Monte Carlo summation and integration applied to multiclass queuing networks

Keith Ross, Danny H K Tsang, Jie Wang

    Research output: Contribution to journalArticle

    Abstract

    Although many closed multiclass queuing networks have a product-form solution, evaluating their performance measures remains nontrivial due to the presence of a normalization constant. We propose the application of Monte Carlo summation in order to determine the normalization constant, throughputs, and gradients of throughputs. A class of importance-sampling functions leads to a decomposition approach, where separate single-class problems are first solved in a setup module, and then the original problem is solved by aggregating the single-class solutions in an execution model. We also consider Monte Carlo methods for evaluating performance measures based on integral representations of the normalization constant; a theory for optimal importance sampling is developed. Computational examples are given that illustrate that the Monte Carlo methods are robust over a wide range of networks and can rapidly solve networks that cannot be handled by the techniques in the existing literature.

    Original languageEnglish (US)
    Pages (from-to)1110-1135
    Number of pages26
    JournalJournal of the ACM
    Volume41
    Issue number6
    DOIs
    StatePublished - Nov 1994

    Fingerprint

    Queuing Networks
    Importance sampling
    Multi-class
    Summation
    Normalization
    Monte Carlo methods
    Importance Sampling
    Throughput
    Performance Measures
    Monte Carlo method
    Product Form Solution
    Decomposition
    Integral Representation
    Gradient
    Decompose
    Closed
    Module
    Range of data
    Class
    Model

    ASJC Scopus subject areas

    • Computational Theory and Mathematics
    • Computer Graphics and Computer-Aided Design
    • Hardware and Architecture
    • Information Systems
    • Software
    • Theoretical Computer Science

    Cite this

    Monte Carlo summation and integration applied to multiclass queuing networks. / Ross, Keith; Tsang, Danny H K; Wang, Jie.

    In: Journal of the ACM, Vol. 41, No. 6, 11.1994, p. 1110-1135.

    Research output: Contribution to journalArticle

    Ross, Keith ; Tsang, Danny H K ; Wang, Jie. / Monte Carlo summation and integration applied to multiclass queuing networks. In: Journal of the ACM. 1994 ; Vol. 41, No. 6. pp. 1110-1135.
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