负顾客及反馈的 Geo/Geo/1 多重工作休假排队系统的稳态队长分布

综合利用离散补充变量法、矩阵几何解及拟生灭链的方法研究了带有负顾客及伯 努利反馈的Geo/Geo/1多重工作休假排队系统. 首先运用离散补充变量方法得 到了此复杂系统的转移概率矩阵. 其次, 再利用矩阵几何解及拟生灭链的技术通 过解方程组获得了队长的稳态分布、平均队长及稳态队长的随机分解结果. 最后, 通过引入数值例子, 作出了系统的二维图形, 进而可以更直观地分析一些参数 对系统性能的影响.

Equilibrium distributions of the queue length in Geo/Geo/1 queue system with negative customer,feedback and multiple working vacations

Applying the discrete supplementary variables method,matrix-geometric solution and quasi birth-death technique,we investigate a discrete time Geo/Geo/1 queue system with negative customer, Bernoulli feedback and multiple working vacations.Firstly,by applying the discrete supplementary variable technique,we give the transition probability matrix of this complex system.Secondly,using the matrix-geometric solution and quasi birth-death technique and solving equation sets,we get the equilibrium distributions for the number of customers,the average number of customers and the stochastic decomposition of the steady-state queue length.Finally,by presenting the numerical examples,we make some two-dimensinal graphs,which help us to intuitively analyze the influence of parameters on the system performance.