The paper explicitly gives the definition of a class of Brown birth and death processes, and has discusses their one dimension distribution, and the distribution and moment of integral-type functional, then obtains the calculation formula.

Characteristic numbers and their probability meaning of two kinds of birth and death processes;

We establish a linear birth and death process model of a population in polluted environment.

Then, by using birth and death process model, this paper compares the utilization ratio and service quality of two typical strategies, which is different in some details, in order to find the best CORBA service strategy for internet.

Firstly,the system state probability is estimated by Markov birth-death process,and then the request loss probability in stable system states is estimated by queuing theory,lastly, combining both of them,therefore the expression for the user perceived availability is established to quantitatively evaluate the sensitivity of user perceive.

The amount model of SS(subscriber station),which needs ranging,is analyzed by using birth-death process under the condition of the given number of SS,and then the steady state solution of the amount is computed.

It is proved by state transfer probability that the amount of bacterial metabolism at t moment is a birth-death process.

Criterion of sevral ergoclicity of a general continuous time quasi-birth and death process and its application;

By using the method of quasi-birth and death process, we obtain stationary distribution for the number of breakdown machines and distribution of the waiting time.

Research on machine-repair model including the use of spares with repairmen s performing secondary task was carried out, which was regarded as a finite queue with servers vacations by using the method of quasi-birth and death process.