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On Uniformization for Continuous-Time Markov Chains

  • Conference paper
Operations Research ’93

  • 124 Accesses

Abstract

The method of uniformization or randomization for continuous-time Markov chains is shown to be extendable to chains with

  1. (i)

    time-inhomogeneous and

  2. (ii)

    unbounded

transition rates. Some approximate computational aspects are addressed also. A special application of uniformization of actual interest is included.

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References

  1. Gihman, I.I. and Skorohod, A.V. (1979): “Controlled Stochastic Processes”. Springer, Berlin.

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  2. Grassman, W. (1990): “Finding Transient Solutions in Markovian Event Systems through Randomization”. Proceedings of The First International Conference on the Numerical Solution of Markov Chains. Januari 8–10, Raleigh, NC. 375–385.

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  3. Gross, D. and Miller, D.R. (1984): “The Randomization Technique as a Modelling Tool and Solution Procedure for Transient Markov Processes”. Oper. Res. 32, 343–361.

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  4. Jensen, A. (1953): “Markovian Chains as an Aid in the Study of Markov Processes”. Skan. Aktuarietdskr. 36, 87–91.

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  5. Melamed, B. and Yadin, M. (1984): “Randomization Procedures in the Computation of Cumulative-Time Distributions over Discrete State Markov Processes”. Oper. Res. 32, 926–943.

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  6. Van Dijk, N.M. (1989): “Aproximation Uniformization for Continuous-Time Markov Chains with an Application ro Performability Analysis”. Stochastic Process Appl. 40, 339–357.

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Author information

Authors and Affiliations

  1. University of Amsterdam, The Netherlands

    Professor Nico M. van Dijk

Authors
  1. Professor Nico M. van Dijk
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Editor information

Editors and Affiliations

  1. Mathematisches Institut, Universität zu Köln, Weyertal 80, D-50931, Köln, Germany

    Achim Bachem

  2. Lehrstuhl für Wirtschaftsinformatik, Universität zu Köln, Pohligstraße 1, D-50969, Köln, Germany

    Ulrich Derigs

  3. Institut für Informatik, Universität zu Köln, Pohligstraße 1, D-50969, Köln, Germany

    Michael Jünger  & Rainer Schrader  & 

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© 1994 Physica-Verlag Heidelberg

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van Dijk, N.M. (1994). On Uniformization for Continuous-Time Markov Chains. In: Bachem, A., Derigs, U., Jünger, M., Schrader, R. (eds) Operations Research ’93. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-46955-8_29

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  • DOI: https://doi.org/10.1007/978-3-642-46955-8_29

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-0794-3

  • Online ISBN: 978-3-642-46955-8

  • eBook Packages: Springer Book Archive

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