具有Bernoulli反馈且带有负顾客的PH/M/1排队系统

在PH/M/1排队模型中,引入了负顾客和Bernoulli反馈,并讨论了服务台容量为有限和无限两类模型,其中,模型一为服务台容量为无限的PH/M/1排队模型,利用拟生灭过程和矩阵几何解法得到了系统的转移速率矩阵,给出了系统正常返的充要条件,并得到了系统的稳态队长、忙期长度的拉普拉斯变换,以及系统的其它相关性能指标.模型二为服务台容量为有限的PH/M/1/N排队模型,同样使用拟生灭过程给出了马尔科夫过程的转移速率矩阵,并利用矩阵分析法进行求解,得到了该系统的稳态解和其它相关指标.

PH/M/1Bernoulli Feedback Queue with Negative Customers

InPH/M/1queue,the strategy of Bernoulli feedback,negative customers is introduced.And the finite' and infinte of the capacities of the system are discussed.In the infinte capacity queue,by quasi birth-and-death process and matrix-geometric solution method,the generator matrix of Markov process is given in QBD process,and the necessary and sufficient condition for positive recurrence of the system is proved,the distributions of the stationary queue length,and the Laplace-Stieltjes transform of busy period are obtained.Some performance measure of the system are also presented.The second finte capacity queue,by quasi birth-and-death process and matrix-geometric solution method too,the generator matrix of Markov process,and steady-state distribution and some performance measure of the system are also obtained.