The Z-Transform Applied to a birth-death Process Having Varying birth and death rates

Abstract

The analysis of a birth-death process using the z-transform was recently reported for processes having fixed transition probabilities between states. The current report extends that analysis to processes having transition probabilities that can differ from state to state. It is then shown that the model can be used to study practical queuing and birth-death systems where the arrival, birth, service and death rates may differ from state to state.