基于拟平稳分布的随机服务系统k阶繁忙期研究

Analysis of k Order Busy Period in Stochastic Service System Based on Quasi-Stationary Distribution

为深入研究随机服务系统的"繁忙期",基于拟平稳分布对其进行探讨。利用生灭过程的拟平稳分布概率特性,得到某个确定初始状态下生灭过程的平均灭绝时间,依据它和随机服务系统平均k阶繁忙期概率分布的相似,得到结果,并以实例进行模拟验证。结果表明:该模型进一步拓展了拟平稳分布的应用空间,能为深入研究随机服务系统的"繁忙期"提供参考。

For further researching of ＂busy period＂ of random service system, discuss it based on quasi-stationary distribution. Use quasi-stationary distribution probability features of birth-death process to acquire mean extinction time of birth-death process under certain initialization state, acquire results according to its similarity with mean k order busy period probability distribution of random service system. Then, carry out simulation verifying by using example. The results show that the model can further expand application fields for quasi-stationary distribution, and provide reference for further researching on ＂busy period＂ of random service system.