  A large deviations principle is established for the joint law of the
empirical measure and the flow measure of a renewal Markov process on a finite
graph. We do not assume any bound on the arrival times, allowing heavy tailed
distributions. In particular, the rate functional is in general degenerate (it
has a nontrivial set of zeros) and not strictly convex. These features show a
behavior highly different from what one may guess with a heuristic
Donsker-Varadhan analysis of the problem.
