Finite-buffer polling systems with threshold-based switching policy

Kostia Avrachenkov (), Efrat Perel () and Uri Yechiali ()
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Kostia Avrachenkov: Inria, Sophia Antipolis
Efrat Perel: Afeka, Tel-Aviv Academic College of Engineering
Uri Yechiali: School of Mathematical Sciences, Tel-Aviv University

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2016, vol. 24, issue 3, No 2, 571 pages

Abstract: 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 ( $$Q_i$$ Q i ) and the number of customers in the other queue, $$Q_j$$ Q j ( $$i,j=1,2$$ i , j = 1 , 2 ; $$j\ne i$$ j ≠ i ), reaches its threshold level, the server immediately switches to $$Q_j$$ Q j whenever $$Q_i$$ Q i is below its threshold. When a served $$Q_i$$ Q i 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 $$Q_i$$ Q i 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.

Keywords: Polling systems; Threshold policy; Finite-buffer queues; Oscillations; Primary; 60K25 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s11750-015-0408-6

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