlying matrices. Numerical examples are presented and extreme cases are investigated.

Original languageEnglish
Pages (from-to)430-450
Number of pages21
JournalStochastic Models
Volume33
Issue number3
DOIs
StatePublished - 3 Jul 2017

Keywords

  • Alternating server
  • PGFs
  • matrix Geometric
  • polling systems
  • threshold policy

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