Modelling Real-time Systems with Bigraphs

Bigraphical Reactive Systems (BRSs) are a graph-rewriting formalism describing systems evolving in two dimensions: spatially, e.g. a person in a room, and non-spatially, e.g. mobile phones communicating regardless of location. Despite use in domains including communication protocols, agent programming, biology, and security, there is no support for real-time systems. We extend BRSs to support real-time systems with a modelling approach that uses multiple perspectives to represent digital clocks. We use Action BRSs, a recent extension of BRSs, where the resulting transition system is a Markov Decision Process (MDP). This allows a natural representation of the choices in each system state: to either allow time to pass or perform a specific action. We implement our proposed approach using the BigraphER toolkit, and demonstrate the effectiveness through multiple examples including modelling cloud system requests.