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.

引用

页码：37 / 57

页数：21

共 50 条

[41] AN EXTENSION OF LAI AND WEI LAW OF THE ITERATED LOGARITHM WITH APPLICATIONS TO TIME-SERIES ANALYSIS AND REGRESSION
CHEN, ZG
[J]. JOURNAL OF MULTIVARIATE ANALYSIS, 1990, 32 (01) : 55 - 69
[42] A REMARK ON LAW OF ITERATED LOGARITHM
FREEDMAN, DA
[J]. ANNALS OF MATHEMATICAL STATISTICS, 1967, 38 (02): : 589 - &
[43] THEOREM ON LAW OF ITERATED LOGARITHM
PETROV, VV
[J]. THEORY OF PROBILITY AND ITS APPLICATIONS,USSR, 1971, 16 (04): : 700 - 702
[44] ASYMPTOTICS IN THE LAW OF THE ITERATED LOGARITHM
Cwiklinska, M. B.
[J]. THEORY OF PROBABILITY AND ITS APPLICATIONS, 2009, 53 (04) : 707 - U143
[45] AN EXTENSION OF THE LAW OF THE ITERATED LOGARITHM
CASSELS, JWS
[J]. PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1951, 47 (01): : 55 - 64
[46] On the Makarov law of the iterated logarithm
Hedenmalm, Hakan
Kayumov, Ilgiz
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 135 (07) : 2235 - 2248
[47] The Law of the Iterated Logarithm for SLE
Kang, Nam-Gyu
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2007, 2007
[48] A NEW LAW OF ITERATED LOGARITHM
ERDOS, P
REVESZ, P
[J]. ACTA MATHEMATICA HUNGARICA, 1990, 55 (1-2) : 125 - 131
[49] VARIANTS ON THE LAW OF THE ITERATED LOGARITHM
BINGHAM, NH
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1986, 18 : 432 - 467
[50] NORMALIZATION IN LAW OF ITERATED LOGARITHM
BULINSKII, AV
[J]. THEORY OF PROBABILITY AND ITS APPLICATIONS, 1977, 22 (02) : 398 - 399

← 1 2 3 4 5 →