Asymptotic throughput of continuous timed Petri nets

We set up a connection between Continuous Timed Petri Nets (the fluid version of usual Timed Petri Nets) and Markov decision processes. We characterize the subclass of Continuous Timed Petri Nets corresponding to undiscounted average cost structure. This subclass satisfies conservation laws and shows a linear growth: one obtains as mere application of existing results for Dynamic Programming the existence of an asymptotic throughput. This rate can be computed using Howard-type algorithms, or by an extension of the well known cycle time formula for timed event graphs. We present an illustrating example and briefly sketch the relation with the discrete case.