Birth-death chains and processes, with a finite or countable number of states, play a central role in stochastic modeling. Over the past three decades different aspects of birth-death models have been ably presented in the following books: Andersen (1991), Bhattacharya and Waymire (1990), Gross and Harris (1985), Karlin and Taylor (1975), Kijima (1997) and Medhi (2003).