修理设备可更换的${N}$ -策略延迟不中断单重休假 ${M/G/1}$可修排队系统分析

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Analysis of ${M/G/1}$ Repairable Queueing System with a Replaceable Repair Facility, ${N}$ -policy and Delayed Uninterrupted Single Vacation

Analysis of M/G/1{M/G/1} Repairable Queueing System with a Replaceable Repair Facility, N{N}-policy and Delayed Uninterrupted Single Vacation

Analysis of ${M/G/1}$ Repairable Queueing System with a Replaceable Repair Facility, ${N}$ -policy and Delayed Uninterrupted Single Vacation

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Abstract:

This paper considers an $M/G/1$ repairable queueing system with $N$ -policy and delayed uninterrupted single vacation, in which the repair facility subject to breakdowns and then replaced during the repair facility busy period. By the renewal process theory, the total probability decomposition technique and the Laplace transform tool, some reliability indices of the service station and the repair facility are discussed, such as the transient-state and steady-state unavailability, and the expected failure number during $(0,t]$ , etc., and the parameter sensitivity analysis is carried out on the steady-state unavailability and the steady-state failure frequency.

Key words: $M/G/1$ repairable queueing system, $N$ -policy, Delayed uninterrupted vacation, Reliability index, Parameter sensitivity analysis

CLC Number:

O213.2

He Yaxing, Tang Yinghui, Liu Qionglin. Analysis of ${M/G/1}$ Repairable Queueing System with a Replaceable Repair Facility, ${N}$ -policy and Delayed Uninterrupted Single Vacation[J].Acta mathematica scientia,Series A, 2023, 43(2): 625-645.

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[1]	Avi-Itzhak B, Naor P. Some queueing problems with service station subject to server breakdown. Operations Research, 1963, 11: 303-320 doi: 10.1287/opre.11.3.303
[2]	Federgruen A, Green L. Queueing systems with service interruptions. Operations Research, 1986, 34: 752-768 doi: 10.1287/opre.34.5.752
[3]	史定华, 田乃硕. 服务台可修的 $GI/M(M/PH)/1$ 排队系统. 应用数学学报, 1995, 18(1): 44-50 doi: 10.12387/C1995006
	Shi D H, Tian N S. Repairable $GI/M(M/PH)/1$ queueing system. Acta Mathematicae Applicatae Sinica, 1995, 18(1): 44-50 doi: 10.12387/C1995006
[4]	李泉林. 服务台可修的 $M/SM/(PH/SM)/1$ 排队系统. 应用数学, 1996, 9(4): 422-428
	Li Q L. $M/SM(PH/SM)/1$ repairable queueing system. Mathematica Applicatae, 1996, 9(4): 422-428
[5]	曹晋华, 程侃. 服务台可修的 $M/G/1$ 排队系统分析. 应用数学学报, 1982, 5(2): 113-127 doi: 10.12387/C1982016
	Cao J H, Cheng K. Analysis of $M/G/1$ queueing system with repairable service station. Acta Mathematicae Applicatae Sinica, 1983, 5(2): 113-127 doi: 10.12387/C1982016
[6]	曹晋华. 服务设备可修的机器服务模型分析. 数学研究与评论, 1985, 5(4): 89-96
	Cao J H. Service model analysis of repairable service equipment. Journal of Mathematical Research and Exposition, 1985, 5(4): 89-96
[7]	Tang Y H. Revisiting the model of servicing machines with repairable service facility-A analyzing idea and some new results. Acta Mathematicae Applicatae Sinica, English Series, 2010, 26(4): 557-566 doi: 10.1007/s10255-008-8029-6
[8]	唐应辉, 赵玮. 可修排队系统可靠性指标的分解特性. 运筹学学报, 2004, 8(4): 73-84
	Tang Y H, Zhao W. The decomposition properties of reliablility indices in repairable queueing systems. Operations Research Transactions, 2004, 8(4): 73-84
[9]	Tang Y H. A single-server $M/G/1$ queueing system subject to breakdowns-some reliability and queueing problems. Microelectronics and Reliability, 1997, 37(2): 315-321 doi: 10.1016/S0026-2714(96)00018-2
[10]	Tang Y H, Mu Y C, Yu M M. Analysis of reliability on $M/G/1$ repairable queueing sysyem with $p$ -entering discipline during second type failure time-Some reliability indices. Journal of Systems Engineering, 2012, 27(4): 559-567
[11]	唐应辉, 唐小我. 推广的 $M/G(M/G)/1(M/G)$ 可修排队系统(II)-一些可靠性指标. 系统工程理论与实践, 2000, 20(2): 84-91 doi: 10.12011/1000-6788(2000)2-84
	Tang Y H, Tang X W. The generalized $M/G(M/G)/1(M/G)$ repairable queueing system(II)-Some reliability indices. System Engineering-Theory and Practice, 2000, 20(2): 84-91 doi: 10.12011/1000-6788(2000)2-84
[12]	Tang Y H. Some reliability problems arising in the repairable queueing system single delay vacation. Journal of Systems Science and Systems Engineering, 2001, 10(3): 306-314
[13]	Wang H, Wang T Y, Peam W L. Optimal control of the $N$ policy $M/G/1$ queueing system with server breakdowns and general startup times. Applied Mathematical Modelling, 2007, 31(10): 2199-2212 doi: 10.1016/j.apm.2006.08.016
[14]	Wang H, Kuo C C, Ke C. Optimal control of the $D$ -policy $M/G/1$ queueing system with server breakdowns. American Journal of Applied Sciences, 2008, 5(5): 565-573 doi: 10.3844/ajassp.2008.565.573
[15]	Wu W Q, Tang Y H, Yu M M, Jiang Y. Reliability analysis of a k-out-of-n: G repairable system with single vacation. Applied Mathematical Modelling, 2014, 38(19/20): 6075-6097 doi: 10.1016/j.apm.2014.05.020
[16]	钟瑶, 唐应辉. 具有两类失效模式的 $D$ -策略 $M/G/1$ 可修排队系统最优控制策略 $D^{*}$ . 运筹学学报, 2020, 24(1): 40-56
	Zhong Y, Tang Y H. Analysis of the $M/G/1$ repairable queueing system with $D$ -policy and two types of failure modes. Operations Research Transactions, 2020, 24(1): 40-56
[17]	旷欣宇, 唐应辉. 带启动时间与双阈值 $(m,N)$ -策略的 $M/G/1$ 可修排队系统的最优控制策略. 运筹与管理, 2021, 30(10): 64-70 doi: 10.12005/orms.2021.0315
	Kuang X Y, Tang Y H. Optimal control policy for the $M/G/1$ repairable queueing system with random start-up time and bi-level threshold $(m,N)$ -policy. Operations Research and Management Science, 2021, 30(10): 64-70 doi: 10.12005/orms.2021.0315
[18]	唐应辉, 余妙妙, 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. 系统工程理论与实践, 2010, 30(2): 347-355 doi: 10.12011/1000-6788(2010)2-347
	Tang Y H, Yu M M, Fu Y H. Reliability indices of $Geom/G1,G2(Geom/G)/1/1$ repairable Erlang loss system and computer simulation analysis. System Engineering-Theory and Practice, 2010, 30( 2): 347-355 doi: 10.12011/1000-6788(2010)2-347
[19]	Tang Y H, Yu M M, Li C L. $Geom/G1,G2/1/1$ repairable Erlang loss system with catastrophe and second optional service. Journal of Systems Science and Complexity, 2011, 24(3): 554-564 doi: 10.1007/s11424-011-8339-2
[20]	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. Journal of Systems Science and Complexity, 2012, 25(6): 1122-1135 doi: 10.1007/s11424-012-1062-9
[21]	兰绍军, 唐应辉. 具有Bernoulli反馈和Min $(N,D)$ -策略控制的 $Ge{{o}^{({{\lambda }_{1}},{{\lambda }_{2}})}}/G/1$ 离散时间可修排队的可靠性分析. 系统科学与数学, 2016, 36(11): 2070-2086 doi: 10.12341/jssms12974
	Lan S J, Tang Y H. Reliability analysis of discrete-time $Ge{{o}^{({{\lambda }_{1}},{{\lambda }_{2}})}}/G/1$ repairable queue with Bernoulli feedback and Min $(N,D)$ -policy. Journal of Systems Science and Mathematical Sciences, 2016, 36(11): 2070-2086 doi: 10.12341/jssms12974
[22]	Lan S J, Tang Y H. Analysis of $D$ -policy discrete-time $Geo/G/1$ queue with second J-optional service and unreliable server. RAIRO-Operations Research, 2017, 51(1): 101-122 doi: 10.1051/ro/2016006
[23]	Lan S J, Tang Y H. Performance and reliability analysis of a repairable discrete-time $Geo/G/1$ queue with Bernoulli feedback and randomized policy. Applied Stochastic Models in Business and Industry, 2017, 33(5): 522-543 doi: 10.1002/asmb.v33.5
[24]	Lan S J, Tang Y H. An unreliable discrete-time retrial queue with probabilistic preemptive priority, balking customers and replacements of repair times. AIMS Mathematics, 2020, 5(5): 4322-4344 doi: 10.3934/math.2020276
[25]	刘金银, 唐应辉, 朱亚丽, 等. 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. 系统工程理论与实践, 2015, 35(2): 413-423 doi: 10.12011/1000-6788(2015)2-413
	Liu J Y, Tang Y H, Zhu Y L, et al. Reliability indices of $M/G/1$ repairable queueing system with warm standby failure and delayed repair. System Engineering-Theory and Practice, 2015, 35(2): 413-423 doi: 10.12011/1000-6788(2015)2-413
[26]	唐应辉, 刘金银, 余妙妙. $N$ -控制策略且温储备失效 $M/G/1$ 可修排队. 系统工程学报, 2015, 30(6): 852-864
	Tang Y H, Liu J Y, Yu M M. $M/G/1$ repairable with $N$ -policy and warm standby failure. Journal of System Engineering, 2015, 30(6): 852-864
[27]	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. 系统工程理论与实践, 2014, 34(4): 944-950 doi: 10.12011/1000-6788(2014)4-944
	Tang Y H, Zhu Y L, Wu W Q. $M/G/1$ repairable queueing system with warm standby failure. System Engineering-Theory and Practice, 2014, 34(4): 944-950 doi: 10.12011/1000-6788(2014)4-944
[28]	高丽君, 唐应辉. $N$ -控制策略且温储备失效 $M/G/1$ 可修排队的可靠性指标. 运筹与管理, 2018, 27(10): 102-112 doi: 10.12005/orms.2018.0237
	Gao L J, Tang Y H. Reliability indices of $M/G/1$ repairable queue with $N$ -policy and warm standby failure. Operations Research and Management Science, 2018, 27(10): 102-112 doi: 10.12005/orms.2018.0237
[29]	蔡晓丽, 唐应辉. 具有温储备失效特征和单重休假 $Min(N,V)$ -控制策略 $M/G/1$ 的可修排队系统. 应用数学学报, 2017, 40(5): 692-701
	Cai X L, Tang Y H. $M/G/1$ repairable queueing system with warm standby failure and $Min(N,V)$ -policy Based on Single vacation. Acta Mathematicae Applicatae Sinica, 2017, 40(5): 692-701
[30]	刘仁彬, 唐应辉. 修理设备可更换且修理有延迟的两不同型部件并联可修系统. 高校应用数学学报, 2006, 21(2): 127-140 doi: 10.1007/BF02791345
	Liu R B, Tang Y H. Two-different-units paralleled repairable system with a replaceable facility and repair delay. Applied Mathematics-A Journal of Chinese Universities, 2006, 21(2): 127-140 doi: 10.1007/BF02791345
[31]	Yu M M, Tang Y H, FuY H, Pan L M, Tang X W. A deteriorating repairable system with stochastic lead time and replaceable repair facility. Computers and Industrial Engineering, 2012, 62(2): 609-615 doi: 10.1016/j.cie.2011.11.023
[32]	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. 系统工程学报, 2013, 28(6): 830-839
	Tang Y H, Feng H X, Wu W Q. Analysis of $M/G/1$ repairable queueing system with a replacement repair facility. Journal of Systems Engineering, 2013, 28(6): 830-839
[33]	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. 系统工程理论与实践, 2014, 34(3): 746-755 doi: 10.12011/1000-6788(2014)3-746
	Tang Y H, Zhu Y L, Wu W Q. Analysis of $M/G/1$ repairable queueing system with $N$ -policy and a replaceable repair facility. Systems Engineering-Theory and Practice, 2014, 34(3): 746-755 doi: 10.12011/1000-6788(2014)3-746
[34]	吴文青, 唐应辉, 兰绍军. 修理设备可更换的 $k/n(G)$ 表决可修系统. 数学学报, 2016, 59(6): 799-820
	Wu W Q, Tang Y H, Lan S J. Analysis of $k/n(G)$ repairable system with replaceable repair facility. Acta Mathematica Sinica, 2016, 59(6): 799-820
[35]	Wu W Q, Tang Y H, Yu M M, Jiang Y, Liu H. Reliability analysis of a k-out-of n:G system with general repair times and replaceable repair equipment. Quality Technology and Quantitative Management, 2018, 15(2): 274-300 doi: 10.1080/16843703.2016.1226712
[36]	潘取玉, 唐应辉. 在延迟Min $(N,D)$ -控制策略下修理设备可更换的 $M/G/1$ 可修排队系统及最优控制策略. 数学物理学报, 2018, 38A(5): 1014-1031
	Pan Q Y, Tang Y H. Analysis of $M/G/1$ repairable queueing system and optimal control policy with a replaceable repair facility under delay Min $(N,D)$ -policy. Acta Mathematica Scientia, 2018, 38A(5): 1014-1031
[37]	魏瑛源, 唐应辉. 基于修理设备可更换和修理延迟策略的两不同型部件冷贮备可修系统. 工程数学学报, 2020, 37(4): 423-441
	Wei Y Y, Tang Y H. Two units cold standby repairable system with a replaceable repair facility and delay repair. Journal of Engineering Mathematics, 2020, 37(4): 423-441
[38]	何亚兴, 唐应辉. 具有 $N$ -策略和延迟单重休假且休假不中断的 $M/G/1$ 排队系统. 应用数学, 2021, 34(1): 130-145
	He Y X, Tang Y H. $M/G/1$ Queueing system with $N$ -policy and Delayed Single vacation without interruption. Mathematica Applicata, 2021, 34(1): 130-145
[39]	唐应辉, 唐小我. 排队论-基础与分析技术. 北京: 科学出版社, 2006
	Tang Y H, Tang X W. Queueing Theory-Foundations and Analysis Techniques. Beijing: Science Press, 2006
[40]	曹晋华, 程侃. 可靠性数学引论(修订版). 北京: 高等教育出版社, 2006
	Cao J H, Cheng K. Introdution to Reliability Mathematics (revised edition). Beijing: Higher Education Press, 2006

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