By using C 0-semigroup theory of linear operators the four indices of M/M/1 queueing system: the average waiting time of the customers, the average staying time of the customers, the average number of the customers and the average number of customers who wait for service, have been studied.

We study spectral properties of the operator corresponding to the M/M/1 retrial queueing model with special retrial times and obtain that-(2λ+α+β)+((α+β)~2+4λβ)~(1/2)/4 is an eigenvalue of the operator with geometric multiplicity one.

The M/M/1 queuing model of the elevator service system is presented in this paper.

Considering the characteristics of the AGV convey system, we setup a M/M/1 queuing model and adopt average queue length and remain time as performance indexes, and then estimate whether the results are reasonable according to system demands and the simulation curves of the M/M/1 model.

In this paper,the author use the method of Laplace transform to the differential equation system,which is M/M/1 queuing system satifies.

The single lattice,UD-lattice and DU-lattice can be defined with respect to the state transition of birth and death process,and the transition function of embedded Markov chain {(n)n≥0} convergence in the weak sense to transient solution of the process {X(t)t≥0} for M/M/1 queuing system has been verified.