延迟多重休假M^x/G/1排队系统的队长分布

Distribution of the queue length for M^x/G/1

考虑延迟多重休假的Mx/G/1排队,在假定延迟时间、休假时间和服务时间都是一般概率分布函数下,研究了队长的瞬态和稳态性质.通过引进"服务员忙期",导出了在任意时刻t瞬态队长分布的L变换的递推表达式和稳态队长分布的递推表达式,以及平稳队长的随机分解.

This paper considers the M^x/G/1 queue with delay multiple server vacations. Assuming that the delay time, the vacation time and the service time have general distribution functions, this paper studies the transient and equilibrium properties of the queue length. By introducing the server busy period and using the different technique the paper derives the recursive expression of the L-transformation of the transient queue length distribution at time t, the recusive expression of the equilibrium queue length distribution, and the stochastic decomposition of the queue length at a random point in equilibrium.