Approximating nonrenewal processes by Markov chains: Use of Super-Erlang (SE) chains

The authors study a class of point processes generated by transitions in Markov chains. They are primarily concerned with approximating superposed phase renewal processes by these point processes. The authors identify a subclass of Markov chains that they call Super-Erlang chains. These chains have special properties that facilitiate the development of approximations. The authors outline an approximation procedure and provide computational results that demonstrate the potential of the approach. The primary motivation for this study is the analysis of open queueing networks.