Nonparametric inference about service time distribution from indirect measurements

• 成果类型: Article
• 署名作者: Hall, P; Park, J
• 署名单位: Australian National University; University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2004.B5725.x
• 发表日期: 2004
• 页码: 861-875
• 关键词: EMPIRICAL CHARACTERISTIC FUNCTION; stationary waiting time; m/g/infinity queue; gi/g/1 queue; renewal

摘要

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.