On monotonicity and continuity: computing problematic configurations in timed continuous Petri nets

摘要

This work is concerned with the computation of problematic configurations in timed continuous Petri nets under the infinite server semantics. Those net structural objects are related to possible bad/paradoxical behaviors of systems, such as non-monotonicities and discontinuities of the equilibrium throughput. The calculation of problematic configurations is a computationally complex task because their number grows exponentially with the input cardinality of join transitions. This work introduces a branch and bound type algorithm to perform such computation and, as an improvement of the calculation, it proposes to reduce the net into a smaller one using three different types of reduction rules that preserve the set of problematic configurations. The transformed net system allows to better understand why undesired behaviors may appear.