关键词: M/G/1排队系统, 反馈, 概率生成函数, 排队长度

Abstract:

The M/G/1 queueing system with fixed times of feedbacks is expended to a generalized situation, i.e., every customer accepts total m times of services and the distribution function of every service time is different from each other. A customer on its ith service is regarded as a classCicustomer. The joint probability generation function of the queue sizes of every class of customers under steady status is presented, and a method to calculate the mean queue sizes of every class of customers is proposed. The results can be widely used in all kinds of communication and computer networks, therefore, a powerful mathematical tool is provided for their performance analysis.

Key words: M/G/1 queueing system, feedback, probability generation function, queue sizes