Automatic-Repeat-Request (ARQ) schemes have been widely used and various methods and representations have been used in their analysis. In this paper, the schemes are represented by ztransform based transition diagrams to yield easily retractable expressions. The approach has enabled the analysis of the Selective Repeat-Stutter 2 (SR-ST2) scheme having variable selective repeat mode retransmissions and the Selective Repeat-Stutter-Go Back N (SR-ST-GBN) scheme having variable stutter mode retransmissions. Using the SR-ST-GBN scheme, it is also shown that it is possible to choose the design parameters of ARQ-based communication systems in order to achieve maximum throughput.