PSTeC: A Location-Time Driven Modelling Formalism for Probabilistic Real-Time Systems

Internet of Things (IoT) and Cyber-Physical Systems (CPS) have become important topics in both theory and industry. In some application domains, such as when specifying the behaviour of precision mechanics, we need to include features of spatial-temporal consistency. How to model probabilistic real-time systems in such domains is a challenge. This paper presents a modelling formalism, called PSTeC, for describing the behaviour of probabilistic real-time systems focusing on spatial-temporal consistency with nondeterministic, probabilistic and real-time aspects. The consistency restricts a process to start and finish at the required location and time. Communications between agents is specified by interactive actions. The language we propose is an extension of STeC, which is a specification language for location-aware real-time systems, adding probabilistic operations so as to support the incorporation of probabilistic aspects. We first give a formal definition of the syntax for PSTeC, then focus on the details of its operational semantics, which maps a PSTeC term onto a Probabilistic Spatial-Temporal Transition System (PSTTS) following the structured operational semantics style. A simple example demonstrates the expressiveness of PSTeC.