Approximating Nonrenewal Processes by Markov Chains: Use of Super-Erlang (SE) Chains
Gabriel R. Bitran, Sriram Dasu
Operations Research · 1993 · Volume 41 · Issue 5
Abstract
We study a class of point processes generated by transitions in Markov chains. We are primarily concerned with approximating superposed phase renewal processes by these point processes. We identify a subclass of Markov chains that we call Super-Erlang chains. These chains have special properties that facilitate the development of approximations. We 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.
Keywords
probability, Markov processes: approximating nonrenewal processes by Markov chains, queues, approximations: approximating arrival processes to queues
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