Efficient simulation of a tandem Jackson network

Dirk P. Kroese, Victor F. Nicola

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    7 Citations (Scopus)

    Abstract

    We consider a two-node tandem Jackson network. Starting from a given state, we are interested in estimating the probability that the content of the second buffer exceeds some high level L before it becomes empty. The theory of Markov additive processes is used to determine the asymptotic decay rate of this probability, for large L. Moreover, the optimal exponential change of measure to be used in importance sampling is derived and used for efficient estimation of the rare event probability of interest. Unlike changes of measures proposed and studied in recent literature, the one derived here is a function of the content of the first buffer, and yields asymptotically efficient simulation for any set of arrival and service rates. The relative error is bounded independent of the level L, except when the first server is the bottleneck and its buffer is infinite, in which case the relative error is bounded linearly in L.
    Original languageEnglish
    Title of host publication Proceedings 1999 Winter Simulation Conference (WSC'99)
    Subtitle of host publication'Simulation - A Bridge to the Future'
    Place of PublicationPiscataway, NJ
    PublisherIEEE
    Pages411-419
    Number of pages8
    ISBN (Print)0-7803-5780-9
    DOIs
    Publication statusPublished - 6 Dec 1999
    Event1999 Winter Simulation Conference: Simulation - A Bridge to the Future - Phoenix, United States
    Duration: 5 Dec 19998 Dec 1999

    Conference

    Conference1999 Winter Simulation Conference
    Abbreviated titleWSC
    CountryUnited States
    CityPhoenix
    Period5/12/998/12/99

    Keywords

    • Buffer overflow
    • Monte Carlo methods
    • Australia
    • Feedforward systems
    • State estimation
    • Network servers
    • Testing
    • Analytical models
    • Discrete event simulation
    • State-space methods

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  • Cite this

    Kroese, D. P., & Nicola, V. F. (1999). Efficient simulation of a tandem Jackson network. In Proceedings 1999 Winter Simulation Conference (WSC'99): 'Simulation - A Bridge to the Future' (pp. 411-419). Piscataway, NJ: IEEE. https://doi.org/10.1109/WSC.1999.823103