具有负载平衡动态路由选择的排队网络的稳定性研究

Stability of a Queueing Network with Load-balanced Dynamic Routing

研究了具有负载平衡动态路由选择的排队网络的稳定性问题.首先在描述排队网络动态行为的关系式组的基础上,利用强大数定律得到了一个与流体模型关系式组和流体极限的定义相关的引理.其次对该关系式组进行流体极限处理后得到了流体模型关系式组,并给出了证明.在该网络稳定和不稳定分别与其对应的流体模型稳定和弱不稳定之间的关系的前提条件下,把排队网络的稳定性问题简化为与该网络对应的流体模型的稳定性问题.最后在一个齐次假设条件下得到了网络稳定的充要条件以及排队网络不稳定的充分条件.

The stability of a queueing network with load-balanced dynamic routing was investigated. First, based on the relations defining the dynamics of the queueing network, a lemma good for the fluid model relations and the definition of fluid limit via strong law of large numbers were obtained. Next, the fluid model relations of the queueing network via applying fluid limits to these relations were gained and proved. Under the conditions on the relation between stable queueing network and corresponding stable fluid model, and the relation between unstable queueing network and corresponding weakly unstable fluid model, the stability of the queueing network reduced to the stability of corresponding fluid model of the queueing network. Finally, under a homogeneity condition, a sufficient and necessary condition such that the queueing network was stable and a suffcient condition such that it was unstable were obtained.