加权Markov分枝过程的上穿/下穿性质

The down/up crossing properties of weighted Markov branching processes

本文考虑具有吸收态的加权Markov分枝过程的上穿/下穿性质,对给定的穿越范围,得到穿越次数的联合概率分布.特别地,本文给出Markov分枝过程在吸收之前死亡总数的概率分布,同时给出MX/M/1排队系统在一个忙期内服务总顾客数和固定批量到达总数的联合概率分布.

We consider the weighted Markov branching processes which stop at state 0. The joint probability distribution of fixed range crossing numbers of such processes is obtained by using a new method. In particular, the probability distribution of the total death number is given for Markov branching process and the joint probability distributions of the total number of served customers and the total number of customers who ever entered the system are also given for bulk-arrival queueing systems.