一个输入依赖于系统状态的排队模型的瞬时队长分布

Distribution of the Transient Queue Length in a Queueing Model with Input Dependent on the System State

探讨了一个有如下特征的排队系统:该系统的第m个到达间隔αm-αm-1(m≥1)的分布依赖系统在时刻αm-1拥有的顾客数目。应用补充变量方法,这个系统的瞬时队长分布的积分表示被得到。在各到达间隔分布和诸服务时间分布均具有密度函数的条件下,这个积分表示的被积项能够递归地求取。

This paper studies a queueing system wherein the distribution of the m-th interarrival time αm-αm-1(m greater than or equal 1) depends on the number of customers in the system at time αm-1. Using the method of supplementary variables, the integral representation of the transient queue length distribution is obtained, of which the integrated term can be calculated recursively under the condition that the interarrival times and service times of the system have density functions.