Skip to main content

Experiments with Improved Approximate Mean Value Analysis Algorithms

  • Conference paper
  • First Online:
Computer Performance Evaluation (TOOLS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1469))

Abstract

Approximate Mean Value Analysis (MVA) is a popular technique for analyzing queueing networks because of the efficiency and accuracy that it affords. In this paper, we present a new software package, called the Improved Approximate Mean Value Analysis Library (IAMVAL), which can be easily integrated into existing commercial and research queueing network analysis packages. The IAMVAL packages includes two new approximate MVA algorithms, the Queue Line (QL) algorithm and the Fraction Line (FL) algorithm, for analyzing multiple class separable queueing networks. The QL algorithm is always more accurate than, and yet has approximately the same computational efficiency as, the Bard-Schweitzer Proportional Estimation (PE) algorithm, which is currently the most widely used approximate MVA algorithm. The FL algorithm has the same computational cost and, in noncongested separable queueing networks where queue lengths are quite small, yields more accurate solutions than both the QL and PE algorithms.

This research was supported by the Natural Science and Engineering Research Council of Canada (NSERC), and by Communications and Information Technology Ontario (CITO).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Y. Bard. Some extensions to multiclass queueing network analysis. In: M. Arato, A. Butrimenko and E. Gelenbe, eds. Performance of Computer Systems, North-Holland, Amsterdam, Netherlands, 1979.

    Google Scholar 

  2. F. Baskett, 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(2):248–260, April 1975.

    Article  MATH  MathSciNet  Google Scholar 

  3. W.-M. Chow. Approximations for large scale closed queueing networks. Performance Evaluation, 3(1):1–12, 1983.

    Article  Google Scholar 

  4. K. M. Chandy and D. Neuse. Linearizer: A heuristic algorithm for queueing network models of computing systems. Communications of the ACM, 25(2):126–134, February 1982.

    Article  Google Scholar 

  5. D. L. Eager and K. C. Sevcik. Analysis of an approximation algorithm for queueing networks. Performance Evaluation, 4(4):275–284, 1984.

    Article  MATH  MathSciNet  Google Scholar 

  6. C. T. Hsieh and S. S. Lam. PAM — A noniterative approximate solution method for closed multichain queueing networks. ACM SIGMETRICS Performance Evaluation Review, 16(1):261–269, May 1988.

    Article  Google Scholar 

  7. S. S. Lavenberg and M. Reiser. Stationary state probabilities of arrival instants for closed queueing networks with multiple types of customers. Journal of Applied Probability, 17(4):1048–1061, December 1980.

    Article  MATH  MathSciNet  Google Scholar 

  8. K. R. Pattipati, M. M. Kostreva and J. L. Teele. Approximate mean value analysis algorithms for queueing networks: existence, uniqueness, and convergence results. Journal of the ACM, 37(3):643–673, July 1990.

    Article  MATH  MathSciNet  Google Scholar 

  9. M. Reiser and S. S. Lavenberg. Mean value analysis of closed multichain queueing networks. Journal of the ACM, 27(2):313–322, April 1980.

    Article  MATH  MathSciNet  Google Scholar 

  10. P. J. Schweitzer. Approximate analysis of multiclass closed networks of queues. Proceedings of International Conference on Stochastic Control and Optimization, 25–29, Amsterdam, Netherlands, 1979.

    Google Scholar 

  11. P. J. Schweitzer, G. Serazzi and M. Broglia. A queue-shift approximation technique for product-form queueing networks. Technical Report, 1996.

    Google Scholar 

  12. K. C. Sevcik and I. Mitrani. The distribution of queueing network states at input and output instants. Journal of the ACM, 28(2):358–371, April 1981.

    Article  MATH  MathSciNet  Google Scholar 

  13. K. Sevcik and H. Wang. An improved approximate mean value analysis algorithm for solving separable queueing network models. submitted for publication, 1998.

    Google Scholar 

  14. E. de Souza e Silva, S. S. Lavenberg and R. R. Muntz. A clustering approximation technique for queueing network models with a large number of chains. IEEE Transactions on Computers, C-35(5):419–430, May 1986.

    Article  Google Scholar 

  15. E. de Souza e Silva and R. R. Muntz. A note on the computational cost of the linearizer algorithm for queueing networks. IEEE Transactions on Computers, 39(6):840–842, June 1990.

    Article  Google Scholar 

  16. H. Wang. Approximate MVA Algorithms for Solving Queueing Network Models. M. Sc. Thesis, Tech. Rept. CSRG-360, University of Toronto, Toronto, Ontario, Canada, 1997.

    Google Scholar 

  17. J. Zahorjan, D. L. Eager and H. M. Sweillam. Accuracy, speed, and convergence of approximate mean value analysis. Performance Evaluation, 8(4):255–270, 1988.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wang, H., Sevcik, K.C. (1998). Experiments with Improved Approximate Mean Value Analysis Algorithms. In: Puigjaner, R., Savino, N.N., Serra, B. (eds) Computer Performance Evaluation. TOOLS 1998. Lecture Notes in Computer Science, vol 1469. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68061-6_23

Download citation

  • DOI: https://doi.org/10.1007/3-540-68061-6_23

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64949-6

  • Online ISBN: 978-3-540-68061-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics