On Numerical Approach to Stochastic Systems Modelling

Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 151)


The paper considers the problem of representing non-Markovian systems that evolve stochastically over time. It is often necessary to use approximations in the case the system is non-Markovian. Phase type distribution is by now indispensable tool in creation of stochastic system models. In the paper is suggested a method and software for evaluating stochastic systems approximations by Markov chains with continuous time and countable state space. The performance of a system is described in the event language is used for generating the set of states and transition matrix between them. The example of a numerical model is presented.


Non-Markovian system Approximation Phase type distribution Markov chain Numerical model 


  1. 1.
    Klinger D, Niekada Y, Menendez M (eds) (1989) AT&T Reliability Manual. Van Nostrand RheinholdGoogle Scholar
  2. 2.
    Stewart WJ (2009) Probability, Markov chains, queues and simulation. Princeton University Press, PrincetonMATHGoogle Scholar
  3. 3.
    Osogami T, Harchol-Balter M (2003) Necessary and sufficient conditions for representing general distributions by coxians, School of Computer Science, Carnegie Mellon UniversityGoogle Scholar
  4. 4.
    Asmussen S (2003) Applied probability and queues. Springer-Verlag, New YorkMATHGoogle Scholar
  5. 5.
    Johnson MA (1993) An empirical study of queuing approximations based on phase-type distributions. Commun Statist Stoch Models 9(4):531–561MATHCrossRefGoogle Scholar
  6. 6.
    Bladt M, Neuts MF (2003) Matrix-exponential distributions: calculus and inerpretations via flows// Stochas models 51(1):113–124Google Scholar
  7. 7.
    Pranevitchius H, Valakevitchius E (1996) Numerical models for systems represented by markovian processes. Kaunas Technologija, KaunasGoogle Scholar
  8. 8.
    Valakevicius E, Pranevicius H (2008) An algorithm for creating Markovian models of complex system. In: Proceedings of the 12th world multi-conference on systemics, cybernetics and informatics, June–July 2008, Orlando, USA, pp 258–262Google Scholar
  9. 9.
    Mickevičius G, Valakevičius E (2006) Modelling of non-Markovian queuing systems. Technological and economic development of economy 7(4):295–300Google Scholar
  10. 10.
    Cox DR (1955) A use of complex probabilities in the theory of stochastic process// Proc Cambr Phil Soc 51:313–319Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Mathematical Research in Systems KaunasUniversity of Technology KaunasKaunasLithuania

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