离散GI/G/1系统等待时间的尾概率估计

Computation of the Tail Probability for the Waiting Time in Discrete GI/G/1 Queueing System

设计了用于估计离散GI/G/1系统等待时间尾概率渐进衰减常数的算法.由于考虑到速率矩阵的特殊结构,所得到的数值算法简洁、高效.与以单纯计算速率矩阵为目标的算法相比较,尾概率渐进衰减常数对速率矩阵不要求有很高的精度,在实际应用中,只需估计出常数的量级即可,因此可以达到快速求解的目的.同时,也对如何计算等待时间的稳态分布边界向量进行了讨论.作为计算尾概率渐进衰减常数的过程中较为重要的量,稳态分布边界向量的快速求解关系到整个算法的效率.几个数值例子表明此算法在离散GI/G/1系统中有良好效果.

An algorithm is presented to estimate the asymptotic constant of tail probability for waiting time in discrete GI/G/1 queueing system. Exploring the special structure of rate matrix, the algorithm is simple and fast. Different from the calculation of rate matrix, the asymptotic constant is usually required to be estimated roughly, which results in much less steps. As a critical part in the course of computing the asymptotic constant, a fast algorithm is designed for the computation of the boundary stationary distribution vector. Numerical examples in the queueing system illustrate the efficiency of the algorithm.