Nonparametric inference about service time distribution from indirect measurements

Peter Hall*, Juhyun Park

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    31 Citations (Scopus)

    Abstract

    In studies of properties of queues, for example in relation to Internet traffic, a subject that is of particular interest is the 'shape' of service time distribution. For example, we might wish to know whether the service time density is unimodal, suggesting that service time distribution is possibly homogeneous, or whether it is multimodal, indicating that there are two or more distinct customer populations. However, even in relatively controlled experiments we may not have access to explicit service time data. Our only information might be the durations of service time clusters, i.e. of busy periods. We wish to 'deconvolve' these concatenations, and to construct empirical approximations to the distribution and, particularly, the density function of service time. Explicit solutions of these problems will be suggested. In particular, a kernel-based 'deconvolution' estimator of service time density will be introduced, admitting conventional approaches to the choice of bandwidth.

    Original languageEnglish
    Pages (from-to)861-875
    Number of pages15
    JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
    Volume66
    Issue number4
    DOIs
    Publication statusPublished - 2004

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