M/M/N Repairable Queue System

This paper mainly researches three kinds of repairable queues with multiple servers,the one kind is the M/M/N repairable queue system with nonpreemptive priority,the other one is the M~x/M/N repairable queue system with batch arrival,and the last one is the M/M/S/K+M repairable queue with negative customers.For the M/M/N repairable queue system with nonpreemptive priority,the differential equations of this system are obtained by receiving the state transition diagram,and then obtain steady-state balanced equations.By analysing the thinking of the key steady probability,we program and derive the steady probability by using Mathematica,and we also give a numberical example.Similarly,we research the M~x/M/N repairable queue system.As to the M/M/S/K+M repairable queue with negative customers,by using the Matrix-Analytic Methods,An analytic solution and some system measures in stability are obtained.And also,a numberical example and some conclusions are given,which can provide the theoretic evidences for optimizing the call center.