Concurrent execution of timed Petri nets

The dynamics of discrete event systems can be effectively described and analyzed using the timed Petri net formalism. The aim of this paper is to comprehensively present the achievements attained in accelerating Petri net executions by using parallel or distributed multiprocessing environments. The basic problem is to generate concurrent Petri net executions insuring correctness in the sense that the partial ordering of transition firings produced is consistent with the total event ordering that would be produced by a (hypothetical) sequential execution. Two lines of thought have been followed: in parallel simulations transition firings evolve as governed by a SIMD iteration mechanism. Distributed simulations aim at a proper synchronization of firings in spatially different net parts to avoid timing inconsistencies and alterations of the execution behavior. In both cases, structural properties of the underlying Petri net can be efficiently used to simplify and/or accelerate concurrent execution implementations.