Skip to main content
SpringerLink
Log in
Book cover

International Conference on Modelling Techniques and Tools for Computer Performance Evaluation

TOOLS 1995: Quantitative Evaluation of Computing and Communication Systems pp 239–253Cite as

Approximate analysis of networks of PH¦PH|1¦K queues: Theory & tool support

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 977))

Abstract

We address the approximate analysis of open networks of PH¦PH¦1 and PH¦PH¦1¦K queues. We start from the analysis of open queueing networks (QNs) as proposed by Whitt, where large QNs are decomposed into individual GI¦G¦1 queues, characterized by the first and second moment of the service and interarrival time distribution. We extend this approach in two ways.

First of all, we use PH¦PH¦1 queues, instead of GI¦G¦1 queues, so that the individual queues can be solved exactly, using matrix-geometric techniques. Secondly, we allow for the inclusion of finite-buffer queues. In doing so, the proposed decomposition becomes an iterative process.

We present the mathematical background of the approach as well as a tool implementation (Qnaut). It turns out that our approach not only yields accurate results (within a few percents from simulation results) but also is very fast in obtaining them (in comparison with simulation).

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L. Gün, A.M. Makowski, “Matrix-Geometric Solutions for Finite-Capacity Queues with Phase-Type Distributions”, in: Performance'87, Editors: P.J. Courtois, G. Latouche, pp.269–282, 1988.

    Google Scholar 

  2. B.R. Haverkort, A.P.A. van Moorsel, D.-J. Speelman, “Xmgm: A Performance Analysis Tool Based on Matrix Geometric Methods”, Proceedings of the 2nd International Workshop on Modelling, Analysis and Simulation of Computer and Telecommunication Systems, IEEE Computer Society Press, pp.152–157, 1994.

    Google Scholar 

  3. B.R. Haverkort, “Approximate Analysis of Networks of PH¦PH¦1¦K Queues: Test Results”, Particicpants Proceedings of the 3rd International Workshop on Queueing Networks with Finite Capacity, Bradford, UK, July 6–7, 1995.

    Google Scholar 

  4. G. Heijenk, M. El Zarki, I.G. Niemegeers, “Modelling Segmentation and Reassembly Processes in Communication Networks”, Proceedings ITC-14, North-Holland, pp.513–524, 1994.

    Google Scholar 

  5. K. Kant, Introduction to Computer System Performance Evaluation, McGraw-Hill, Inc., 1992.

    Google Scholar 

  6. W. Krämer, M. Langenbach-Belz, “Approximate Formulae for the Delay in the Queueing System GI¦G¦1”, Proceedings ITC-8, pp.235–1/8, 1976.

    Google Scholar 

  7. U. Krieger, B. Müller-Clostermann, M. Sczittnick, “Modelling and Analysis of Communication Systems Based on Computational Methods for Markov Chains”, IEEE JSAC 8(9), pp.1630–1648, 1990.

    Google Scholar 

  8. K.T. Marshall, “Some Inequalities in Queueing”, Operations Research 16(3), pp.651–665, 1968.

    Google Scholar 

  9. M.F. Neuts, Matrix Geometric Solutions in Stochastic Models: An Algorithmic Approach, Johns Hopkins University Press, Baltimore, 1981.

    Google Scholar 

  10. H.G. Perros, Queueing Networks with Blocking, Oxford University Press, 1994.

    Google Scholar 

  11. H.C. Tijms, Stochastic Modelling and Analysis: A Computational Approach, John Wiley & Sons, 1986.

    Google Scholar 

  12. K.S. Trivedi, Probability & Statistics with Reliability, Queueing and Computer Science Applications, Prentice-Hall, 1982.

    Google Scholar 

  13. A.J. Weerstra, “Using Matrix-Geometric Methods to Enhance the QNA Method for Solving Large Queueing Networks; Vol. I & II”, M.Sc. thesis, University of Twente, 1994.

    Google Scholar 

  14. W. Whitt, “The Queueing Network Analyzer”, The Bell System Technical Journal 62(9), pp.2779–2815, 1983.

    Google Scholar 

  15. W. Whitt, “Performance of the Queueing Network Analyzer”, The Bell System Technical Journal 62(9), pp.2817–2843, 1983.

    Google Scholar 

  16. M. El Zarki, N. Shroff, “Performance Analysis of Packet-Loss Recovery Schemes in Interconnected LAN-WAN-LAN Networks”, Proceedings of the Third IFIP WG 6.4 Conference on High-Speed Networking, Editors: A. Danthine. O. Spaniol, North-Holland, pp.337–351, 1991.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Twente, P.O. Box 217, 7500, AE Enschede, the Netherlands

    Boudewijn R. Haverkort

Authors
  1. Boudewijn R. Haverkort
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Heinz Beilner Falko Bause

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Haverkort, B.R. (1995). Approximate analysis of networks of PH¦PH|1¦K queues: Theory & tool support. In: Beilner, H., Bause, F. (eds) Quantitative Evaluation of Computing and Communication Systems. TOOLS 1995. Lecture Notes in Computer Science, vol 977. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024319

Download citation

  • DOI: https://doi.org/10.1007/BFb0024319

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60300-9

  • Online ISBN: 978-3-540-44789-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation