服务台"修复非新"的M/G/1排队系统更换模型研究

研究了M/G/1服务台“修复非新”的排队系统的最优更换策略。在假定服务台可修且不能“修复如新”和服务台的寿命服从指数分布的前提下,利用几何过程和更新过程,以被服务的顾客数N为其更换策略,以系统经长期运行单位时间內的期望效益为目标函数,选择最优的更换策略N~*,使得这一目标函数达到最大值。求出了系统经长期运行单位时间內期望效益的明显表达式。最后对结果进行了讨论。

Research on replacement model for M/G/1 queuing system with repairable service station of ‘not as good as new'

The optimal replacement policy for the M/G/1 queuing system of ' not as good as new' with repairable service station is studied. Assuming that the service station after repair is ' not as good as new' and the life distribution obeys the exponential one, by using geometric process and renewal process. We have taken the number N of the customer that have been serviced at the service station and the long-run expected benefit of the system in unity time as its replacement policy and the objective function respectively, then the objective (unction has achieved its maximum with choosing the optimal replacement policy N . The explicit expressions of long-run expected benefit of system in unity time are derived in this paper and finally its result is discussed also.