Studying an Overload System Using Rotation
For a finite Markov chain, by rotating the transition matrix by
180 degrees, or relabelling the states, one can define a new Markov
chain. This Markov chain in fact is the imbedded Markov chain of
an inverse process. Duality properties about this Markov chain
sometimes are not difficult to obtain. Similarly, one can discuss
an infinite Markov chain with states 0, 1, 2, ....
However, many applications involve transition matrices with
various boundary modifications where rotation cannot directly
apply. After introducing some duality properties for a boundary-free
or finite Markov chain, we will mainly focus on some interesting
application problems and show how to use the duality from
rotation to these problems.
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