Representation Transformations for Finding Markovian Representations

  • András Mészáros
  • Gábor Horváth
  • Miklós Telek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7984)

Abstract

In this paper we consider existing and new representation transformation methods for non-Markovian generalizations of Markov chain driven stochastic models which intend transforming non-Markovian representations into Markovian ones and evaluate their efficiency through numerical experiments. One of the new features of the considered methods is the ability to obtain a Markovian representation of larger size.

Keywords

Markov arrival process Rational arrival process representation transformation Markovian representation 

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References

  1. 1.
    Neuts, M.F.: Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. Dover (1981)Google Scholar
  2. 2.
    Neuts, M.F.: A versatile Markovian point process. Journal of Applied Probability 16(4), 764–779 (1979)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    He, Q.M., Neuts, M.F.: Markov arrival processes with marked transitions. Stochastic Processes and their Applications 74, 37–52 (1998)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Bladt, M., Neuts, M.F.: Matrix-exponential distributions: Calculus and interpretations via flows. Stochastic Models 19(1), 113–124 (2003)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Bean, N., Nielsen, B.: Quasi-birth-and-death processes with rational arrival process components. Stochastic Models 26(3), 309–334 (2010)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Buchholz, P., Telek, M.: On minimal representations of rational arrival processes. Annals of Operations Research, 1–24 (2011)Google Scholar
  7. 7.
    Telek, M., Horváth, G.: A minimal representation of Markov arrival processes and a moments matching method. Performance Evaluation 64(9), 1153–1168 (2007)CrossRefGoogle Scholar
  8. 8.
    Buchholz, P., Kemper, P., Kriege, J.: Multi-class Markovian arrival processes and their parameter fitting. Performance Evaluation 67(11), 1092–1106 (2010)CrossRefGoogle Scholar
  9. 9.
    Harris, C.M., Marchal, W.G., Botta, R.F.: A note on generalized hyperexponential distributions. Stochastic Models 8(1), 179–191 (1992)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    O’Cinneide, C.A.: Triangular order of triangular phase-type distributions. Stochastic Models 9(4), 507–529 (1993)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • András Mészáros
    • 1
  • Gábor Horváth
    • 1
    • 3
  • Miklós Telek
    • 1
    • 2
  1. 1.Budapest University of Technology and EconomicsHungary
  2. 2.MTA-BME Information Systems Research GroupHungary
  3. 3.Inter-University Center of Telecommunications and InformaticsHungary

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