An extension to Norton's equivalent
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The aggregation method for queueing networks known as the Norton's equivalent is interpreted as a conditional estimate of the intensities of associated point processes. For multi-class Markovian queueing networks, it is shown that a first-order equivalent system of an isolated station can be obtained via the conditional estimates of intensities of the arrival and departure processes to and from that station. Based on these conditional estimates, separation results for optimal flow control problems in queueing networks can be obtained. Several examples which illustrate these concepts are given. The results obtained here generalize those which require the “product form” networks.
S. Balsamo, and G. Iazeolla, An extension of Norton's theorem for queueing networks, IEEE Trans. on Software Engineering, SE-8 (1982) 298–305.
F. Basket, K.M. Chandy, R.R. Muntz and F.G. Palacios, Open, closed, and mixed networks of queues with different classes of customers, Journal of the ACM 22, no. 2 (April 1975) 248–260.
A. Brandwajn, Equivalence and decomposition in queueing systems-a unified approach, Performance Evaluation 5 (1985) 175–186.
P. Bremaud,Point Processes and Queues: Martingale Dynamics (Springer-Verlag, New York, 1981).
P. Bremaud, Théorie des files d'attente et de leurs réseaux, preprint, 1986.
K.M. Chandy, U. Herzog and L. Woo, Parametric analysis of queueing networks, IBM J. Res. Develop. 19 (1975) 36–42.
P.J. Courtois,Decomposability: Queueing and Computer Applications (Academic Press, New York, 1977).
M.T. Hsiao and A.A. Lazar, Bottleneck modeling and decentralized optimal flow control — I. Global objectives,Proc. Eighteenth Conf. on Information Sciences and Systems (Princeton University, Princeton, NJ, March 1984).
M.T. Hsiao and A.A. Lazar, Bottleneck modeling and decentralized optimal flow control — II. Individual objectives,Proc. Nineteenth Conf. on Information Sciences and Systems (Johns Hopkins University, Baltimore, MD, March 1985).
M.T. Hsiao and A.A. Lazar, Optimal flow control of multi-class queueing networks with decentralized information, CTR Technical Report, CU-CTR-TR-11, Center for Telecommunications Research, Columbia University, 1986.
M.T. Hsiao and A.A. Lazar, Optimal decentralized flow control of Markovian queueing networks with multiple controllers, CTR Technical Report, CU-CTR-TR-19, Center for Telecommunications Research, Columbia University, 1986.
P.S. Kritzinger, S. van Wyk and A.E. Krzesinski, A generalisation of Norton's theorem for multiclass queueing networks, Performance Evaluation 2 (1982) 98–107.
A. Kumar, Equivalent queueing networks and their use in approximate equilibrium analysis, The Bell System Technical Journal 62, No. 10 (1983) 2893–2910.
J. Walrand, A note on Norton's theorem, Journal of Applied Probability 20 (1983) 442–444.
- An extension to Norton's equivalent
Volume 5, Issue 4 , pp 401-411
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- Kluwer Academic Publishers
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- Norton's equivalent
- conditional estimates
- Markovian queueing networks
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