Birth-death Markov models have been widely used in the study of natural and physical processes. The analysis of such processes, however, is mostly performed using time series analysis. In this report, a finite state birth----death Markov process is analyzed using the z----transform approach. The performance metrics of the system and their variation with the system parameters are then derived and presented.

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In digital communication systems, ARQ and HARQ schemes are employed in order to ensure efficient transmission of information and utilisation of the channel by retransmitting information that has not being received correctly at the receiver. In some applications, however, such as real-time services, the quality of information is degraded if too many retransmission trials are employed for each unit of erroneously received information. The  retransmissions are therefore limited leading to truncated ARQ and HARQ schemes. In this study we develop a new method for deriving the  expressions for the throughput efficiencies of truncated ARQ and HARQ schemes and investigate how the efficiencies vary with the number of allowed retransmissions. Keywords: ARQ, HARQ, Throughput Efficiency, Truncated ARQ.

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