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Efficient Solutions for a Class of Non-Markovian Models

In: Computations with Markov Chains

Author

Listed:
  • Edmundo de Souza e Silva

    (Federal University of Rio de Janeiro, NCE and Computer Science Department)

  • H. Richard Gail

    (IBM Thomas J. Watson Research Center)

  • Richard R. Muntz

    (UCLA Computer Science Department)

Abstract

Although the use of embedded Markov chains has been known for some time, the application of this technique has been very ad hoc and has not been established as a standard approach for a wide class of models. Recently however, there has been progress in the direction of identifying an interesting class of models which are not Markovian but which can yield to a well defined solution method based on the analysis of an embedded Markov chain. Example applications that yield to this approach include polling models with deterministic timeout periods and models with deterministic service time queues. In this paper we derive efficient methods for computing both the transition probabilities for the embedded chain and performance measures expressible as Markov reward functions. Calculating the transition probabilities for the embedded chain requires transient analysis, and our computational procedures are based on uniformization. Examples are given to demonstrate the effectiveness of the methods and the extended class of models that are solvable with these techniques.

Suggested Citation

  • Edmundo de Souza e Silva & H. Richard Gail & Richard R. Muntz, 1995. "Efficient Solutions for a Class of Non-Markovian Models," Springer Books, in: William J. Stewart (ed.), Computations with Markov Chains, chapter 27, pages 483-506, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-2241-6_27
    DOI: 10.1007/978-1-4615-2241-6_27
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