具有备用服务员的可修排队系统分析

Analysis of a repairable queuing system with spare servers

研究了具有备用服务员的可修排队系统,其中一个服务员上岗,另一个服务员备用。上岗服务员发生故障时,若修理工空闲,则故障服务员可以立即得到修理,同时备用服务员立即替换上岗;否则,需等待修理。利用矩阵几何解的方法讨论了系统的稳态平衡条件和稳态概率分布,并给出了系统的一些稳态性能指标和数值结果。

A repairable queuing system with spare servers was considered, in which one server goes on duty, and the other is kept on standby. When the server breaks down, if the repairman is idle, it can be repaired and replaced by the spare server immediately. Otherwise, it needs to wait for repairs. Using the matrix-geometric solution method, the existing condition of steady-state equilibrium and steady-state probability vectors were discussed. Some performance measures of the system and numerical results were given.