A FUNCTIONAL-APPROACH TO THE STATIONARY WAITING TIME AND IDLE PERIOD DISTRIBUTIONS OF THE GI/G/1 QUEUE

• 成果类型: Article
• 署名作者: GRUBEL, R; PITTS, SM
• 署名单位: University of London; University College London
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989528
• 发表日期: 1992
• 页码: 1754-1778
• 关键词: renewal; perturbation

摘要

The GI/G/1 queueing model is regarded as a functional which maps the service and interarrival time distributions onto output quantities of interest, such as the stationary waiting time distribution. For the case where the input distributions have densities, techniques from infinite-dimensional analysis are used to obtain derivatives and Taylor series expansions for the functionals. These yield approximations to the output distributions which can be viewed as nonparametric alternatives to parametric approximations such as those provided by infinitesimal perturbation analysis or the phase method.