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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 2 Hits
1 Ehmet Kasim,Geni Gupur College of Mathematics and Systems Science,Xinjiang University,Urumqi 830046,China;Other Eigenvalues of the M/M/1 Operator[J];应用泛函分析学报;2011-01
2 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];应用泛函分析学报;2010-02
【Citations】
Chinese Journal Full-text Database 4 Hits
1 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];应用泛函分析学报;2000-02
2 Gem Gupur, MIijit Abaif (Department of Mathematics, Xinjiang University, Urumqi 830046, China Institute of Systems Science, Academia Sinica, Beijing 100080, China);An Eigenvalue of M/M/1 Operator and Its Application[J];应用泛函分析学报;1999-02
3 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];应用泛函分析学报;1999-01
4 Geni.Gupur (Mathematics Department, Xinjiang University, Urumqi 830046);Existence of the Unique Non negative Solution for M/M/1 Model[J];系统工程理论与实践;1998-10
【Co-citations】
Chinese Journal Full-text Database 10 Hits
1 Liu Yumin;Yuan Wenzhi;Dept of Mathematics,Taiyuan Normal University;;The Resolvent Operator of a Operator by Definition of Infinite Dimension Matrix[J];太原师范学院学报(自然科学版);2014-02
2 ALIM Mijit(Xinjiang Radio & TV University,Urumqi 830049,China);Well-Posedness of a Queueing Model[J];安徽师范大学学报(自然科学版);2013-02
3 Abduwali Jilil1,Alimu Abulikemu2(1.College of Mathematics and Systems Science,Xinjiang University,Urumqi,Xinjiang 830046,China;2.School of Mathematics and Informational Technology,Educational Institute of Xinjiang,Urumqi,Xinjiang 830043,China);Research on the Exhaustive-service M/D/1 Queueing Model with Optional Server Vacations[J];新疆大学学报(自然科学版);2013-01
4 Geni Gupur College of Mathematics and Systems Science,Xinjiang University,Urumqi 830046,China;Advances in Queueing Models' Research[J];应用泛函分析学报;2011-03
5 ZHENG Fu~(1,2),GAO Chao~1,ZHU Guangtian~3 1.Beijing Institute of Information and Control,Beijing 100048,China 2.Department of Mathematics,Bohai University,Jinzhou 121002,China 3.Academy of Mathematics and Systems Science,CAS,Beijing 100190,China;Asymptotic Stability of the M/G/1 Queueing System[J];应用泛函分析学报;2011-02
6 Ehmet Kasim,Geni Gupur College of Mathematics and Systems Science,Xinjiang University,Urumqi 830046,China;Other Eigenvalues of the M/M/1 Operator[J];应用泛函分析学报;2011-01
7 Liu Yumin(Department of Mathematics,Taiyuan Normal University,Taiyuan 030012,China);Dynamic Solution and Stability of the M/M/1 Queueing Model with Variable Import Rate[J];太原师范学院学报(自然科学版);2010-04
8 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];江南大学学报(自然科学版);2010-03
9 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];应用泛函分析学报;2010-02
10 LIU Yu-min,LI Xiao-fen,WANG Wen-xia,SONG Ru-ying(Department of Mathematics,Taiyuan Normal University,Taiyuan 030012,China);Dynamic Solution and Asymptotic Stability of the M/M/n Model with Variable Import Rate[J];应用数学;2009-04
【Co-references】
Chinese Journal Full-text Database 8 Hits
1 ZHANG Long, Geni GupurCollege of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China;Another Eigenvalue of the M/M/1 Operator[J];应用泛函分析学报;2008-01
2 SHANG Yan ying LI Yang rong Dept. of Mathematics, Southwest China Normal University, Chongqing 400715; China;M/M/1 Queueing Model and the Spectral Properties of the Corresponding Operator[J];西南师范大学学报(自然科学版);2002-05
3 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];数学的实践与认识;2002-03
4 LI Yang\|rong (Dept. of Mathematics, Southwest China Normal University, Chong qing 400715);The spectral gap formula for M/M/1 queeing model[J];西南师范大学学报(自然科学版);2000-04
5 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];应用泛函分析学报;2000-02
6 Gem Gupur, MIijit Abaif (Department of Mathematics, Xinjiang University, Urumqi 830046, China Institute of Systems Science, Academia Sinica, Beijing 100080, China);An Eigenvalue of M/M/1 Operator and Its Application[J];应用泛函分析学报;1999-02
7 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];应用泛函分析学报;1999-01
8 Geni.Gupur (Mathematics Department, Xinjiang University, Urumqi 830046);Existence of the Unique Non negative Solution for M/M/1 Model[J];系统工程理论与实践;1998-10
【Secondary References】
Chinese Journal Full-text Database 1 Hits
1 Geni GUPUR;Ehmet KASIM;College of Mathematics and System Sciences,Xinjiang University;;FUNCTIONAL ANALYSIS METHOD FOR THE M/G/1 QUEUEING MODEL WITH OPTIONAL SECOND SERVICE[J];Acta Mathematica Scientia;2014-04
【Secondary Citations】
Chinese Journal Full-text Database 2 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];应用泛函分析学报;1999-01
2 LI YANGRONG *;THE Abstract CAUCHY PROBLEM AND A GENERALIZATION OF THE LUMER-PHILLIPS THEOREM[J];Chinese Annals of Mathematics;1998-03
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