Lender processes competing for shared resources: Beyond the S4PR paradigm

Formal models, as Petri nets, applied to the resource allocation problem have been a fruitful approach in the last years from a double perspective. Firstly, the consolidation of an abstraction process of systems leading to models structured around the concepts of processes and resources, which can be easily translated into Petri nets. Secondly, the obtention of analysis results characterizing deadlock states, as well as methods to amend the problem. Thanks to abstraction, this methods can be applied to many different application domains, although manufacturing is yet predominant. In this paper we follow the same philosophy, but extending the kind of systems that can be tackled. These extensions allow to consider nested iterations within the processes, and to hold resources in the initial state. We will show that these extensions are very relevant, from the real-world system point of view, in order to extend these techniques to a broader scope of scenarios. Nevertheless, the behaviours of the resulting models are much more complex than those of the previous restricted models, e.g., non-directedness.