Towards Probabilistic Modeling and Analysis of Real-Time Systems

Schedulability analysis of software-intensive systems requires solution techniques that go beyond worst-case assumptions, fostering a cross-fertilization between the areas of real-time systems and performance engineering. We address probabilistic schedulability analysis of tasks in single-processor non-preemptive real-time systems. To this end we consider periodic tasks with osets, scheduled by Fixed Priority (FP) or Earliest Deadline First (EDF), and managed by the discarding policy or the rejection policy to control deadline misses. Each task has a Worst Case Execution Time (WCET) which can be a deterministic value or a random variable, notably characterized by a non-Markovian distribution possibly with bounded support. A continuous-time stochastic model of task-set is specied through Stochastic Time Petri Nets (STPNs) and solved by regenerative transient analysis based on stochastic state classes. The evaluation of performance measures on resource allocation and missed deadlines enables the analysis of design choices and the estimation of over-provisioned resources that are likely to be unused at run-time. Feasibility and effectiveness of the approach are validated on randomly generated task-sets for different processor utilizations.