[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Skip to main content

Modelling LRD and SRD Traffic with the Batch Renewal Process: Review of Results and Open Issues

  • Chapter
Network Performance Engineering

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 5233))

  • 2128 Accesses

Abstract

The batch renewal process is the least biased choice of a process given only the measures of count and interval correlations at all lags. This article reviews the batch renewal process for modelling both LRD (long range dependent) and SRD (short range dependent) traffic flows. The exposition focuses mainly in the discrete-space discrete-time domain and in the wider context of general traffic in that domain. However, corresponding results in the continuous-time domain are also presented. Moreover, some applications of the batch renewal process in simple queues and in queueing network models are undertaken and associated analytic performance results are devised. The article concludes with open research problems and issues relating to the batch renewal process.

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

Access this chapter

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
GBP 19.95
Price includes VAT (United Kingdom)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
GBP 93.50
Price includes VAT (United Kingdom)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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.

Similar content being viewed by others

References

  1. Dimakopoulos, G.A.: On the Approximation of Complex Traffic Models on ATM Networks, M.Phil. Dissertation. Postgraduate School of Computing and Mathematics, University of Bradford (2000)

    Google Scholar 

  2. Disney, R.L., Kiessler, P.C.: Traffic Processes in Queueing Networks: A Markov Renewal Approach. The John Hopkins University Press, Baltimore (1987)

    MATH  Google Scholar 

  3. Fretwell, R.J., Dimakopoulos, G.A., Kouvatsos, D.D.: Ignoring Count Correlation in SRD Traffic. In: Bradley, J.T., Davies, N.J. (eds.) Proc. 15th UK Perf. Eng. Workshop, pp. 285–294. UK Performance Engineering Workshop Publishers (1999)

    Google Scholar 

  4. Fowler, H.J., Leland, W.E.: Local Area Network Traffic Characteristics, with Implications for Broadband Network Congestion Management. IEEE JSAC 9(7), 1139–1149 (1991)

    Google Scholar 

  5. Andrade, J., Martinez-Pascua, M.J.: Use of the IDC to Characterize LAN Traffic. In: Kouvatsos, D. (ed.) Proc. 2nd. Workshop on Performance Modelling and Evaluation of ATM Networks, pp. 15/1–15/12 (1994)

    Google Scholar 

  6. Gelenbe, E.: Random Neural Networks with Positive and Negative Signals and Product Form Solution. Neural Computation 1(4), 502–510 (1989)

    Article  Google Scholar 

  7. Gordon, J.J.: Pareto Process as a Model of Self-Similar Packet Traffic. In: Proc. Globecom 1995, Singapore, pp. 2232–2236 (1995)

    Google Scholar 

  8. Gusella, R.: Characterizing the Variability of Arrival Processes with Indexes of Dispersion. IEEE JSAC 9(2), 203–211 (1991)

    Google Scholar 

  9. Heffes, H., Lucantoni, D.M.: A Markov Modulated Characterization of Packetized Voice and Data Traffic and Related Statistical Multiplexer Performance. IEEE JSAC 4(6), 856–868 (1986)

    Google Scholar 

  10. Kouvatsos, D.D., Tabel-Aouel, N.M., Denazis, S.G.: Approximate Analysis of Discrete-time Networks with or without Blocking. In: Perros, H.G., Viniotis, Y. (eds.) High Speed Networks and their Performance, vol. C-21, pp. 399–424. North-Holland, Amsterdam (1994)

    Google Scholar 

  11. Kouvatsos, D.D., Fretwell, R.: Discrete Time Batch Renewal Processes with Application to ATM Switch Performance. In: Hillston, J., et al. (eds.) Proc. 10th. UK Computer and Telecomms. Performance Eng. Workshop, September 1994, pp. 187–192. Edinburgh University Press, Edinburgh (1994)

    Google Scholar 

  12. Kouvatsos, D., Fretwell, R.: Closed Form Performance Distributions of a Discrete Time GIG/D/1/N Queue with Correlated Traffic. In: Fdida, S., Onvural, R.O. (eds.) Enabling High Speed Networks, October 1995, pp. 141–163. IFIP Publication, Chapman and Hall (1995)

    Google Scholar 

  13. Kouvatsos, D.D., Awan, I.U., Fretwell, R., Dimakopoulos, G.: A Cost-effective Approximation for SRD Traffic in Arbitrary Multi-buffered Networks. Computer Networks 34, 97–113 (2000)

    Article  Google Scholar 

  14. Laevens, K.: The Output Process of a Discrete Time GIG/D/1 Queue. In: Proc. 6th IFIP Workshop on Performance Modelling and Evaluation of ATM Networks, Research Papers, pp. 20/1–20/10 (July 1998)

    Google Scholar 

  15. Leland, W.E., Taqqu, M.S., Willinger, W., Wilson, D.V.: On the Self-Similar Nature of Ethernet Traffic (Extended Version). IEEE/ACM Transactions on Networking 2(1), 1–14 (1994)

    Article  Google Scholar 

  16. Li, W.: Performance Analysis of Queues with Correlated Traffic, PhD Thesis (University of Bradford) (2007)

    Google Scholar 

  17. Lucantoni, D.M.: The BMAP/G/1 Queue: A Tutorial. In: Donatiello, L., Nelson, R. (eds.) SIGMETRICS 1993 and Performance 1993. LNCS, vol. 729, pp. 330–358. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  18. Neuts, M.F.: A Versatile Markovian Point Process. J. Appl. Prob. 16, 764–779 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  19. Sriram, K., Whitt, W.: Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data. IEEE JSAC 4(6), 833–846 (1986)

    Google Scholar 

  20. Wittevrongel, S., Bruneel, H., Vinck, B.: Analysis of the discrete-time G(G)/Geom/c queueing model. In: Gregori, E., Conti, M., Campbell, A.T., Omidyar, G., Zukerman, M. (eds.) NETWORKING 2002. LNCS, vol. 2345, pp. 757–768. Springer, Heidelberg (2002)

    Google Scholar 

  21. Xiong, Y., Bruneel, H.: Buffer Contents and Delay for Statistical Multiplexers with Fixed Length Packet Train Arrivals. Performance Evaluation 17(1), 31–42 (1993)

    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

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Fretwell, R.J., Kouvatsos, D.D. (2011). Modelling LRD and SRD Traffic with the Batch Renewal Process: Review of Results and Open Issues. In: Kouvatsos, D.D. (eds) Network Performance Engineering. Lecture Notes in Computer Science, vol 5233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02742-0_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02742-0_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02741-3

  • Online ISBN: 978-3-642-02742-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics