NONPARAMETRIC-ESTIMATION OF THE STATIONARY WAITING TIME DISTRIBUTION FUNCTION FOR THE GI/G/1 QUEUE

• 成果类型: Article
• 署名作者: PITTS, SM
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176325635
• 发表日期: 1994
• 页码: 1428-1446
• 关键词: renewal function

摘要

The GI/G/1 queueing model is regarded as a functional that maps the service and interarrival time distribution functions onto the stationary waiting time distribution function. By considering the output of the functional when it is applied to nonparametric estimators of the input distribution functions, we obtain a nonparametric estimator of the stationary waiting: time distribution function. Using appropriate continuity and differentiability properties of the functional, we show that statistical properties of the input estimators carry over to corresponding properties for the stationary waiting time distribution function estimator.