带有止步的成批到达的M^x/M/1/N多重工作休假排队系统

M^x/M/1/N queuing system with balking, batch arrival and multiple working vacations

研究了带有止步的M^x/M/1/N多重工作休假排队系统。顾客成批到达,到达后每批中的顾客,或者以概率决定进入队列等待服务,或者以概率1止步。系统中一旦没有顾客,服务员立即进入多重工作休假。利用马尔科夫过程理论和矩阵解法求出了稳态概率的矩阵解,并得到了系统的平均队长、平均等待队长以及顾客的平均止步率等性能指标。

An M^x/M/1/N queuing system was considered with balking and multiple working vacations. Customers arrive in batch and each arriving customer either decides to enter the queue with a probabilityor balk with a probability. The server takes multiple working vacations immediately when it becomes idle at a service completion instant. The matrix form solution of the steady-state probability was derived by the Markfov process method and the matrix solution method. Some performance measures of the system such as th...