具有加入最短队列规则的大型排队网络的稳定性研究

On Stability of a Large Queuing Network with the Rule of Joining the Shortest Queue

研究具有N个队列的排队网络(N很大,但有限),每个队列的顾客以指数服务间隔到达,另外还有一个智能到达,智能到达的顾客加入排队网络中的最短队列,从而达到平衡网络负载的作用。首先建立平均场交互模型研究排队网络的极限行为,得到队列长度的经验分布收敛到非线性主方程的解;其次证得平稳分布的存在性。

Consider a queuing network with N queues(N is large but finite),customers in each queue arrive at exponential service intervals,in addition,there is a smart arrival,balancing the network load by directing its arrivals to the shortest queue(s).A mean field interaction model was set up to study the limiting behavior of the queuing network.Obtained the empirical distribution of the queue length converges to the solution of the nonlinear master equation and proved the existence of a stationary distribution.