Resolution of Actual Conflicts in Constant Speed Continuous Petri Nets

A computation of an instantaneous firing speed in an invariant behavior state of a Constant speed Continuous Petri Net is presented in this article. The instantaneous firing speeds, constrained by a system of inequalities, are represented by polytopes in order to clarify a nondeterminism issued by an actual conflict. The instantaneous firing speeds are determined by a subset of the polytope vertices or, when the actual conflicts are resolved by global priorities, they are found by one formulation of a linear programming problem per each priority level. An example of water production shows consequencies of the fact that an infinitely small quantity of the marking in a conservative component enables to run the water production system at its maximum speed.