带有反馈、启动期、休假中断的多级适应性休假M/M/1排队  

M/M/1 Queue with Feedback,Start-up,Vacation Interruption of Multi-stage Adaptive Vacation

作　　者：朱少成[1] 刘力维[1] 

机构地区：[1]南京理工大学理学院,南京210094

出　　处：《重庆工商大学学报（自然科学版）》2016年第5期1-5,共5页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：国家自然科学基金(11471160)

摘　　要：研究带有Bernoulli反馈、启动期、休假中断的多级适应性休假M/M/1排队系统,结合模型的平衡方程,采用生成函数的方法求出系统中顾客数的概率母函数(PGF)、平均顾客数、系统服务员处在忙期的概率、服务员处在假期的概率、服务员处在启动期的概率以及服务员处在空闲的概率;同时利用强马尔可夫的性质,求出系统中顾客逗留时间的拉普拉斯变换(LST)。This paper studies M / M /1 queuing system with Bernoulli feedback,start-up,vacation interruption of multi-stage adaptive vacation,by combining with the equilibrium equation of the model,uses generating function to solve the probability generating function（ PGF） of the expected number of customers in the system,average number of customers,the probability of system waiter in a busy period,the probability of a waiter in a holiday,the probability of an attendant at start-up stage,and the probability of an attendant in the free period. In addition,by using the properties of strong Markov,the Laplace transform of the customers sojourn in the system is solved.

关 键 词：反馈 启动期 多级适应性休假 强马尔可夫性 逗留时间 

分 类 号：O226[理学—运筹学与控制论]