π of a Markov chain arising in a queueing/production context. The approach
we develop can also handle "cascades," which are situations where the fluid limit of
the large deviation path from the origin to the increasingly rare event is nonlinear. Our
approach considers a process that starts at the rare event. In our production example,
we can have two sequences of states that asymptotically lie on the same line, yet π
has different asymptotics on the two sequences.
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