R个修理工同步多重休假的温贮备机器维修问题分析

Analysis of a machine repair system with warm standbys and R repairmen under multiple synchronous vacations

研究了带有多个温贮备部件的机器维修问题,系统中有R个修理工,修理工进行同步多重休假,同时考虑了顾客止步和中途退出的现象。文中利用马尔可夫过程理论建立了系统稳态概率满足的方程组,并采用矩阵分块的方法得到了系统稳态概率的精确表达式,从而得到了系统相关的排队指标,建立了相关费用函数。最后利用数值分析的方法研究了修理工个数对系统费用函数的影响。

In this paper, a machine repair system with warm standbys is studied. There are R repairmen under multiple synchronous vacations in the system. In addition, balking and reneging is also considered. The steady-state probability equations are obtained by Markov process method, and the explicit expression of the steady-state probability is derived by using the blocked matrix method. Then some queuing performance measures are presented. Based on these, a cost model is developed to determine the optimal number of servers to minimize the total expected cost of the system per unit time. Finally, the influence of the number of servers on the cost model is obtained by numerical methods.