Strong approximation method and the (functional) law of iterated logarithm for GI/G/1 queue

被引：2

作者：

Guo, Yongjiang ^{[1
]}

Hou, Xiyang ^{[2
]}

机构：

[1] Beijing Univ Posts & Telecommun, Sch Sci, Beijing 100876, Peoples R China

[2] Beijing Univ Posts & Telecommun, Automat Sch, Beijing 100876, Peoples R China

来源：

JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY | 2017年 / 30卷 / 05期

基金：

中国国家自然科学基金;

关键词：

GI/G/1; queue; renewal process (RP); strong approximation (SA) method; the functional LIL (FLIL); the law of the iterated logarithm (LIL); NETWORKS;

D O I：

10.1007/s11424-017-5226-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, a unified method based on the strong approximation (SA) of renewal process (RP) is developed for the law of the iterated logarithm (LIL) and the functional LIL (FLIL), which quantify the magnitude of the asymptotic rate of the increasing variability around the mean value of the RP in numerical and functional forms respectively. For the GI/G/1 queue, the method provides a complete analysis for both the LIL and the FLIL limits for four performance functions: The queue length, workload, busy time and idle time processes, covering three regimes divided by the traffic intensity.

引用

页码：1097 / 1106

页数：10

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