混合服务强度的Fork-Join排队网络的弱极限定理

Weak Convergence Theorems for Fork-Join Queuing Network in Various Conditions

Fork -Join排队网络是在计算机通讯和柔性制造系统 (FMS)等方面应用十分广泛的一类排队模型 ,有十分重要的实际意义。运用概率测度弱收敛理论 ,研究了混合服务强度的Fork -Join排队网络。首先对深度为 1的服务台 ,分别证明它们排队指标的弱极限定理。然后 ,我们利用归纳推理的方法 ,由深度为d的服务台的弱极限 ,对深度为d +1的服务台的服务强度分 3种情况 ,分别推出它的弱极限定理。获得了各服务台服务强度在各种取值范围时的一些排队指标 ,包括闲期、虚等待时间。

Fork-Join queuing network is one kind of queue model which is wildly used in computer communication, FMS, etc. In this paper, we consider Fork-join queueing network in various conditions. On the whole, the research method in this article is the reduction on the depth of the server station. At first, the weak convergence of server station whose depth is 1 is obtained. Then, it is assumed that the weak convergence of the server station whose deption is d(d is integer and d≥1) is obtained. On the basis of the result, the weak convergence theorem of the server station whose depth is d+1 is obtained. So we obtain the weak convergence theorems for the idle processes, the waiting time processes, the queuing length processed and the throughtput time processes with the traffic intensity in various scopes.