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On Discrete—Form Expressions for Time—Inhomogeneous Cumulative Reward Structures

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Part of the book series: Operations Research Proceedings ((ORP,volume 1997))

Abstract

The technique of uniformization, introduced by Jensen [3] and also known as randomization, is widely known as a fruitful tool to transform (homogeneous) continuous-time Markov chains into discrete-time Markov chains, both for theoretical and computational purposes, most notably to evaluate performance measure such as arising in manufacturing, telecommunications and computer performance (see e.g. [1], [2], [4]).

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References

  1. Grassman, W.: Finding transient solutions in Markovian event systems through randomization. In: Numerical Solution of Markov Chains (W. J. Stewart, ed.), Marcel Dekker, New York 1990, pp. 375–385.

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  2. Gross, D., Miller, D.R.: The randomization technique as a modelling tool and solution procedure for transient Markov processes. Oper. Res. 32 (1984), 343–361.

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  3. Jensen, A.: Markovian chains as an aid in the study of Markov processes. Scand. Actuar. J. 36 (1953), 87–91.

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  4. Van Dijk, N.M.: Approximate uniformization for continuous-time Markov chains with an application to performability analysis. Stoch. Process. Appl. 40 (1992), 339–357.

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  5. Van Dijk, N. M.: Uniformization for nonhomogeneous Markov chains. Oper. Res. Lett. 12 (1992), 283–291.

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  6. Van Dijk, N.M., Sladký, K.: On Approximative Expressions for Cumulative Rewards of Time-Inhomogeneous Nonnegative Systems. Research Report, Institute of Information Theory and Automation, No. 1903, Prague, July 1997.

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© 1998 Springer-Verlag Berlin Heidelberg

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van Dijk, N.M., Sladký, K. (1998). On Discrete—Form Expressions for Time—Inhomogeneous Cumulative Reward Structures. In: Operations Research Proceedings 1997. Operations Research Proceedings, vol 1997. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58891-4_25

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  • DOI: https://doi.org/10.1007/978-3-642-58891-4_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64240-4

  • Online ISBN: 978-3-642-58891-4

  • eBook Packages: Springer Book Archive

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