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Nonparametric inference about service time distribution from indirect measurements

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  • Peter Hall
  • Juhyun Park

Abstract

Summary. 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.

Suggested Citation

  • Peter Hall & Juhyun Park, 2004. "Nonparametric inference about service time distribution from indirect measurements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 861-875, November.
    • Handle: RePEc:bla:jorssb:v:66:y:2004:i:4:p:861-875
    DOI: 10.1111/j.1467-9868.2004.B5725.x
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    References listed on IDEAS

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    1. N.H. Bingham & Bruce Dunham, 1997. "Estimating Diffusion Coefficients From Count Data: Einstein-Smoluchowski Theory Revisited," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(4), pages 667-679, December.
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    Cited by:

    1. Schweer, Sebastian & Wichelhaus, Cornelia, 2015. "Nonparametric estimation of the service time distribution in the discrete-time GI/G/∞ queue with partial information," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 233-253.
    2. Park, Juhyun, 2007. "On the choice of an auxiliary function in the M/G/[infinity] estimation," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5477-5482, August.
    3. Martin Bøgsted & Susan Pitts, 2010. "Decompounding random sums: a nonparametric approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(5), pages 855-872, October.
    4. Aleksandrina Goeva & Henry Lam & Huajie Qian & Bo Zhang, 2019. "Optimization-Based Calibration of Simulation Input Models," Operations Research, INFORMS, vol. 67(5), pages 1362-1382, September.
    5. Li, Dongmin & Hu, Qingpei & Wang, Lujia & Yu, Dan, 2019. "Statistical inference for Mt/G/Infinity queueing systems under incomplete observations," European Journal of Operational Research, Elsevier, vol. 279(3), pages 882-901.
    6. Wenwen Li & Alexander Goldenshluger, 2024. "Adaptive minimax estimation of service time distribution in the $$M_t/G/\infty $$ M t / G / ∞ queue from departure data," Queueing Systems: Theory and Applications, Springer, vol. 108(1), pages 81-123, October.
    7. Azam Asanjarani & Yoni Nazarathy & Peter Taylor, 2021. "A survey of parameter and state estimation in queues," Queueing Systems: Theory and Applications, Springer, vol. 97(1), pages 39-80, February.

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