带有止步和中途退出的M/M/S/N同步多重休假排队系统的性能分析

研究了带有止步和中途退出的M/M/S/N同步多重休假的排队系统.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,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、平均等待队长及顾客的平均损失率等性能指标.在此基础上建立了系统的费用模型来确定最优服务员数,以使系统单位时间的平均费用达到最小.最后进行了敏感性分析并考察了系统各参数值的变化对最优费用和最优服务员数的影响.

Performance Analysis of M/M/S/N Queuing System with Balking,Reneging and Multiple Synchronous Vacations

In this paper,an M/M/S/N queuing system with balking,reneging and multiple synchronous vacations is studied.First,the steady-state probability equations are obtained by Markov process method.Second,a matrix form solution of the steady-state probability is derived by matrix solution method.Some performance measures of the system such as the expected number of customers in the system,the expected number of customers in the queue and the average rate of the customer loss are also presented.Based on these,a cost model is developed to determine the optimal number of servers to minimize the total expected cost of the system per unit time.Finally,a sensitivity analysis is performed and the effect of the changes in specific values of the system parameters on the optimal number of servers and the optimal cost of the system is investigated.