A Probabilistic Calculus for Probabilistic Real-Time Systems

Challenges within real-time research are mostly in terms of modeling and analyzing the complexity of actual real-time embedded systems. Probabilities are effective in both modeling and analyzing embedded systems by increasing the amount of information for the description of elements composing the system. Elements are tasks and applications that need resources, schedulers that execute tasks, and resource provisioning that satisfies the resource demand. In this work, we present a model that considers component-based real-time systems with component interfaces able to abstract both the functional and nonfunctional requirements of components and the system. Our model faces probabilities and probabilistic real-time systems unifying in the same framework probabilistic scheduling techniques and compositional guarantees varying from soft to hard real time. We provide an algebra to work with the probabilistic notation developed and form an analysis in terms of sufficient probabilistic schedulability conditions for task systems with either preemptive fixed-priority or earliest deadline first scheduling paradigms.