Nonparametric inference about service time distribution from indirect measurements

• Published in: Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 66; no. 4; pp. 861 - 875
• Main Authors: Hall, Peter, Park, Juhyun
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing 01.11.2004; Blackwell Publishers; Blackwell; Royal Statistical Society; Oxford University Press
• Series: Journal of the Royal Statistical Society Series B
• Subjects: Alternating renewal process; Bandwidth; Cafeterias; Density estimation; Distribution functions; Distribution theory; Eigenfunctions; Estimation; Estimation methods; Estimators; Exact sciences and technology; Inference; Kernel methods; Mathematical expressions; Mathematics; Measurement; Methodology; Nonparametric density estimation; Nonparametric inference; Probability and statistics; Probability theory and stochastic processes; Queuing theory; Renewal process; Sample size; Sciences and techniques of general use; Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications); Statistical methods; Statistics; Studies; Traffic estimation; Density estimation; Bandwith selection; Renewal process; Non parametric estimation; Kernel estimation; Kernel method; Statistical method; Time distribution; Service time; Busy period; Distribution shape; Bandwidth; Queueing theory
• ISSN: 1369-7412; 1467-9868
• DOI: 10.1111/j.1467-9868.2004.B5725.x

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.