[1]阿力木·米吉提.附有必选和可选服务的M/G/1/1反馈排队模型主算子的谱特征[J].江西师范大学学报(自然科学版),2018,(03):260-266.[doi:10.16357/j.cnki.issn1000-5862.2018.03.08]
　ALIM Mijit.The Spectral Properties of the Operator Corresponding to the M/G/1/1 Feedback Queue with Regular and Optional Services[J].Journal of Jiangxi Normal University:Natural Science Edition,2018,(03):260-266.[doi:10.16357/j.cnki.issn1000-5862.2018.03.08]
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附有必选和可选服务的M/G/1/1反馈排队模型主算子的谱特征()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2018年03期
页码:
260-266
栏目:
数学与应用数学
出版日期:
2018-06-20

文章信息/Info

Title:
The Spectral Properties of the Operator Corresponding to the M/G/1/1 Feedback Queue with Regular and Optional Services
文章编号:
1000-5862(2018)03-0260-07
作者:
阿力木·米吉提
新疆广播电视大学,新疆 乌鲁木齐 830049
Author(s):
ALIM Mijit
Xinjiang Radio and TV University,Urumqi Xinjiang 830049,China
关键词:
M/G/1/1 反馈排队;  必选和可选服务;  特征值;  几何重数;  豫解集
Keywords:
M/G/1/1 feedback queue;  regular and optional service;  eigenvalue;  geometric multiplicity;  resolvent set
分类号:
O 177.7
DOI:
10.16357/j.cnki.issn1000-5862.2018.03.08
文献标志码:
A
摘要:
在一定条件下,通过研究附有必选和可选服务的M/G/1/1反馈排队模型主算子的谱特征,得到该反馈排队模型时间依赖解的渐近行为.为此,首先证明0是此模型主算子的几何重数为1的特征值; 其次求出此反馈排队模型主算子的共轭算子表达式,并证明0是此共轭算子的几何重数为1的特征值; 然后在一定条件下推出虚轴上除了0外,其他的所有点都属于该反馈排队模型主算子的豫解集; 最后在同样条件下,将上述结果结合在一起推出:该模型的时间依赖解强收敛于其稳态解.
Abstract:
Under a certain condition,by studying the spectral properties of the underlying operator which corresponding to the M/G/1/1 feedback queue with regular and optional service,the asymptotic behavior of the time dependent solution of this queueing model has been obtained.First,it is proved that zero is an eigenvalue of the underlying operator with geometric multiplicity one.Next,by studying the expression of the adjoint operator of the underlying operator,it is proved that zero is an eigenvalue of the adjoint operator with geometric multiplicity one.Then,under a certain condition,it has been deduced that all points on the imaginary axis except zero belong to the resolvent set of the underlying operator corresponding to the system model.Thus,under the same condition,by combining the above results,it is obtained that the time-dependent solution of the system model converges strongly to its steady state solution.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2017-11-25
基金项目:新疆少数民族科技人才特殊培养计划科研(2016D0211)和国家自然科学基金(11601464)资助项目.
作者简介:阿力木·米吉提(1978-),男,新疆阿克陶人,副教授,主要从事排队模型的动态分析研究.E-mail:alimjanmijit@aliyun.com
更新日期/Last Update: 2018-06-20