On existence and asymptotic behavior of the time-dependent solution of the M/G/1 queueing model with optional deterministic server vacations

被引：2

作者：

Kasim, Ehmet ^{[1
]}

Gupur, Geni ^{[1
]}

机构：

[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China

来源：

AFRIKA MATEMATIKA | 2020年 / 31卷 / 3-4期

基金：

中国国家自然科学基金;

关键词：

M/G/1 queueing model with optional deterministic server vacations; C-0-semigroup; Dispersive operator; Resolvent set; Eigenvalue;

D O I：

10.1007/s13370-019-00739-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the M/G/1 queueing model with optional deterministic server vacations. Firstly, we convert the system into an abstract Cauchy problem, then we prove well-posedenss of the system by using the operator semigroup methods. Next, we investigate asymptotic behavior of its time-dependent solution by studying spectral properties of the corresponding operator. Therefore, we conclude that the time-dependent solution of the model strongly converges to its steady-state solution.

引用

页码：507 / 537

页数：31

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[1] On existence and asymptotic behavior of the time-dependent solution of the M/G/1 queueing model with optional deterministic server vacations
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