带有止步和中途退出的成批到达的M^x/M/1/N多重休假排队系统的性能分析

Performance Analysis of M^x/M/1/N Queuing System with Balking,Reneging,Batch Arrival and Multiple Vacations

本文研究了带有止步和中途退出的Mx/M/1/N多重休假排队系统。顾客成批到达,到达后每批中的顾客,或者以概率b决定进入队列等待服务,或者以概率1-b止步(不进入系统)。顾客进入系统后可能因为等待的不耐烦而在没有接受服务的情况下离开系统(中途退出)。系统中一旦没有顾客,服务员立即进行多重休假。首先,利用马尔科夫过程理论建立了系统稳态概率满足的方程组。其次,在利用高等代数相关知识证明了相关矩阵可逆性的基础上,利用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损失率等性能指标。

In this paper, we consider an M^x/M/1/N queuing system with balking, reneging and multiple vacations. Customers arrive in batch and each arriving customer either decides to enter the queue with a probability b or balk （do not enter） with a probabilityl-b. The impatient customer in the queue may leave the system （renege） if it has not been served after a period of waiting time. The server takes multiple vacations immediately when it becomes idle at a service completion instant. First, we obtain the steady - state probability equations by the Markfov process method. Second, by the solution of the steady-state probability. Some performance matrix solution method we derive the matrix form measures of the system such as the expected number of the customers in the system or in the queue and the average rate of the customer loss are also presented.