Abstract
In this paper we approach the problem of Mixed Criticality (MC) for probabilistic real-time systems where tasks execution times are described with probabilistic distributions. In our analysis, the task enters high criticality mode if its response time exceeds a certain threshold, which is a slight deviation from a more classical approach in MC. We do this to obtain an application oriented MC system in which criticality mode changes depend on actual scheduled execution. This is in contrast to classical approaches which use task execution time to make criticality mode decisions, because execution time is not affected by scheduling while the response time is. We use a graph-based approach to seek for an optimal MC schedule by exploring every possible MC schedule the task set can have. The schedule we obtain minimizes the probability of the system entering high criticality mode. In turn, this aims at maximizing the resource efficiency by the means of scheduling without compromising the execution of the high criticality tasks and minimizing the loss of lower criticality functionality. The proposed approach is applied to test cases for validation purposes.
Highlights
Real-time applications demand timing guarantees at all of their execution scenarios
We look for a probabilistic Mixed Criticality (MC) scheduling analysis which provides a reliable probabilistic picture of the system, and safe timing guarantees, especially for high criticality tasks, or low probability of occurrence of critical events
Given a MC periodic non-preemptive task set known beforehand to be executed on a uniprocessor machine, with each task described with a probabilistic Worst Case Execution Time (pWCET), instead of a Worst Case Execution Times (WCET), and given a maximum probability of deadline miss for the tasks, how do we find a schedule such that the probability of the system entering high criticality mode is minimum?
Summary
Classical approaches apply Worst Case Execution Times (WCET) in order to have safe/pessimistic models of task executions. Predictability is assured with schedulability analysis that applies worst-case models like WCETs. This work is a result of the CISTER Research Unit (UID/CEC/04234), supported by FCT/MCTES (Portuguese Foundation for Science and Technology). A recent approach to timing analysis involves defining execution times using a probabilistic Worst Case Execution Time (pWCET). The pWCET generalizes the notion of WCET with multiple worst-case execution time values, each with the associated worst case probability of being exceeded. The probabilistic models are less pessimistic because they are close approximation to the actual task execution. They contain more information about execution time than single-valued deterministic WCET
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