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Traffic Modeling with Phase-Type Distributions and VARMA Processes

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Quantitative Evaluation of Systems (QEST 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9826))

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Abstract

In discrete event systems event times are often correlated among events of one event stream and also between different event streams. If this correlation is neglected, then resulting simulation models do not describe the real behavior in a sufficiently accurate way. In most input modeling approaches, no correlation or at most the autocorrelation of one event stream is considered, correlation between different event streams is usually neglected. In this paper we present an approach to combine multi-dimensional time series and acyclic phase type distributions as a general model for event streams in discrete event simulation models. The paper presents the basic model and methods to determine its parameters from measured traces.

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References

  1. Biller, B., Gunes, C.: Introduction to simulation input modeling. In: Proceedings of the Winter Simulation Conference (2010)

    Google Scholar 

  2. Biller, B., Nelson, B.L.: Modeling and generating multivariate time-series input processes using a vector autoregressive technique. ACM Trans. Model. Comput. Simul. 13(3), 211–237 (2003)

    Article  Google Scholar 

  3. Bobbio, A., Horváth, A., Scarpa, M., Telek, M.: Acyclic discrete phase type distributions: properties and a parameter estimation algorithm. Perform. Eval. 54(1), 1–32 (2003)

    Article  Google Scholar 

  4. Box, G., Jenkins, G.: Time Series Analysis: Forecasting and Control. Holden-Day, San Francisco (1970)

    MATH  Google Scholar 

  5. Buchholz, P., Kriege, J.: A heuristic approach for fitting MAPs to moments and joint moments. In: Proceedings of the QEST, pp. 53–62 (2009)

    Google Scholar 

  6. Buchholz, P., Kriege, J., Felko, I.: Input Modeling with Phase-Type Distributions and Markov Models - Theory and Applications. Springer, Heidelberg (2014)

    Book  MATH  Google Scholar 

  7. Cario, M.C., Nelson, B.L.: Autoregressive to anything: time-series input processes for simulation. Oper. Res. Lett. 19(2), 51–58 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  8. Chan, J.C., Eisenstat, E.: Gibbs samplers for VARMA and its extensions. Technical report, Australian National University, School of Economics (2013)

    Google Scholar 

  9. Civelek, I., Biller, B., Scheller-Wolf, A.: The impact of dependence on queueing systems. Research Showcase 8-2009, Carnegie Mellon University (2009)

    Google Scholar 

  10. Cumani, A.: On the canonical representation of homogeneous Markov processes modeling failure-time distributions. Micorelectron. Reliab. 22(3), 583–602 (1982)

    Article  MathSciNet  Google Scholar 

  11. Devroye, L.: Non-Uniform Random Variate Generation. Springer, New York (1986)

    Book  MATH  Google Scholar 

  12. Drezner, Z., Wesolowsky, G.O.: On the computation of the bivariate normal integral. J. Stat. Comput. Simul. 35, 101–107 (1990)

    Article  MathSciNet  Google Scholar 

  13. Fishman, G.S.: Concepts and Methods in Discrete Event Digital Simulation. Wiley, New York (1973)

    Google Scholar 

  14. Fu, S., Xu, C.: Quantifying temporal and spatial correlation of failure events for proactive management. In: Proceedings of the SRDS (2007)

    Google Scholar 

  15. Henderson, T., Kotz, D., Abyzov, I.: The Changing usage of a mature campus-wide wireless network. In: Proceedings of the MobiCom (2004)

    Google Scholar 

  16. Khayari, R.E.A., Sadre, R., Haverkort, B.: Fitting world-wide web request traces with the EM-algorithm. Perform. Eval. 52, 175–191 (2003)

    Article  Google Scholar 

  17. Kriege, J., Buchholz, P.: Correlated phase-type distributed random numbers as input models for simulations. Perform. Eval. 68(11), 1247–1260 (2011)

    Article  Google Scholar 

  18. Kriege, J., Buchholz, P.: Online Companion to the Paper “Traffic Modeling with Phase-Type Distributions and VARMA Processes” (2016). http://www4.cs.tu-dortmund.de/download/kriege/publications/qest2016_online_companion.pdf

  19. Law, A.M.: Simulation Modleing and Analysis. McGraw-Hill, New York (2013)

    Google Scholar 

  20. Leland, W., Taqqu, M., Willinger, W., Wilson, D.: On the self-similar nature of ethernet traffic. IEEE/ACM Trans. Networking 2(1), 1–15 (1994)

    Article  Google Scholar 

  21. Lütkepohl, H.: Introduction to Multiple Time Series Analysis. Springer, Heidelberg (1993)

    Book  MATH  Google Scholar 

  22. Nash, J.: Compact Numerical Methods for Computers: Linear Algebra and Function Minimisation, 2nd edn. Adam Hilger, Bristol (1990)

    MATH  Google Scholar 

  23. Neuts, M.F.: A versatile Markovian point process. J. Appl. Prob. 16(4), 764–779 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  24. Press, W., Teukolsky, S., Vetterling, W., Flannery, B.: Numerical Recipes in C - The Art of Scientific Computing, 2nd edn. Cambridge University Press, Cambridge (1993)

    MATH  Google Scholar 

  25. Reinecke, P., Horváth, G.: Phase-type distributions for realistic modelling in discrete-event simulation. In: Proceedings of the SimuTools (2012)

    Google Scholar 

  26. Smith, R.D.: The dynamics of internet traffic: self-similarity, self-organization, and complex phenomena. Adv. Complex Syst. 14(6), 905–949 (2011)

    Article  MathSciNet  Google Scholar 

  27. Stanfield, P., Wilson, J., King, R.: Flexible modelling for correlated operation times with application in product-reuse facilities. Int. J. Prod. Res. 42(11), 2179–2196 (2004)

    Article  MATH  Google Scholar 

  28. Thümmler, A., Buchholz, P., Telek, M.: A novel approach for phase-type fitting with the EM algorithm. IEEE Trans. Dependable Sec. Comput. 3(3), 245–258 (2006)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, TU Dortmund, Dortmund, Germany

    Jan Kriege & Peter Buchholz

Authors
  1. Jan Kriege
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  2. Peter Buchholz
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Corresponding author

Correspondence to Jan Kriege .

Editor information

Editors and Affiliations

  1. University of Illinois , Urbana, Illinois, USA

    Gul Agha

  2. University of Antwerp , Antwerp, Belgium

    Benny Van Houdt

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Kriege, J., Buchholz, P. (2016). Traffic Modeling with Phase-Type Distributions and VARMA Processes. In: Agha, G., Van Houdt, B. (eds) Quantitative Evaluation of Systems. QEST 2016. Lecture Notes in Computer Science(), vol 9826. Springer, Cham. https://doi.org/10.1007/978-3-319-43425-4_20

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  • DOI: https://doi.org/10.1007/978-3-319-43425-4_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-43424-7

  • Online ISBN: 978-3-319-43425-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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