Advertisement

Traffic Modeling of IP Networks Using the Batch Markovian Arrival Process

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2324)

Abstract

In this paper, we identify the batch Markovian arrival process (BMAP) as an analytically tractable model of choice for aggregated traffic modeling of IP networks. The key idea of this aggregated traffic model lies in customizing the batch Markovian arrival process such that the different lengths of IP packets are represented by rewards (i.e., batch sizes of arrivals) of the BMAP. The utilization of the BMAP is encouraged by the observation that IP packet lengths follow to a large extent a discrete distribution. A comparative study with the MMPP and the Poisson process illustrates the effectiveness of the customized BMAP for IP traffic modeling by visual inspection of sample paths over four different time-scales, by presenting important statistical properties, and by analysis of traffic burstiness using R/S statistics. Additionally, we show that the BMAP model outperforms MMPP and Poisson traffic models by comparison of queuing performance.

Keywords

Poisson Process Sample Path Batch Size Internet Service Provider Packet Length 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Andersson, S., Ryden, T.: Maximum Likelihood Estimation of a Structured MMPP with Applications to Traffic Modeling. Proc. 13th ITC Specialist Seminar on Measurement and Modeling of IP Traffic, Monterey CA (2000) 20.1–20.10Google Scholar
  2. 2.
    Ash, G.R.: Traffic Engineering & QoS Methods for IP-, ATM-, & TDM-Based Multiservice Networks. Internet Draft draft-ietf-tewg-qos-routing-01.txt (2001)Google Scholar
  3. 3.
    Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society 39 (1976) 1–38MathSciNetGoogle Scholar
  4. 4.
    Fischer, W., Meier-Hellstern, K.: The Markov-modulated Poisson Process (MMPP) Cookbook. Performance Evaluation 18 (1993) 149–171zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Gross, D., Miller, D.R.: The Randomization Technique as a Modeling Tool and Solution Procedure for Transient Markov Processes. Operations Research 32 (1984) 345–361MathSciNetCrossRefGoogle Scholar
  6. 6.
    Kilpi, J., Norros, I.: Call Level Traffic Analysis of a Large ISP. Proc. 13th ITC Specialist Seminar on Measurement and Modeling of IP Traffic, Monterey CA (2000) 6.1–6.9Google Scholar
  7. 7.
    Kruse, H., Allman, M., Griner, J., Ostermann, S., Helvey, E.: Satellite Network Performance Measurements Using Simulated Multi-User Internet Traffic. Proc. 7th Int. Conf. on Telecommunication Systems (1999)Google Scholar
  8. 8.
    Ledesma, S., Liu, D.: Synthesis of Fractional Gaussian Noise using Linear Approximation for Generating Self-similar Network Traffic. Computer Communication Review 30 (2000) 4–17CrossRefGoogle Scholar
  9. 9.
    Lucantoni, D. M.: New Results on the Single Server Queue with a Batch Markovian Arrival Process. Comm. in Statistics: Stochastic Models 7 (1991) 1–46zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    McCreary, S., Claffy K.C.: Trends in Wide Area IP Traffic Patterns: A View from Ames Internet Exchange. Proc. 13th ITC Specialist Seminar on Measurement and Modeling of IP Traffic, Monterey CA (2000) 1.1–1.12Google Scholar
  11. 11.
    Nuzman, C.J., Saniee, I., Sweldens, W., Weiss, A.: A Compound Model for TCP Connection Arrivals. Proc. 13th ITC Specialist Seminar on Measurement and Modeling of IP Traffic, Monterey CA (2000) 1–9Google Scholar
  12. 12.
    Ryden, T.: An EM Algorithm for Parameter Estimation in Markov Modulated Poisson Processes. Computational Statistics and Data Analysis 21 (1996) 431–447zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Skelly, P., Schwartz, M., Dixit, S.: A Histogram-Based Model for Video Traffic Behavior in an ATM Multiplexer. IEEE Trans. on Networking 1 (1993) 446–459CrossRefGoogle Scholar
  14. 14.
    Thompson, K., Miller, G. J., Wilder, R.: Wide-Area Internet Traffic Patterns and Characteristics. IEEE Network Magazine 11 (1997) 10–23CrossRefGoogle Scholar
  15. 15.
    Willinger, W., Paxson, V., Taqqu, M.S.: Self-similarity and Heavy Tails: Structural Modeling of Network Traffic. In: A Practical Guide to Heavy Tails. Chapman & Hall (1998) 27–53Google Scholar
  16. 16.
    Yoshihara, T., Kasahara, S., Takahashi, Y.: Practical Time-Scale Fitting of Self-Similar Traffic with Markov-Modulated Poisson Process. Telecommunication Systems 17 (2001) 185–211zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of DortmundDortmundGermany

Personalised recommendations