GI/G/1排队系统的几种收敛速度

Several Types of Convergence Rates of the GI/G/1 Queueing System

对随机模型,可以从不同角度研究其稳定性,一种是研究其转移概率函数趋向于平稳分布的速度,即各种遍历性;另一种是研究平稳分布的尾部衰减速度.本文从这两个方面着手,找它们之间的关系,对GI/G/1排队系统,给出等待时间列几何遍历、平稳分布轻尾与服务时间分布轻尾三者等价,l-遍历、平稳分布的尾部(l-1)-阶衰减与服务时间分布的尾部l-阶衰减三者等价,最后证明出等待时间列不是强遍历.

For stochastic models,ergodicity and the decay rate of stationary distribution in tail are two fundamental issues.They are usually studied separately since their concepts are obviously different.In this paper,we study the waiting time process of GI/G/1 queuing system in the two aspects.We shall give that geometric ergodicity,the geometric decay of stationary distribution in tail,and the geometric decay of the service distribution in tail are equivalent.Then we shall prove that l-ergodicity,（l- 1）-th declay of stationary distribution in tail,and the l-th decay of the service distribution in tail are equivalent.Finally,we prove that it is not strong ergodicity.