Finite-buffer polling systems with threshold-based switching policy

Kostia Avrachenkov, Efrat Perel, Uri Yechiali

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a system of two separate finite-buffer M / M / 1 queues served by a single server, where the switching mechanism between the queues is threshold-based, determined by the queue which is not being served. Applications may be found in data centers, smart traffic-light control and human behavior. Specifically, whenever the server attends queue i (Qi) and the number of customers in the other queue, Qj (i, j= 1 , 2 ; j≠ i), reaches its threshold level, the server immediately switches to Qj whenever Qi is below its threshold. When a served Qi becomes empty we consider two scenarios: (i) non-work-conserving; and (ii) work-conserving. We present occasions where the non-work-conserving policy is more economical than the work-conserving policy when high switching costs are involved. An intrinsic feature of the process is an oscillation phenomenon: when the occupancy of Qi decreases the occupancy of the other queue increases. This fact is illustrated and discussed. By formulating the system as a three-dimensional continuous-time Markov chain we provide a probabilistic analysis of the system and investigate the effects of buffer sizes and arrival rates, as well as service rates, on the system’s performance. Numerical examples are presented and extreme cases are investigated.

Original languageEnglish
Pages (from-to)541-571
Number of pages31
JournalTOP
Volume24
Issue number3
DOIs
StatePublished - 1 Oct 2016

Keywords

  • Finite-buffer queues
  • Oscillations
  • Polling systems
  • Threshold policy

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