Monte carlo summation applied to product-form loss networks

Keith Ross, Jie Wang

    Research output: Contribution to journalArticle

    Abstract

    Loss networks with direct routing have a product-form solution for their equilibrium probabilities. The product-form solution typically involves a normalization constant calling for a multidimensional summation over an astronomical number of states. We propose the application of Monte Carlo summation in order to determine the normalization constant, the blocking probabilities, and the revenue sensitivities. We show that if the proper sampling technique is employed, then the computational effort of Monte Carlo summation is independent of link capacities. We also discuss the application of importance sampling, antithetic variates, and indirect estimation via Little's formula. The method is illustrated with a four-leaf star network supporting multirate traffic.

    Original languageEnglish (US)
    Pages (from-to)323-348
    Number of pages26
    JournalProbability in the Engineering and Informational Sciences
    Volume6
    Issue number3
    DOIs
    StatePublished - Jul 1992

    ASJC Scopus subject areas

    • Statistics and Probability
    • Statistics, Probability and Uncertainty
    • Management Science and Operations Research
    • Industrial and Manufacturing Engineering

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