Birth and death process (BDP) models with applications - Queueing communication systems chemical models, biological models: The state-of-the-art with a time-dependent perspective

The applications of birth and death models, which justifies the birth and death processes (BDP), are discussed. In the analysis of BDPs, the emphasis is often laid on steady state solutions while transient or time-dependent analysis has received less attention. Transient solutions are available for a wide class of problems and contribute to a more finely tuned analysis of costs and benefits of systems. In power law, it is impossible to find closed form transient solutions for system size probabilities. The transient system size probabilities, probability of extinction and its mean corresponding to the finite process, are also computed.