A Fast Cross-Entropy Method for Estimating Buffer Overflows in Queueing Networks

P.T. de Boer, D.P. Kroese, R.Y. Rubinstein

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    38 Citations (Scopus)
    10 Downloads (Pure)

    Abstract

    In this paper, we propose a fast adaptive importance sampling method for the efficient simulation of buffer overflow probabilities in queueing networks. The method comprises three stages. First, we estimate the minimum cross-entropy tilting parameter for a small buffer level; next, we use this as a starting value for the estimation of the optimal tilting parameter for the actual (large) buffer level. Finally, the tilting parameter just found is used to estimate the overflow probability of interest. We study various properties of the method in more detail for the M/M/1 queue and conjecture that similar properties also hold for quite general queueing networks. Numerical results support this conjecture and demonstrate the high efficiency of the proposed algorithm.
    Original languageEnglish
    Pages (from-to)883-895
    Number of pages13
    JournalManagement science
    Volume50
    Issue number7
    DOIs
    Publication statusPublished - Jul 2004

    Keywords

    • Cross-entropy
    • Rare events
    • Queueing networks
    • Simulation
    • Importance sampling

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