Exact Statistics of a Complex Markov Chain through State Reduction: A Satellite On-board Switching Example

Satellite on-board switching offers the possibility of covering a wide area with increased total capacity. In order to show a mechanism for reducing a highly dimensional complex Markov chain, in this paper we use a terrestrial packet grouping approach to minimize the on-board switching operations. By carefully redirecting some transitions to different states, we can evaluate exact statistics of the original complex Markov chain from the analysis of a much simpler reduced Markov chain. Although we use a communication example close to our research interest, the method can have a much wider area of application.