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]


  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)/Ck/1/N queues". ACM SIGMETRICS Performance Evaluation Review. 9 (2): 117. doi:10.1145/1009375.806155.
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