MARTE/pCCSL: Modeling and refining stochastic behaviors of CPSs with probabilistic logical clocks

Cyber-Physical Systems (CPSs) are networks of heterogeneous embedded systems immersed within a physical environment. Several ad-hoc frameworks and mathematical models have been studied to deal with challenging issues raised by CPSs. In this paper, we explore a more standard-based approach that relies on SysML/MARTE to capture different aspects of CPSs, including structure, behaviors, clock constraints, and non-functional properties. The novelty of our work lies in the use of logical clocks and MARTE/CCSL to drive and coordinate different models. Meanwhile, to capture stochastic behaviors of CPSs, we propose an extension of CCSL, called pCCSL, where logical clocks are adorned with stochastic properties. Possible variants are explored using Statistical Model Checking (SMC) via a transformation from the MARTE/pCCSL models into Stochastic Hybrid Automata. The whole process is illustrated through a case study of energy-aware building, in which the system is modeled by SysML/MARTE/pCCSL and different variants are explored through SMC to help expose the best alternative solutions.