Kelly network

In queueing theory, a discipline within the mathematical theory of probability, a Kelly network is a general multiclass queueing network.[1] In the network each node is quasireversible and the network has a product-form stationary distribution, much like the single-class Jackson network.

The model is named after Frank Kelly who first introduced the model in 1975 in his paper Networks of Queues with Customers of Different Types.[2]

References

Chen, H.; Yao, D. D. (2001). "Kelly Networks". Fundamentals of Queueing Networks. Stochastic Modelling and Applied Probability. Vol. 46. pp. 69–96. doi:10.1007/978-1-4757-5301-1_4. ISBN 978-1-4419-2896-2.
Kelly, F. P. (1975). "Networks of Queues with Customers of Different Types" (PDF). Journal of Applied Probability. 12 (3): 542–554. doi:10.2307/3212869. JSTOR 3212869. S2CID 51917794. Archived from the original (PDF) on 2019-02-24.

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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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