N-控制策略且温储备失效M/G/1可修排队的可靠性指标
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摘要
本文研究N-门限值进入控制策略且温储备失效M/G/1可修排队系统,其中系统在处于温储备失效的状态下最多容许N(1)个顾客进入系统。运用全概率分解技术和拉普拉斯变换工具,对服务台第一次失效前的寿命概率分布、不可用度、(0,t]时间内的平均失效次数以及处于温储备失效而等待修理的概率等可靠性指标进行了讨论,并给出了其稳态结果表达式。最后,通过数值实例分析了服务台因温储备故障的稳态不可用度和稳态故障频度随一些参数的变化情况。
The M/G/1 repairable queueing system with N-threshold entering-control policy and warm standby failure is studied in this paper. Under such a policy,at most N( 1) customers are allowed to enter into the system during warm standby failure times. We use the probability decomposition method and the tool of the Laplace transform,the probability distribution of the first failure time、the unavailability、the expected failure number during a given time interval( 0,t] and the probability that the service station is waiting for repairing in the warm standby failure are discussed. Furthermore,we obtain the expressions of these reliability indices under the steady state. Finally,several numerical examples are presented to analyze the sensitivity of the steady-state unavailability and the failure frequency in the second type failure of the service station.
The M/G/1 repairable queueing system with N-threshold entering-control policy and warm standby failure is studied in this paper. Under such a policy,at most N( 1) customers are allowed to enter into the system during warm standby failure times. We use the probability decomposition method and the tool of the Laplace transform,the probability distribution of the first failure time、the unavailability、the expected failure number during a given time interval( 0,t] and the probability that the service station is waiting for repairing in the warm standby failure are discussed. Furthermore,we obtain the expressions of these reliability indices under the steady state. Finally,several numerical examples are presented to analyze the sensitivity of the steady-state unavailability and the failure frequency in the second type failure of the service station.
引文
[1]曹晋华,程侃.服务台可修的M/G/1排队系统分析[J].应用数学学报,1982,5(2):113-127.
[2]唐应辉.服务台可修的M/G/1排队系统的进一步分析[J].系统工程理论与实践,1996,16(4):45-51.
[3]唐应辉,唐小我.推广的MX/G(M/G)/1(M/G)可修排队系统(II)——一些可靠性指标[J].系统工程理论与实践,2000,20(2):84-91.
[4]唐应辉,唐小我,赵玮.单重延误休假MX/G(M/G)/1可修排队系统分析(I)--一些排队指标[J].系统工程理论与实践,2000,20(1):41-50.
[5] Tang Y H. Some Reliability Problems arising in the MX/G(M/G)/1 repairable queueing system with single delay vacation[J]. Journal of Systems Science&Systems Engineering,2001,10(3):306-314.
[6]唐应辉,赵玮.可修排队系统可靠性指标的分解特性[J].运筹学学报,2004,8(4):73-84.
[7]余玅妙,唐应辉.多级适应性延误休假MX/G(M/G)/1可修排队系统的可靠性指标[J].运筹学学报,2008,12(3):103-112.
[8]唐应辉,李才良,黄蜀娟,云曦.延误多重休假离散时间GeomX/G/1可修排队系统的可靠性指标[J].系统工程理论与实践,2009,29(4):135-143.
[9] Ke J C,Huang K B. Analysis of an unreliable server MX/G/1 system with a randomized vacation policy and delayed repair[J]. Stochastic Models,2010,26(2):212-241.
[10]唐应辉,余玅妙,付永红. Geom/G1,G2(Geom/G)/1/1可修Erlang消失系统的可靠性指标及其计算机仿真分析[J].系统工程理论与实践,2010,30(2):347-355.
[11] Tang Y H,Yu M M,Li C L. Geom/G1,G2/1/1 repairable Erlang loss system with catastrophe and second optional service[J]. Journal of Systems Science and Complexity,2011,24(3):554-564.
[12]刘云颇,唐应辉.多重休假中以概率p进入的M/G/1可修排队系统[J].系统工程学报,2011,26(5):718-723.
[13] Tang Y H,Yu M M,Yun X,Huang S J. Reliability indices of discrete-time GeoX/G/1 queueing system with unreliable service station and multiple adaptive delayed vacations[J]. Journal of Systems Science&Complexity,2012,25(6):1122-1135.
[14]唐应辉,冯慧侠,吴文青.修理设备可更换的M/G/1可修排队系统分析[J].系统工程学报,2013,28(6):830-838.
[15]唐应辉,朱亚丽,吴文青.修理设备可更换的N-策略M/G/1可修排队系统分析[J].系统工程理论与实践,2014,34(3):746-754.
[16] Wu W Q,Tang Y H,Yu M M. Analysis of an M/G/1queue with multiple vacations, N-policy, unreliable service station and repair facility failures[J]. International Journal of Supply and Operations Management,2014,1(1):1-19.
[17] Wu W Q,Tang Y H,Yu M M. Analysis of an M/G/1queue with N-policy,single vacation,unreliable service station and repairable repair facility[J],OPSEARCH,2015,52(4):670-691.
[18]高丽君,唐应辉.具有Min(N,D)-策略控制的M/G/1可修排队系统及最优控制策略[J].数学物理学报,2017,37A(2):352-365.
[19]赵玮,岳德权.服务设备可修的机器服务模型的某些结果[J].西安电子科技大学学报,1992,19(2):64-71.
[20] Tang Y H. A single-serve M/G/1 queueing system subject to breakdowns:some reliability and queueing problems[J]. Microelectronics and Reliability,1997,37(2):315-321.
[21]李才良,唐应辉,牟永聪.在第二类故障期间内以概率p进入的M/G/1可修排队系统:一些排队指标[J].数学物理学报,2012,32A(6):1149-1157.
[22]唐应辉,牟永聪,于玅妙.在第二类故障期间内以概率p进入的M/G/1可修排队系统:一些可靠性指标[J].系统工程学报,2012,27(4):559-567.
[23]牟永聪.在闲期内可能发生故障的MX/G/1可修排队系统分析[D].四川师范大学硕士学位论文,2011.
[24]唐应辉,朱亚丽,吴文青.具有温储备失效的M/G/1可修排队系统[J].系统工程理论与实践,2014,34(4):944-950.
[25]刘金银,唐应辉,朱亚丽,余玅妙.具有温储备失效和延迟修理的M/G/1可修排队系统的可靠性指标[J].系统工程理论与实践,2015,35(2):413-423.
[26]唐应辉,刘金银,余玅妙. N-控制策略且温储备失效M/G/1可修排队[J].系统工程学报,2015,30(6):852-864.
[27]唐应辉,唐小我.排队论—基础与分析技术[M].北京:科学出版社,2006.
[28]曹晋华,程侃.可靠性数学引论[M].北京:科学出版社,1986.
[2]唐应辉.服务台可修的M/G/1排队系统的进一步分析[J].系统工程理论与实践,1996,16(4):45-51.
[3]唐应辉,唐小我.推广的MX/G(M/G)/1(M/G)可修排队系统(II)——一些可靠性指标[J].系统工程理论与实践,2000,20(2):84-91.
[4]唐应辉,唐小我,赵玮.单重延误休假MX/G(M/G)/1可修排队系统分析(I)--一些排队指标[J].系统工程理论与实践,2000,20(1):41-50.
[5] Tang Y H. Some Reliability Problems arising in the MX/G(M/G)/1 repairable queueing system with single delay vacation[J]. Journal of Systems Science&Systems Engineering,2001,10(3):306-314.
[6]唐应辉,赵玮.可修排队系统可靠性指标的分解特性[J].运筹学学报,2004,8(4):73-84.
[7]余玅妙,唐应辉.多级适应性延误休假MX/G(M/G)/1可修排队系统的可靠性指标[J].运筹学学报,2008,12(3):103-112.
[8]唐应辉,李才良,黄蜀娟,云曦.延误多重休假离散时间GeomX/G/1可修排队系统的可靠性指标[J].系统工程理论与实践,2009,29(4):135-143.
[9] Ke J C,Huang K B. Analysis of an unreliable server MX/G/1 system with a randomized vacation policy and delayed repair[J]. Stochastic Models,2010,26(2):212-241.
[10]唐应辉,余玅妙,付永红. Geom/G1,G2(Geom/G)/1/1可修Erlang消失系统的可靠性指标及其计算机仿真分析[J].系统工程理论与实践,2010,30(2):347-355.
[11] Tang Y H,Yu M M,Li C L. Geom/G1,G2/1/1 repairable Erlang loss system with catastrophe and second optional service[J]. Journal of Systems Science and Complexity,2011,24(3):554-564.
[12]刘云颇,唐应辉.多重休假中以概率p进入的M/G/1可修排队系统[J].系统工程学报,2011,26(5):718-723.
[13] Tang Y H,Yu M M,Yun X,Huang S J. Reliability indices of discrete-time GeoX/G/1 queueing system with unreliable service station and multiple adaptive delayed vacations[J]. Journal of Systems Science&Complexity,2012,25(6):1122-1135.
[14]唐应辉,冯慧侠,吴文青.修理设备可更换的M/G/1可修排队系统分析[J].系统工程学报,2013,28(6):830-838.
[15]唐应辉,朱亚丽,吴文青.修理设备可更换的N-策略M/G/1可修排队系统分析[J].系统工程理论与实践,2014,34(3):746-754.
[16] Wu W Q,Tang Y H,Yu M M. Analysis of an M/G/1queue with multiple vacations, N-policy, unreliable service station and repair facility failures[J]. International Journal of Supply and Operations Management,2014,1(1):1-19.
[17] Wu W Q,Tang Y H,Yu M M. Analysis of an M/G/1queue with N-policy,single vacation,unreliable service station and repairable repair facility[J],OPSEARCH,2015,52(4):670-691.
[18]高丽君,唐应辉.具有Min(N,D)-策略控制的M/G/1可修排队系统及最优控制策略[J].数学物理学报,2017,37A(2):352-365.
[19]赵玮,岳德权.服务设备可修的机器服务模型的某些结果[J].西安电子科技大学学报,1992,19(2):64-71.
[20] Tang Y H. A single-serve M/G/1 queueing system subject to breakdowns:some reliability and queueing problems[J]. Microelectronics and Reliability,1997,37(2):315-321.
[21]李才良,唐应辉,牟永聪.在第二类故障期间内以概率p进入的M/G/1可修排队系统:一些排队指标[J].数学物理学报,2012,32A(6):1149-1157.
[22]唐应辉,牟永聪,于玅妙.在第二类故障期间内以概率p进入的M/G/1可修排队系统:一些可靠性指标[J].系统工程学报,2012,27(4):559-567.
[23]牟永聪.在闲期内可能发生故障的MX/G/1可修排队系统分析[D].四川师范大学硕士学位论文,2011.
[24]唐应辉,朱亚丽,吴文青.具有温储备失效的M/G/1可修排队系统[J].系统工程理论与实践,2014,34(4):944-950.
[25]刘金银,唐应辉,朱亚丽,余玅妙.具有温储备失效和延迟修理的M/G/1可修排队系统的可靠性指标[J].系统工程理论与实践,2015,35(2):413-423.
[26]唐应辉,刘金银,余玅妙. N-控制策略且温储备失效M/G/1可修排队[J].系统工程学报,2015,30(6):852-864.
[27]唐应辉,唐小我.排队论—基础与分析技术[M].北京:科学出版社,2006.
[28]曹晋华,程侃.可靠性数学引论[M].北京:科学出版社,1986.
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