Skip to main content
SpringerLink
Log in

Efficient Implementations of the EM-Algorithm for Transient Markovian Arrival Processes

  • Conference paper
  • First Online:
Analytical and Stochastic Modelling Techniques and Applications (ASMTA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9845))

  • 681 Accesses

Abstract

There are real life applications (e.g., requests of http sessions in web browsing) with a finite number of events and correlated inter-arrival times. Terminating point processes can be used to model such behavior. Transient Markov arrival processes (TMAPs) are computationally appealing terminating point processes which are terminating versions of Markov arrival processes.

In this work we propose algorithms for creating a TMAP based on empirical measurement data and compare various (series/parallel, CPU/GPU) implementations of the EM method for TMAP fitting.

This work was supported by the Hungarian research project OTKA K119750.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Daley, D.J., Vere-Jones, D.: Finite point processes. In: Daley, D.J., Vere-Jones, D. (eds.) An Introduction to the Theory of Point Processes, pp. 111–156. Springer, New York (2003)

    Google Scholar 

  2. Anderson, T.W., Goodman, L.A.: Statistical inference about Markov chains. Ann. Math. Stat. 28, 89–110 (1957)

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  4. Buchholz, P.: An EM-algorithm for MAP fitting from real traffic data. In: Kemper, P., Sanders, W.H. (eds.) TOOLS 2003. LNCS, vol. 2794, pp. 218–236. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  5. Hautphenne, S., Latouche, G.: The Markovian binary tree applied to demography. J. Math. Biol. 64, 1109–1135 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hautphenne, S., Telek, M.: Extension of some MAP results to transient MAPs and Markovian binary trees. Perform. Eval. 70(9), 607–622 (2013)

    Article  Google Scholar 

  7. Horváth, G., Okamura, H.: A fast EM algorithm for fitting marked Markovian arrival processes with a new special structure. In: Balsamo, M.S., Knottenbelt, W.J., Marin, A. (eds.) EPEW 2013. LNCS, vol. 8168, pp. 119–133. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  8. Latouche, G., Remiche, M.-A., Taylor, P.: Transient Markov arrival processes. Ann. Appl. Probab. 13, 628–640 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  9. Okamura, H., Dohi, T.: Faster maximum likelihood estimation algorithms for Markovian arrival processes. In: Sixth International Conference on the Quantitative Evaluation of Systems, QEST 2009, pp. 73–82. IEEE (2009)

    Google Scholar 

  10. 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 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Kaunas University of Technology, Kaunas, Lithuania

    Mindaugas Bražėnas

  2. Department of Networked Systems and Services, Budapest University of Technology and Economics, Budapest, Hungary

    Gábor Horváth & Miklós Telek

  3. MTA-BME Information Systems Research Group, Budapest, Hungary

    Miklós Telek

Authors
  1. Mindaugas Bražėnas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gábor Horváth
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Miklós Telek
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gábor Horváth .

Editor information

Editors and Affiliations

  1. Ghent University , Gent, Belgium

    Sabine Wittevrongel

  2. University of Tsukuba , Tsukuba, Japan

    Tuan Phung-Duc

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Bražėnas, M., Horváth, G., Telek, M. (2016). Efficient Implementations of the EM-Algorithm for Transient Markovian Arrival Processes. In: Wittevrongel, S., Phung-Duc, T. (eds) Analytical and Stochastic Modelling Techniques and Applications. ASMTA 2016. Lecture Notes in Computer Science(), vol 9845. Springer, Cham. https://doi.org/10.1007/978-3-319-43904-4_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-43904-4_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-43903-7

  • Online ISBN: 978-3-319-43904-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation