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

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.