两水平修理策略下的M/(M_r,G_s)/1/N/N机器维修模型稳态概率算法与性能分析  

Steady-state probability algorithm and performance evaluation for M/(M_r,G_s)/1/N/N machine repair model under bi-level repair policy

作　　者：付永红[1] 余玅妙[2] 唐应辉[3] 李才良[4] 

机构地区：[1]四川理工学院计算机科学与技术学院,四川自贡643000 [2]四川理工学院理学院,四川自贡643000 [3]四川师范大学数学与软件科学学院,四川成都610066 [4]成都电子机械高等专科学校信息与计算科学系,四川成都610032

出　　处：《山东大学学报（理学版）》2009年第4期72-78,共7页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(70871084);教育部高校博士点专项研究基金资助项目(200806360001);四川省教育厅自然科学基金资助项目(08ZC028)资助

摘　　要：应用补充变量方法研究了一个具有两水平(r,s)修理策略和两类修理工的并联机器维修模型,使用Laplace变换迭代方法和Laplace变换零点导数迭代方法获得了稳态下任意时刻系统故障机器数的概率分布。讨论了系统平均故障机器数,平均待修机器数,平均运行机器数,单位时间故障次数,机器的稳态可用度,故障机器平均待修时间及平均停工时间等一系列性能指标。最后给出了几种特殊情形下的数值算例,并从性能指标入手比较了单阈值r修理策略和两水平(r,s)修理策略的差异。Applying the supplementary variable technique, we study a machine repair model with bi-level （r, s） repair policy and two types repairman. Using recursive method of Laplace transform and recursive method for derivative at point zero of Laplace transform, we obtain the steady-state probability distribution of the number of down machines at an arbitrary time epoch. Furthermore, we investigate various system performance measures, such as average number of down machines in the system and waiting for repair, average number of operating machines, the number of the machine failures per unit time, the steady-state machine availability, average waiting time for repair of the down machine, and average shutdown time of the down machine. Finally, we present some numerical examples under some special cases and compare the difference between single threshold r repair policy and bi-level （ r, s） repair policy from the performance characteristic.

关 键 词：机器维修模型 有限源排队系统 补充变量方法 迭代 (r s)修理策略 

分 类 号：O226[理学—运筹学与控制论]