超模序及其在离散排队系统中的应用

Supermodular Order and Its Application in Discrete-time Queue

总结了超模序的一些性质,这些性质充分地说明了超模序能刻划随机向量的正相关性的强度。并证明了一个新的性质。最后给出了超模序在有正相关到达的离散时间排队系统中的应用,得到了队长的一些随机比较结果,并分析了有Bernoulli相关到达和消息长度相关的N源消息到达2个具体的模型。

The supermodular order is introduced and it is shown that the supermodular order can compare the strength of the positive dependence of random vectors.And then the discrete_time with postive dependent arrival is analysed by using the supermodular order and concerned stochastic order.The result is obtained that the buffer contents are ordered under increasing convex order, when arrival processes are ordered under supermodular order. Finally, the result is applied to some special discrete_time queues such as Bernoulli correlated arrival and N_source arrival with correlated messages.