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Acta Mathematica Sinica,English Series 2020年第10期36卷 1183-1202页

作者： Nurehemaiti YIMING geni gupur College of Mathematics and Systems Science Xinjiang UniversityUrumqi 830046P.R.China

We describe the point spectrum of the operator which corresponds to the M/M/1 queueing model with vacations and multiple phases of operation.Then by using this result we prove that the essential growth bound of the C0-semigroup generated by the operator is 0,the C0-semigroup is not compact,not eventually compact,even not quasi-compact.Moreover,we verify that it is impossible that the time-dependent solution of the M/M/1 queueing model with vacations and multiple phases of operation exponentially converges to its steady-state solution.In addition,we obtain the spectral radius and essential spectral radius of the C0-semigroup.Lastly,we discuss other spectrum of the operator and obtain a set which belongs to the union of its continuous spectrum and residual spectrum.

关键词： M/M/1 queueing model with vacations and multiple phases of operation time-dependent solution C0-semigroup point spectrum spectrum

Existence and Uniqueness of Endemic States for the Age-structured MSEIR Epidemic Model

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Acta Mathematicae Applicatae Sinica 2002年第3期18卷 441-454页

作者： geni gupur Department of Mathematics Xinjiang UniversityUrumqi 830046China

The existence and uniqueness of positive steady states for the age-structured MSEIR epidemic model with age-dependent transmission coefficient is considered. Threshold results for the existence of endemic states are e... 详细信息

关键词： MSEIR epidemic model age-structure Co-semigroup abstract Cauchy problem endemic state threshold value

WELL-POSEDNESS OF THE MODEL DESCRIBING A REPAIRABLE,STANDBY,HUMAN & MACHINE SYSTEM

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Journal of Systems Science & Complexity 2003年第4期16卷 483-493页

作者： geni gupur College of Mathematics and Systems Sciences Xinjiang University Urumqi 830046 China

By using the strong continuous semigroup theory of linear operators we prove the existence of a unique positive time-dependent solution of the model describing a re-pairable, standby, human & machine system.

关键词：人机系统可修理性可信任性适定性强连续半群线性算子积分微分方程

Point Spectra of the Operator Corresponding to the M/M/1 Queueing Model with Working Vacation and Vacation Interruption

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Journal of Mathematical Research with Applications 2019年第1期39卷 75-88页

作者： Ehmet KASIM geni gupur College of Mathematics and Systems Science Xinjiang University

In this paper, we consider point spectra of the operator corresponding to the M/M/1 queueing model with working vacation and vacation interruption. We prove that the underlying operator has uncountable eigenvalues on the left real line and these results describe the point spectra of the operator. Then, we show that the essential growth bound of the C;-semigroup generated by the operator is 0 and therefore it is not quasi compact, the essential spectral bound of the C;-semigroup is equal to 1. Moreover, our results imply it is impossible that the time-dependent solution of the model exponentially converges to its steady-state solution.

关键词： M/M/1 queueing model working vacation and vacation interruption C0-semigroup eigenvalue essential spectral bound

服务失效状态为吸收状态及重试率为常数的M^([X])/M/1排队模型的主算子的谱分析

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新疆大学学报（自然科学版中英文） 2024年第3期41卷 296-309页

作者：鞠泽南艾尼·吾甫尔新疆大学数学与系统科学学院新疆乌鲁木齐830017

研究服务失效状态为吸收状态及重试率为常数的M^([X])/M/1排队模型的主算子在左半复平面中的谱.当顾客的到达率λ,服务员的服务率ν,顾客的重试率α和服务员的服务完成率b满足一定的条件时,证明了实部为-(λ+ν+b)的所有复数都不是该模... 详细信息

研究服务失效状态为吸收状态及重试率为常数的M^([X])/M/1排队模型的主算子在左半复平面中的谱.当顾客的到达率λ,服务员的服务率ν,顾客的重试率α和服务员的服务完成率b满足一定的条件时,证明了实部为-(λ+ν+b)的所有复数都不是该模型主算子的特征值;当λ,ν, α, b满足一定的条件时,证明了区间(-(λ+ν+b),0)中无穷多个点是该主算子的几何重数为1的特征值.

关键词： M^([X])/M/1排队模型主算子谱特征值几何重数

Time-dependent analysis for a queue modeled by an infinite system of partial differential equations

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Science China Mathematics 2012年第5期55卷 985-1004页

作者： gupur geni College of Mathematics and Systems Science Xinjiang University

By studying the spectrum of the underlying operator corresponding to the exhaustive-service M/G/1 queueing model with single vacations we prove that the time-dependent solution of the model strongly converges to its s... 详细信息

关键词：偏微分方程系统时间变化 M/G/1排队队列建模排队模型时间依赖解单重休假

FUNCTIONAL ANALYSIS METHOD FOR THE M/G/1 QUEUEING MODEL WITH OPTIONAL SECOND SERVICE

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Acta Mathematica Scientia 2014年第4期34卷 1301-1330页

作者：艾尼.吾甫尔艾合买提.卡斯木 College of Mathematics and System Sciences Xinjiang University

By studying the spectral properties of the underlying operator corresponding to the M/G/1 queueing model with optional second service we obtain that the time-dependent solution of the model strongly converges to its steady-state solution. We also show that the time-dependent queueing size at the departure point converges to the corresponding steady-state queueing size at the departure point.

关键词： M/G/1 queueing model with optional second service eigenvalue resolvent set

由两个同型部件和一个修理设备组成的系统的主算子的谱

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新疆大学学报（自然科学版）（中英文） 2022年第1期39卷 26-33页

作者：艾尼·吾甫尔新疆大学数学与系统科学学院新疆乌鲁木齐830017

文章研究了由两个同型部件和一个修理设备组成的系统的主算子在左半复平面中的谱.在一定的条件下,该系统的主算子在左半复平面中的任何带形区域至多有有限多个特征值,且这些特征值的几何重数为1.该模型的主算子的共轭算子在左半复平面... 详细信息

文章研究了由两个同型部件和一个修理设备组成的系统的主算子在左半复平面中的谱.在一定的条件下,该系统的主算子在左半复平面中的任何带形区域至多有有限多个特征值,且这些特征值的几何重数为1.该模型的主算子的共轭算子在左半复平面中的任何带形区域至多有有限多个特征值,且这些特征值的几何重数为1.0是该系统的主算子及其共轭算子的严格占优特征值.

关键词：由两个同型部件和一个修理设备组成的系统 C_(0)−半群特征值谱算子