The analysis of a birth-death process using the z-transform was recently reported for processes hav-ing fixed transition probabilities between states. The current report extends that analysis to proc-esses 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, ser-vice and death rates may differ from state to state.

Keywords: Markov processes, birth-death models, frame synchronization, queuing systems, z-transform