Modular rewritable Petri nets: An efficient model for dynamic distributed systems

Modern distributed systems are becoming pervasive and increasingly provided with adaptation, (self-)reconfiguration and mobility capability. On one side, to face the challenges of the highly dynamic environments where they are deployed. On the other side, to keep production/maintenance costs down. Therein lies the increasing demand for formal models encompassing all of these aspects (besides concurrency). Hardly any of the classical formalisms like Petri Nets, Automata, and Process Algebra, even though powerful, permits designers to easily specify dynamic structural changes to systems and evaluate their impact on system behaviour. That has led to several extensions of classical formal models (e.g., the Pi calculus or the Nets-within-Nets paradigm) rarely accompanied by suitable analysis techniques. A recent formalization of a class of Rewritable Place-Transition Nets (RwPT) in Maude has proved potentially convenient to specify dynamically reconfigurable systems. Concerning analogous proposals, the RwPT formalism provides more abstraction/flexibility in modelling and efficiency in analysis. Nevertheless, its ability to scale the size of distributed systems built of several similar (nested) components is limited. This paper presents a compositional approach to define large RwPT models in a typical algebraic way and to exploit the modular structure of models during the analysis: Symmetries are implicitly captured by composite node-labelling (reflecting the model's hierarchical structure) that is preserved by net rewrites. A distributed, gracefully degrading production system is used as a case study. Experimental evidence points out the dramatic impact of the approach against a non-modular one and the advantages over alternative techniques. Even if the emphasis is on state-space-based verification, the paper shows the convenience of combining it with structural analysis, which is typical of Petri nets as well. For that purpose, rewrite-rule abstractions are given in the form of guidelines.