skip to main content
10.1145/317499.317546acmconferencesArticle/Chapter ViewAbstractPublication PagesmetricsConference Proceedingsconference-collections
Article
Free Access

A generalization of mean value analysis to higher moments: moment analysis

Authors Info & Claims
Published:01 May 1986Publication History

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.

References

  1. B.J.P.Buzen: Computational Algorithms for Closed Queueing Networks with Exponential Servers. Comm. ACM 16, 9 (1973), p. 527. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. BB.St.C.Bruell, G.Balbo: Computational Algorithms for Closed Queueing Networks. North Holland, New York, Oxford, 1980Google ScholarGoogle Scholar
  3. 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 ScholarGoogle ScholarDigital LibraryDigital Library
  4. CH.W.M.Chow: Approximations for Large Scale Closed Queueing Networks. Perf. Eval. 3 (1983), p. 1Google ScholarGoogle Scholar
  5. CHW.K.M.Chandy, U.Herzog,L.Woo: P#rarnetric Analysis of Queueing Networks. IBM J. Res. and Develop. 19(1) (1075), p. 36Google ScholarGoogle Scholar
  6. CN.K.M.Chandy, D.Neuse: Linearizer: A Heuristic Algorithm for Queueing Network Models of Computing Systems. CACM 25,2 (1982), p. 126 Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. 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 ScholarGoogle ScholarDigital LibraryDigital Library
  8. D.R.Dinarto: Berechnung h#herer Moments der Kundenza#len bei geschlouenen Wartenetzen mit Produktforml6sung. Diploma Thesis, Universit/#t Bonn, 1985.Google ScholarGoogle Scholar
  9. GN.W.J.Gordon and G.J.Newell: Closed Queueing Systems with Exponential Servers. Operations Research x5 (19e ), p. s4.Google ScholarGoogle Scholar
  10. H.H.Heffes: Moment Formulae for a Class of Mixed Multi-Job-Type Queueing Networks. Bell System Technical Journal 61, 5 (1982), p. 709Google ScholarGoogle ScholarCross RefCross Ref
  11. J.J.R.J#ckson: Networks of Waiting Lines. Operations Research 5 (1957), p. 518.Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. 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 ScholarGoogle ScholarDigital LibraryDigital Library
  13. KL.L.Kleinrock: Queueing Systems (Volume 2). John Wiley Sons, New York, 1976.Google ScholarGoogle Scholar
  14. KO.H.Kobayashi: Modelling and Analysis. Addison Wesley Publ. Comp., Reading, Mass., 1978.Google ScholarGoogle Scholar
  15. 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 ScholarGoogle Scholar
  16. P.B.Pittel: Closed Exponential Networks of Queues, Asymptotic Analysis. IBM Research Report RC61T4, Yorktown Heights, N.Y., I976Google ScholarGoogle Scholar
  17. 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 ScholarGoogle ScholarDigital LibraryDigital Library
  18. R2.M.Reiser: A Queueing Network Analysis of Computer Communication Networks with Window Flow Control. IEEE Trans. Comm. 27, 8 (1979), p. 1199.Google ScholarGoogle ScholarCross RefCross Ref
  19. R3.M.Reiser: Mean-Value Analysis and Convolution Method for Queue-Dependent Servers in Closed Queueing Networks. Perf. Eval. I (1981), p.7Google ScholarGoogle ScholarCross RefCross Ref
  20. RL.M.Reiser, S.S.Lavenberg: Mean-Value Analysis of Closed Multichain Queueing Networks. JACM 27,2 ( gs0), p. sxs. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. S.J.E.Shore: Information Theoretic Approximations for M/G/1 and G/G/1 Systems. Acta Informatica 17 (1982), p.43Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. SCHWA.M.Schwartz: Computer-Communication Network Design and Analysis. Prentice-Hall, Inc., Englewood Cliffs, N.J., 1977 Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. SCHWE.P.J.Schweitzer: Approximate Analysis of Multicla#s Closed Networks of Queues. Int. Conf on Stoch# stic Control and Optimization, Amsterdam (1979)Google ScholarGoogle Scholar
  24. ST.J.Chr.Strelen: Eine Differentialgleichung fiir die Normierungskonstante yon geschlossenen M-vollstKndigen Wsrteschlangennetzwerken. Bericht des Instituts fiir Informatik, Universit&t Bonn, 1984Google ScholarGoogle Scholar
  25. T.H. Tzschach:The Principle of Maximum Entropy Applied to Queueing Systems. Inform#tikbericht TI-2/83, Technische Hochschule Darmstadt, 1983Google ScholarGoogle Scholar
  26. TZ.H.Tzschax:h: M-VollstiLndigkeit fiir Wartschlangensysteme. Forschungsbericht TI 31/78, Technische Hochschule Darmstadt, 1978.Google ScholarGoogle Scholar
  27. Z.J.Zahorjan: The Approximate Solution of Large Queueing Network Models. Technical Report CSRG-122, University of Toronto, 1980Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. A generalization of mean value analysis to higher moments: moment analysis

            Recommendations

            Comments

            Login options

            Check if you have access through your login credentials or your institution to get full access on this article.

            Sign in
            • Published in

              cover image ACM Conferences
              SIGMETRICS '86/PERFORMANCE '86: Proceedings of the 1986 ACM SIGMETRICS joint international conference on Computer performance modelling, measurement and evaluation
              May 1986
              262 pages
              ISBN:0897911849
              DOI:10.1145/317499

              Copyright © 1986 ACM

              Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

              Publisher

              Association for Computing Machinery

              New York, NY, United States

              Publication History

              • Published: 1 May 1986

              Permissions

              Request permissions about this article.

              Request Permissions

              Check for updates

              Qualifiers

              • Article

              Acceptance Rates

              Overall Acceptance Rate459of2,691submissions,17%

            PDF Format

            View or Download as a PDF file.

            PDF

            eReader

            View online with eReader.

            eReader