A Constraint Programming Approach for Generating Firing Sequences in Timed Petri Nets With Token Identification
Résumé
Timed Petri Nets are a good modeling framework to express the behavior of discrete event systems, such as transport or manufacturing systems. They allow to represent easily the distribution of tasks within a complex system, with the capacity to handle time constraints on the duration of these tasks. However, when synchronization is needed between several layers of the system, such models suffer from a lack of mechanisms to identify the components that are handled. Thus, it is difficult to obtain firing sequences avoiding confusion of tokens when activation or coordination patterns are used. Such issues are well addressed with High Level Petri Nets, like Colored PNs where data structures are attached to tokens, allowing to represent a complex behaviour while keeping a compact PN model. However, such models introduce a modeling material that makes it difficult to use direct incremental solving approaches like mathematical or constraint programming, i.e. approaches that do not need to unfold the net and build its whole reachability graph. In this paper, we propose to extend the expressivity of Timed Petri Nets by associating integer identifiers with tokens. Such approach can avoid the confusion of parts in a plant, or trains in a railway network, and allow to model much more possible coordination situations. A constraint programming model is built to follow this new firing semantics, and benchmarks are given to assess its efficiency.