Decomposition method (queueing theory)

In queueing theory, a discipline within the mathematical theory of probability, the decomposition method is an approximate method for the analysis of queueing networks where the network is broken into subsystems which are independently analyzed. The individual queueing nodes are considered to be independent G/G/1 queues where arrivals are governed by a renewal process and both service time and arrival distributions are parametrised to match the first two moments of data.

In queueing theory, a discipline within the mathematical theory of probability, the decomposition method is an approximate method for the analysis of queueing networks where the network is broken into subsystems which are independently analyzed.^[1]^[2]

The individual queueing nodes are considered to be independent G/G/1 queues where arrivals are governed by a renewal process and both service time and arrival distributions are parametrised to match the first two moments of data.

References

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^ Kuehn, P. (1979). "Approximate Analysis of General Queuing Networks by Decomposition". IEEE Transactions on Communications. 27: 113–126. doi:10.1109/TCOM.1979.1094270.
^ Caldentey, R. (2001). "Approximations for Multi-Class Departure Processes" (PDF). Queueing Systems. 38 (2): 205–212. doi:10.1023/A:1010910531975. S2CID 14383294.

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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