ABSTRACT
Closed product-form queueing networks are considered. Recursive schemata are proposed for the higher moments of the number of customers in the queues, called “moment analysis”. As with mean value analysis (MVA), in general no state probabilities are needed. Approximation techniques for these schemata similar to those existing for MVA are introduced.
- B.J.P.Buzen: Computational Algorithms for Closed Queueing Networks with Exponential Servers. Comm. ACM 16, 9 (1973), p. 527. Google ScholarDigital Library
- BB.St.C.Bruell, G.Balbo: Computational Algorithms for Closed Queueing Networks. North Holland, New York, Oxford, 1980Google Scholar
- BCMP.F.Baskett, K.M.Chandy, R.R.Muntz, F.G.Palacios: Open, Closed, and Mixed Networks of Queues with Different Classes of Customers. JACM 22, 2 (1975), p. 248 Google ScholarDigital Library
- CH.W.M.Chow: Approximations for Large Scale Closed Queueing Networks. Perf. Eval. 3 (1983), p. 1Google Scholar
- CHW.K.M.Chandy, U.Herzog,L.Woo: P#rarnetric Analysis of Queueing Networks. IBM J. Res. and Develop. 19(1) (1075), p. 36Google Scholar
- CN.K.M.Chandy, D.Neuse: Linearizer: A Heuristic Algorithm for Queueing Network Models of Computing Systems. CACM 25,2 (1982), p. 126 Google ScholarDigital Library
- CS.K.M.Chandy, C.H.Sauer: Computational Algorithms for Product Form Queueing Networks, IBM Res. Rep. RC7950, IBM Thomas ,}. Watson Research Center, Yorktown Heights, NY (1980) (Also in: Proceedings Supplement, Performance 80, ACM Press, Toronto, Ont.) Google ScholarDigital Library
- D.R.Dinarto: Berechnung h#herer Moments der Kundenza#len bei geschlouenen Wartenetzen mit Produktforml6sung. Diploma Thesis, Universit/#t Bonn, 1985.Google Scholar
- GN.W.J.Gordon and G.J.Newell: Closed Queueing Systems with Exponential Servers. Operations Research x5 (19e ), p. s4.Google Scholar
- H.H.Heffes: Moment Formulae for a Class of Mixed Multi-Job-Type Queueing Networks. Bell System Technical Journal 61, 5 (1982), p. 709Google ScholarCross Ref
- J.J.R.J#ckson: Networks of Waiting Lines. Operations Research 5 (1957), p. 518.Google ScholarDigital Library
- KG.A.Krzesinski, J.Greyling: Improved Line, riser Methods for Queueing Networks with Queue Dependent Centres. ACM Performance Evaluation Review 12,3 (1984), p. 41 Google ScholarDigital Library
- KL.L.Kleinrock: Queueing Systems (Volume 2). John Wiley Sons, New York, 1976.Google Scholar
- KO.H.Kobayashi: Modelling and Analysis. Addison Wesley Publ. Comp., Reading, Mass., 1978.Google Scholar
- M.R.R.Muntz: Poisson Departure Process and Queueing Networks. Proc. of the 7th Annual Princeton Conf. on Information Sciences and System, Princeton Univ., Princeton, N.J., March 1973, pp. 435-440Google Scholar
- P.B.Pittel: Closed Exponential Networks of Queues, Asymptotic Analysis. IBM Research Report RC61T4, Yorktown Heights, N.Y., I976Google Scholar
- R.M.Reiser: Mean-Value Analysis of Queueing Networks, a New Look at an Old Problem. Pros. 4th Int. Syrup. on Modelling and Performance Evaluation of Computer Systems, Vienna (1979) Google ScholarDigital Library
- R2.M.Reiser: A Queueing Network Analysis of Computer Communication Networks with Window Flow Control. IEEE Trans. Comm. 27, 8 (1979), p. 1199.Google ScholarCross Ref
- R3.M.Reiser: Mean-Value Analysis and Convolution Method for Queue-Dependent Servers in Closed Queueing Networks. Perf. Eval. I (1981), p.7Google ScholarCross Ref
- RL.M.Reiser, S.S.Lavenberg: Mean-Value Analysis of Closed Multichain Queueing Networks. JACM 27,2 ( gs0), p. sxs. Google ScholarDigital Library
- S.J.E.Shore: Information Theoretic Approximations for M/G/1 and G/G/1 Systems. Acta Informatica 17 (1982), p.43Google ScholarDigital Library
- SCHWA.M.Schwartz: Computer-Communication Network Design and Analysis. Prentice-Hall, Inc., Englewood Cliffs, N.J., 1977 Google ScholarDigital Library
- SCHWE.P.J.Schweitzer: Approximate Analysis of Multicla#s Closed Networks of Queues. Int. Conf on Stoch# stic Control and Optimization, Amsterdam (1979)Google Scholar
- ST.J.Chr.Strelen: Eine Differentialgleichung fiir die Normierungskonstante yon geschlossenen M-vollstKndigen Wsrteschlangennetzwerken. Bericht des Instituts fiir Informatik, Universit&t Bonn, 1984Google Scholar
- T.H. Tzschach:The Principle of Maximum Entropy Applied to Queueing Systems. Inform#tikbericht TI-2/83, Technische Hochschule Darmstadt, 1983Google Scholar
- TZ.H.Tzschax:h: M-VollstiLndigkeit fiir Wartschlangensysteme. Forschungsbericht TI 31/78, Technische Hochschule Darmstadt, 1978.Google Scholar
- Z.J.Zahorjan: The Approximate Solution of Large Queueing Network Models. Technical Report CSRG-122, University of Toronto, 1980Google ScholarDigital Library
Index Terms
- A generalization of mean value analysis to higher moments: moment analysis
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