Skip to main content
SpringerLink
Log in

Reducing the Cost of Generating APH-Distributed Random Numbers

  • Conference paper
Book cover Measurement, Modelling, and Evaluation of Computing Systems and Dependability and Fault Tolerance (MMB&DFT 2010)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 5987))

Abstract

Phase-type (PH) distributions are proven to be very powerful tools in modelling and analysis of a wide range of phenomena in computer systems. The use of these distributions in simulation studies requires efficient methods for generating PH-distributed random numbers. In this work, we discuss algorithms for generating random numbers from PH distributions and propose two algorithms for reducing the cost associated with generating random numbers from Acyclic Phase-Type distributions (APH).

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Fallahi, A., Hossain, E.: Distributed and Energy-Aware MAC for Differentiated Services Wireless Packet Networks: A General Queuing Analytical Framework. IEEE Transactions on Mobile Computing 6(4), 381–394 (2007)

    Article  Google Scholar 

  2. Reinecke, P., Wolter, K.: Phase-Type Approximations for Message Transmission Times in Web Services Reliable Messaging. In: Kounev, S., Gorton, I., Sachs, K. (eds.) SIPEW 2008. LNCS, vol. 5119, pp. 191–207. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  3. Reinecke, P., Wittkowski, S., Wolter, K.: Response-time Measurements Using the Sun Java Adventure Builder. In: QUASOSS 2009: Proceedings of the 1st International Workshop on Quality of Service-oriented Software Systems, pp. 11–18. ACM, New York (2009)

    Chapter  Google Scholar 

  4. Horváth, A., Telek, M.: PhFit: A General Phase-Type Fitting Tool. In: Field, T., Harrison, P.G., Bradley, J., Harder, U. (eds.) TOOLS 2002. LNCS, vol. 2324, pp. 82–91. Springer, Heidelberg (2002)

    Google Scholar 

  5. Thümmler, A., Buchholz, P., Telek, M.: A Novel Approach for Phase-Type Fitting with the EM Algorithm. IEEE Trans. Dependable Secur. Comput. 3(3), 245–258 (2006)

    Article  Google Scholar 

  6. Reinecke, P., Wolter, K., Bodrog, L., Telek, M.: On the Cost of Generating PH-distributed Random Numbers. In: Horváth, G., Joshi, K., Heindl, A. (eds.) Proceedings of the Ninth International Workshop on Performability Modeling of Computer and Communication Systems (PMCCS-9), Eger, Hungary, September 17-18 (2009)

    Google Scholar 

  7. Neuts, M.F.: Matrix-Geometric Solutions in Stochastic Models. An Algorithmic Approach. Dover Publications, Inc., New York (1981)

    MATH  Google Scholar 

  8. Telek, M., Heindl, A.: Matching Moments for Acyclic Discrete and Continous Phase-Type Distributions of Second Order. International Journal of Simulation Systems, Science & Technology 3(3-4), 47–57 (2002)

    Google Scholar 

  9. O’Cinneide, C.A.: Characterization of Phase-Type Distributions. Stochastic Models 6, 1–57 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  10. Cumani, A.: On the Canonical Representation of Homogeneous Markov Processes Modelling Failure-time Distributions. Microelectronics and Reliability 22, 583–602 (1982)

    Article  Google Scholar 

  11. O’Cinneide, C.A.: Phase-Type Distributions and Invariant Polytopes. Advances in Applied Probability 23(3), 515–535 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  12. He, Q.M., Zhang, H.: Spectral Polynomial Algorithms for Computing Bi-Diagonal Representations for Phase Type Distributions and Matrix-Exponential Distributions. Stochastic Models 22, 289–317 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  13. Pulungan, R.: Reduction of Acyclic Phase-Type Representations. PhD thesis, Universität des Saarlandes, Saarbrücken, Germany (2009)

    Google Scholar 

  14. Brown, E., Place, J., de Liefvoort, A.V.: Generating Matrix Exponential Random Variates. Simulation 70, 224–230 (1998)

    Article  MATH  Google Scholar 

  15. Szekli, R.: Stochastic Ordering and Dependence in Applied Probability. Springer, Heidelberg (1995)

    MATH  Google Scholar 

  16. Johnson, S.M.: Generation of Permutations by Adjacent Transposition. Mathematics of Computation 17(83), 282–285 (1963)

    Article  MATH  MathSciNet  Google Scholar 

  17. Knuth, D.E.: The Art of Computer Programming, vol. 3. Addison-Wesley, Reading (1997)

    Google Scholar 

  18. Mocanu, S., Commault, C.: Sparse Representations of Phase-type Distributions. Commun. Stat., Stochastic Models 15(4), 759–778 (1999)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik, Freie Universität Berlin, Takustraße 9, 14195, Berlin, Germany

    Philipp Reinecke & Katinka Wolter

  2. Department of Telecommunications, Budapest University of Technology and Economics, 1521, Budapest, Hungary

    Miklós Telek

Authors
  1. Philipp Reinecke
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Miklós Telek
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Katinka Wolter
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute for Computer Science and Business Information Systems, University of Duisburg-Essen, Schützenbahn 70, 45127, Essen, Germany

    Bruno Müller-Clostermann  & Klaus Echtle  & 

  2. Institute for Experimental Mathematics, Computer Networking Technology Group, University of Duisburg-Essen, Ellernstr. 29, D-45326, Essen, Germany

    Erwin P. Rathgeb

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Reinecke, P., Telek, M., Wolter, K. (2010). Reducing the Cost of Generating APH-Distributed Random Numbers. In: Müller-Clostermann, B., Echtle, K., Rathgeb, E.P. (eds) Measurement, Modelling, and Evaluation of Computing Systems and Dependability and Fault Tolerance. MMB&DFT 2010. Lecture Notes in Computer Science, vol 5987. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12104-3_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-12104-3_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12103-6

  • Online ISBN: 978-3-642-12104-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation