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International Conference on Quantitative Evaluation of Systems

QEST 2015: Quantitative Evaluation of Systems pp 105–112Cite as

mapfit: An R-Based Tool for PH/MAP Parameter Estimation

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9259))

Abstract

In this paper, we present a tool for estimating parameters of phase-type distribution (PH) and Markovian arrival process (MAP) on the statistical analysis package R. PH and MAP are useful for the analysis of non-Markovian models approximately. By approximating general distributions and point processes with PH and MAP, the non-Markovian models is reduced to continuous-time Markov chains (CTMCs) that can be solved by analytical approaches. The significant features of our tool are (i) PH/MAP fitting from grouped data and (ii) PH fitting from probability density functions.

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Notes

  1. 1.

    http://home.math.au.dk/asmus/pspapers.html.

  2. 2.

    http://webspn.hit.bme.hu/~telek/tools.htm.

  3. 3.

    http://www.cs.cmu.edu/~osogami/code/momentmatching/index.html.

  4. 4.

    http://webspn.hit.bme.hu/~telek/tools/butools/butools.html.

  5. 5.

    http://ls4-www.cs.tu-dortmund.de/home/thummler/mainE.html.

  6. 6.

    http://copa.uniandes.edu.co/?p=141.

  7. 7.

    http://www.mi.fu-berlin.de/inf/groups/ag-tech/projects/HyperStar/index.html.

  8. 8.

    http://www.cs.cmu.edu/~osogami/code/momentmatching/index.html.

  9. 9.

    http://webspn.hit.bme.hu/~telek/tools/butools/butools.html.

  10. 10.

    http://ita.ee.lbl.gov/html/contrib/BC.html.

References

  1. Asmussen, S., Nerman, O., Olsson, M.: Fitting phase-type distributions via the EM algorithm. Scand. J. Stat. 23(4), 419–441 (1996)

    MATH  Google Scholar 

  2. Bobbio, A., Horváth, A., Telek, M.: Matching three moments with minimal acyclic phase type distributions. Stoch. Models 21(2/3), 303–326 (2005)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  4. Okamura, H., Dohi, T.: Faster maximum likelihood estimation algorithms for Markovian arrival processes. In: Proceedings of 6th International Conference on Quantitative Evaluation of Systems (QEST2009), pp. 73–82 (2009)

    Google Scholar 

  5. Okamura, H., Dohi, T., Trivedi, K.S.: Markovian arrival process parameter estimation with group data, in submission

    Google Scholar 

  6. Okamura, H., Dohi, T., Trivedi, K.S.: A refined EM algorithm for PH distributions. Perform. Eval. 68(10), 938–954 (2011)

    Article  Google Scholar 

  7. Okamura, H., Dohi, T., Trivedi, K.S.: Improvement of EM algorithm for phase-type distributions with grouped and truncated data. Appl. Stochast. Models Bus. Ind. 29(2), 141–156 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Osogami, T., Harchol-Balter, M.: Closed form solutions for mapping general distributions to minimal PH distributions. Perform. Eval. 63(6), 524–552 (2006)

    Article  Google Scholar 

  9. Panchenko, A., Thümmler, A.: Efficient phase-type fitting with aggregated traffic traces. Perform. Eval. 64, 629–645 (2007)

    Article  Google Scholar 

  10. Perez, J.F., Riano, G.: jPhase: an object-oriented tool for modeling phase-type distributions. In: In SMCtools 2006: Proceeding from the 2006 Workshop on Tools for Solving Structured Markov Chains, p. 5. ACM (2006)

    Google Scholar 

  11. Rydén, T.: An EM algorithm for estimation in Markov-modulated poisson processes. Comput. Stat. Data Anal. 21(4), 431–447 (1996)

    Article  MATH  Google Scholar 

  12. Takahasi, H., Mori, M.: Double exponential formulas for numerical integration. Publ. RIMS Kyoto Univ. 9, 721–741 (1974)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Information Engineering, Graduate School of Engineering, Hiroshima University, 1–4–1 Kagamiyama, Higashi-Hiroshima, 739–8527, Japan

    Hiroyuki Okamura & Tadashi Dohi

Authors
  1. Hiroyuki Okamura
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  2. Tadashi Dohi
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Corresponding author

Correspondence to Hiroyuki Okamura .

Editor information

Editors and Affiliations

  1. Universidad de Zaragoza, Zaragoza, Spain

    Javier Campos

  2. University of Twente, Enschede, The Netherlands

    Boudewijn R. Haverkort

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Okamura, H., Dohi, T. (2015). mapfit: An R-Based Tool for PH/MAP Parameter Estimation. In: Campos, J., Haverkort, B. (eds) Quantitative Evaluation of Systems. QEST 2015. Lecture Notes in Computer Science(), vol 9259. Springer, Cham. https://doi.org/10.1007/978-3-319-22264-6_7

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  • DOI: https://doi.org/10.1007/978-3-319-22264-6_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22263-9

  • Online ISBN: 978-3-319-22264-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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