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新疆大学数学与系统科学学院
Published:2024
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[1]鞠泽南,艾尼·吾甫尔.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[J].新疆大学学报(自然科学版)(中英文),2024,41(03):296-309.
[1]鞠泽南,艾尼·吾甫尔.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[J].新疆大学学报(自然科学版)(中英文),2024,41(03):296-309. DOI: 10.13568/j.cnki.651094.651316.2023.10.03.0001.
DOI:10.13568/j.cnki.651094.651316.2023.10.03.0001.
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.
We study spectra of the underlying operator of the M[X]/M/1 queueing model with service failure state as absorbent state and constant rate of repeated attempts on the left half complex plane. When the arrival rate of customers λ
the service rate of the server ν
the repeated rate of customers α and the service completion rate of the server b satisfy a certain condition
we prove that all complex numbers whose real part-(λ+ν +b) are not eigenvalue of the underlying operator. When λ
ν
α
b satisfy some conditions
we prove that infinitely many numbers in the interval(-(λ+ν +b)
0) are eigenvalues of the underlying operator with geometric multiplicity one.
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买丽古丽·达看,艾尼·吾甫尔.服务中断和重试率为常数的M[X]/M/1排队模型的主算子的负实谱[J].数学的实践与认识,2022,52(11):240-246.DAKAN M,GUPUR G.On the negative real spectrum of the operator corresponding to the M[X]/M/1 retrial queueing model with sever breakdowns and constant rate of repeated attempts[J].Mathematics in Practice and Theory,2022,52(11):240-246.(in Chinese)
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艾尼·吾甫尔.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[J].新疆大学学报(自然科学版)(中英文),2022,39(1):26-33.GUPUR G.On the spectrum of the operator corresponding to the system consisting of two identical units and a repairman[J].Journal of Xinjiang University(Natural Science Edition in Chinese and English),2022,39(1):26-33.(in Chinese)
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