ABSTRACT
A variety of continuous-time birth and death processes are studied in this chapter. First, a general birth and death process is formulated. Then conditions are stated for existence of a unique positive stationary probability distribution of this general birth and death process. It is shown that if the process is nonexplosive, then the general birth and death process converges to this stationary probability distribution. Some simple but classical birth and death processes are presented in Section 6.4: birth, death, birth and death, and birth and death with immigration processes. Explicit formulas are derived for the moment generating functions. In addition, for the simple birth and simple death processes, explicit formulas are derived for their probability distributions. Queueing processes are discussed in Section 6.5, an important application of birth and death processes, where births and deaths are arrivals and departures in the queue.
