Timing and deadlock - freeness in Continuous Petri nets ?

Timing an unforced (discrete or continuous) net model preserves deadlock-freeness, but not the stronger liveness property, in general. The converse is not true, and if the autonomous net model has deadlocks, the timing may transform it into deadlock-free. Under infinite servers semantics, here we investigate the conditions on the firing rates of continuous timed models that makes deadlock-free a given timed system.