A Law of the Iterated Logarithm for the Sojourn Time Process in Queues in Series

被引：3
|
作者：
Minkevicius, Saulius [1 ]
Dolgopolovas, Vladimiras [1 ]
Sakalauskas, Leonidas L. [1 ]
机构：
[1] Inst Math & Informat VU, Akad 4, LT-08663 Vilnius, Lithuania
来源：
METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY | 2016年 / 18卷 / 01期
关键词：
Queueing systems; Queues in series; Heavy traffic; A law of the iterated logarithm; Sojourn time of a customer; Maximum of the sojourn time of a customer; Statistical modeling; Monte Carlo simulation; IDENTICAL SERVICE TIMES; OPEN QUEUING-NETWORKS; EXTREME VALUES; SYSTEMS; APPROXIMATION; TANDEM; COUNTERS; MODEL;
D O I：
10.1007/s11009-014-9402-y
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
The object of this research in the sphere of queueing theory is the law of the iterated logarithm under the conditions of heavy traffic in queues in series. In this paper, the laws of the iterated logarithm are proved for the values of important probabilistic characteristics of the queueing system, like the sojourn time of a customer, and maximum of the sojourn time of a customer. Also, we prove that the sojourn time of a customer can be approximated by some recurrent functional. We also provide the results of statistical simulations for various system parameters and distributions.
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页码：37 / 57
页数：21
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