Flow-equivalent server method

In queueing theory, a discipline within the mathematical theory of probability, the flow-equivalent server method (also known as flow-equivalent aggregation technique,^[1] Norton's theorem for queueing networks or the Chandy–Herzog–Woo method^[2]) is a divide-and-conquer method to solve product form queueing networks inspired by Norton's theorem for electrical circuits.^[3] The network is successively split into two, one portion is reconfigured to a closed network and evaluated.

Marie's algorithm is a similar method where analysis of the sub-network are performed with state-dependent Poisson process arrivals.^[4]^[5]

References

^ Casale, G. (2008). "A note on stable flow-equivalent aggregation in closed networks" (PDF). Queueing Systems. 60 (3–4): 193–202. doi:10.1007/s11134-008-9093-6.
^ Chandy, K. M.; Herzog, U.; Woo, L. (1975). "Parametric Analysis of Queuing Networks". IBM Journal of Research and Development. 19: 36. doi:10.1147/rd.191.0036.
^ Harrison, Peter G.; Patel, Naresh M. (1992). Performance Modelling of Communication Networks and Computer Architectures. Addison-Wesley. pp. 249–254. ISBN 0-201-54419-9.
^ Marie, R. A. (1979). "An Approximate Analytical Method for General Queueing Networks". IEEE Transactions on Software Engineering (5): 530–538. doi:10.1109/TSE.1979.234214.
^ Marie, R. A. (1980). "Calculating equilibrium probabilities for λ(n)/C_k/1/N queues". ACM SIGMETRICS Performance Evaluation Review. 9 (2): 117. doi:10.1145/1009375.806155.

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[1] Casale, G. (2008). "A note on stable flow-equivalent aggregation in closed networks" (PDF). Queueing Systems. 60 (3–4): 193–202. doi:10.1007/s11134-008-9093-6.

[2] Chandy, K. M.; Herzog, U.; Woo, L. (1975). "Parametric Analysis of Queuing Networks". IBM Journal of Research and Development. 19: 36. doi:10.1147/rd.191.0036.

[3] Harrison, Peter G.; Patel, Naresh M. (1992). Performance Modelling of Communication Networks and Computer Architectures. Addison-Wesley. pp. 249–254. ISBN 0-201-54419-9.

[4] Marie, R. A. (1979). "An Approximate Analytical Method for General Queueing Networks". IEEE Transactions on Software Engineering (5): 530–538. doi:10.1109/TSE.1979.234214.

[5] Marie, R. A. (1980). "Calculating equilibrium probabilities for λ(n)/C_k/1/N queues". ACM SIGMETRICS Performance Evaluation Review. 9 (2): 117. doi:10.1145/1009375.806155.

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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
Category