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《Acta Analysis Functionalis Applicata》 2008-01
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Another Eigenvalue of the M/M/1 Operator

ZHANG Long, Geni GupurCollege of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China  
We prove that 2 2~(1/(λμ))-λ-μ is an eigenvalue of the operator corresponding the M/M/1 queueing model described by partial-differential equations, with geometric multiplicity one.
【Fund】: 教育部重点项目(205180);; 新疆维吾尔自治区高校研究计划优秀青年学者奖励基金(XJEDU2004E05);; 新疆大学科学基金
【CateGory Index】: O226
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【References】
Chinese Journal Full-text Database 1 Hits
1 ZHAO Zhixue~1,SHAO Chen~2,XU Genqi~1 1.Department of Mathematics,Tianjin University,Tianjin 300072,China 2.Applied Science College,Harbin University of Science and Technology,Harbin 150050,China;Spectral Analysis of Operator in M/M/1 Queueing Model Described by Ordinary Differential Equations[J];Acta Analysis Functionalis Applicata;2010-02
【Citations】
Chinese Journal Full-text Database 4 Hits
1 Geni.Gupur (Mathematics Department, Xinjiang University, Urumqi 830046);Existence of the Unique Non negative Solution for M/M/1 Model[J];SYSTEMS ENGINEERING-THEORY & PRACTICE;1998-10
2 GUPUR Geni, LI Xue-zhi (Department of Mathematics, Xinjiang University, Urumqi 830046, China Department of Mathematics, Xinyang Teachers College, Henan 464000, China Institute of Systems Science, Academia Sinica, Beijing 100080, China);A Note on the M/M/1 Queueing Model Described by Ordinary Differential Equations[J];ACTA ANALYSIS FUNCTIONALIS APPLICATA;1999-01
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4 LI Yang- rong Departmentof Mathematics,Southwest China Normal University,Chongqing 40 0 71 5,China;l~1-Solution and stability of the M/M/1 Queueing Model[J];Acta Analysis Functionalis Applicata;2000-02
【Co-citations】
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1 HAN Songxia, YE Jianjun(Dept. of Applied Mathematics, Southwest Jiaotong University, Chengdu610031, China);Properly posed problem of Kolmogorov backward differential equations[J];Journal of Gansu University of Technology;2002-04
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3 WANG Xiu-ling1,XING Xi-min2(1.Department of Mathematics,Suqian Higher Normal School,Suqian 223800,China;2.Hetian Seismostation of Seismological Bureau of Xinjiang Uygur Autonomous Region,Hetian 848000,China);Well-Posedness of M/G1/1 Models with Service to Negative Customers[J];Journal of Jiangnan University(Natural Science Edition);2010-03
4 Liu Yumin (Department of Mathematics,Taiyuan Teachers College, Taiyuan 030012, China);An Application on Major Operator's Eigenvalue of the M/M/n Queueing Model[J];Journal of Shanxi Educational College;2005-03
5 LIU Yu\|min, XU Gen\|qi (Department of Mathematics, Shanxi University, Taiyuan 030006, China);Dynamic Solution and Stability on the M/M/n Queueing Model[J];Mathematics In Practice and Theory;2002-03
6 Geni Gupur 1,3 , CAO Jun2 (1.College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China)(2.Deprtment of Mathematics, Xinyang Normal University, Henan 464000, China)(3.Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China);Asymptotic Properties of the Four Indices for M/M/1 Queue System[J];Mathematics In Practice and Theory;2003-01
7 GAO De-zhi(Information Science and Engineering College,Shandong University of Science and Technology,Qingdao Shandong 266510,China);On Asymptotic Stability of Two Kinds of M/M/1 Queueing Systems[J];Mathematics in Practice and Theory;2008-17
8 HAN Song-xia(School of Mathematics and Computer Engineering,Xihua University,Chengdu 610039,China);Regular Value and Point Specyrum of Kolmogorov Differential Equations[J];Journal of Xuchang University;2006-05
9 Zhang Long (Xinjiang Engineering College,Urumqi 830091,Xinjiang);Asymptotic Stability for Saaty's Queueing Model[J];Journal of Xinjiang Education Institute;2008-02
10 LIU Shu-xin, CAO Ling, Muyidin Helil(College of Mathematics and Systems Science, Xinjiang University,Urumqi,Xinjiang 830046, China);Study on a M/M/2 Queueing Model[J];Journal of Xinjiang University (Natural Science Edition);2005-01
【Co-references】
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1 CHEN Yang, ZHU Yi-jun, CHEN Yan (Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013,China);Analysis of repairable system with three kinds of states[J];Journal of Jiangsu University (National Science Edition);2005-01
2 LIU Yu\|min, XU Gen\|qi (Department of Mathematics, Shanxi University, Taiyuan 030006, China);Dynamic Solution and Stability on the M/M/n Queueing Model[J];Mathematics In Practice and Theory;2002-03
3 Geni Gupur 1,3 , CAO Jun2 (1.College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China)(2.Deprtment of Mathematics, Xinyang Normal University, Henan 464000, China)(3.Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China);Asymptotic Properties of the Four Indices for M/M/1 Queue System[J];Mathematics In Practice and Theory;2003-01
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8 Geni.Gupur (Mathematics Department, Xinjiang University, Urumqi 830046);Existence of the Unique Non negative Solution for M/M/1 Model[J];SYSTEMS ENGINEERING-THEORY & PRACTICE;1998-10
9 GUPUR Geni, LI Xue-zhi (Department of Mathematics, Xinjiang University, Urumqi 830046, China Department of Mathematics, Xinyang Teachers College, Henan 464000, China Institute of Systems Science, Academia Sinica, Beijing 100080, China);A Note on the M/M/1 Queueing Model Described by Ordinary Differential Equations[J];ACTA ANALYSIS FUNCTIONALIS APPLICATA;1999-01
10 LI Yang- rong Departmentof Mathematics,Southwest China Normal University,Chongqing 40 0 71 5,China;l~1-Solution and stability of the M/M/1 Queueing Model[J];Acta Analysis Functionalis Applicata;2000-02
【Secondary Citations】
Chinese Journal Full-text Database 1 Hits
1 GUPUR Geni, LI Xue-zhi (Department of Mathematics, Xinjiang University, Urumqi 830046, China Department of Mathematics, Xinyang Teachers College, Henan 464000, China Institute of Systems Science, Academia Sinica, Beijing 100080, China);A Note on the M/M/1 Queueing Model Described by Ordinary Differential Equations[J];ACTA ANALYSIS FUNCTIONALIS APPLICATA;1999-01
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