The continuous integration of new functionality increases the complexity of embedded systems, while each functionality might impose precedence constraints between the programs fulfilling it. In addition, the prevalence of several processors may create the illusion of higher computation capacity easing the associated scheduling problem. However, this capacity is not exploitable in critical real time systems because of the increased variability of the execution times due to processor features designed to provide excellent average time behaviour and not necessarily ensuring small worst case bounds. This difficulty is added to the existence of scheduling anomalies when the systems are built on top of several processors. In this paper, we study the feasibility of independent tasks scheduled according to a given preemptive fixed-priority partitioned policy on identical processors. Each task is composed of several dependent subtasks related between them according to a directed acyclic graph (DAG). We provide a worst case response time analysis for DAG tasks when each sub-tasks have an individual priority level. This assumption allows to decrease the number of possible execution scenarios, making our analysis easier and less pessimistic.

In this paper we present a probabilistic response time analysis for mixed criticality real-time systems running on a single processor according to a fixed priority pre-emptive scheduling policy. The analysis extends the existing state of the art probabilistic analysis to the case of mixed criticalities, taking into account both the level of assurance at which each task needs to be certified, as well as the possible criticalities at which the system may execute. The proposed analysis is formally presented as well as explained with the aid of an illustrative example.

The authors propose to study the average response time distribution of tasks owing to the pessimism introduced by the analysis of the synchronous case and unsafe response time obtained by simulation. In this regard, the problem we address is twofold. First, we need to determine a relevant and safe probabilistic feasibility interval that is representative of the systems behaviour over its entire lifetime. Second, we need to compute the response time distribution of any job of a task within this feasibility interval in order to combine them into an average distribution. This is a complex problem due to the fact that job arrivals are variable as well as their execution times.

In this paper, we consider a probabilistic model for real-time task systems with probabilistic worst-case execution times, probabilistic minimum inter-arrival times and probabilistic deadlines. We propose an analysis computing response time distributions of the tasks scheduled on one processor under a task-level fixed-priority preemptive scheduling policy. The complexity of our method is analyzed and it is improved by re-sampling techniques on worst-case execution time distributions and/or minimal inter-arrival time distributions. The improvements are shown through experimental results. Also, experiments are conducted in order to investigate the improvement obtained by using a probabilistic model in terms of precision and schedulability gained as opposed to a deterministic worst-case reasoning.

Static timing analysis is the state-of-the-art practice of ascertaining the timing behavior of current-generation real-time embedded systems. The adoption of more complex hardware to respond to the increasing demand for computing power in next-generation systems exacerbates some of the limitations of static timing analysis. In particular, the effort of acquiring (1) detailed information on the hardware to develop an accurate model of its execution latency as well as (2) knowledge of the timing behavior of the program in the presence of varying hardware conditions, such as those dependent on the history of previously executed instructions. We call these problems the timing analysis walls. In this vision-statement article, we present probabilistic timing analysis , a novel approach to the analysis of the timing behavior of next-generation real-time embedded systems. We show how probabilistic timing analysis attacks the timing analysis walls; we then illustrate the mathematical foundations on which this method is based and the challenges we face in the effort of efficiently implementing it. We also present experimental evidence that shows how probabilistic timing analysis reduces the extent of knowledge about the execution platform required to produce probabilistically accurate WCET estimations.

A challenging research issue of analyzing a real-time system is to model the tasks composing the system and the resource provided to the system. In this paper, we propose a probabilistic component-based model which abstracts in the interfaces both the functional and non-functional requirements of such systems. This approach allows designers to unify in the same framework probabilistic scheduling techniques and compositional guarantees that go from soft to hard real-time. We provide sufficient schedulability tests for task systems using such framework when the scheduler is either preemptive Fixed-Priority or Earliest Deadline First.