Deriving exact stochastic response times of periodic tasks in hybrid priority-driven soft real-time systems

The aim of this paper is to allow for hybrid task sets in the context of stochastic real-time analysis. The paper goes beyond previous work by allowing for the presence of aperiodic tasks in the system. Instead of representing a task with a fixed activation period and a worst-case execution time (WCET), here a task is characterized by an arrival profile (AP) and an execution time profile (ETP), both given by random variables with known distributions. Any number of aperiodic tasks, with arbitrary arrival and execution time profiles, can be dealt with. To cope with the unbounded interference introduced by aperiodic tasks in the system, sporadic and aperiodic tasks are encapsulated within servers. The paper presents the calculus for obtaining the exact ETP of servers, which allows us to derive exact response time distributions of periodic tasks. Also, an example is used to show the potential and validity of the proposed approach.