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In queueing theory, a discipline within the mathematical theory of probability, a polling system or polling model is a system where a single server visits a set of queues in some order.^[1] The model has applications in telecommunications, manufacturing and road traffic management. The term polling system was coined at least at early as 1968.^[2]^[3]

Typically it is assumed that the server visits the different queues in a cyclic manner.^[1] Exact results exist for waiting times, marginal queue lengths and joint queue lengths^[4] at polling epochs in certain models.^[5] Mean value analysis techniques can be applied to compute average quantities.^[6]

In a fluid limit, where a very large number of small jobs arrive the individual nodes can be viewed as fluid queues (with a two state process).^[7]

External links

Bibliography on polling models (1984–1993) by Hideaki Takagi

References

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[boxma-1] Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1007/978-3-642-75079-3_8, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with |doi=10.1007/978-3-642-75079-3_8 instead.

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 Typically it is assumed that the server visits the different queues in a cyclic manner.<ref name="boxma" /> Exact results exist for waiting times, marginal queue lengths and joint queue lengths<ref>{{cite doi|10.1007/BF01149263}}</ref> at polling epochs in certain models.<ref>{{cite doi|10.1007/BF01245325}}</ref> [[Mean value analysis]] techniques can be applied to compute average quantities.<ref>{{cite doi|10.1016/j.peva.2007.06.015}}</ref>
+In a [[fluid limit]], where a very large number of small jobs arrive the individual nodes can be viewed as [[fluid queue]]s (with a two state process).<ref>{{cite doi|10.1007/s11134-009-9129-6}}</ref>
 ==External links==

v t e Queueing theory
Single queueing nodes	D/M/1 queue M/D/1 queue M/D/c queue M/M/1 queue Burke's theorem M/M/c queue M/M/∞ queue M/G/1 queue Pollaczek–Khinchine formula Matrix analytic method M/G/k queue G/M/1 queue G/G/1 queue Kingman's formula Lindley equation Fork–join queue Bulk queue
Arrival processes	Poisson point process Markovian arrival process Rational arrival process
Queueing networks	Jackson network Traffic equations Gordon–Newell theorem Mean value analysis Buzen's algorithm Kelly network G-network BCMP network
Service policies	FIFO LIFO Processor sharing Round-robin Shortest job next Shortest remaining time
Key concepts	Continuous-time Markov chain Kendall's notation Little's law Product-form solution Balance equation Quasireversibility Flow-equivalent server method Arrival theorem Decomposition method Beneš method
Limit theorems	Fluid limit Mean-field theory Heavy traffic approximation Reflected Brownian motion
Extensions	Fluid queue Layered queueing network Polling system Adversarial queueing network Loss network Retrial queue
Information systems	Data buffer Erlang (unit) Erlang distribution Flow control (data) Message queue Network congestion Network scheduler Pipeline (software) Quality of service Scheduling (computing) Teletraffic engineering
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