Probabilistic Schedulability Analysis for Fault Tolerant Tasks under Stochastic Error Occurrences

In dependable real-time systems, provision of schedulability guarantees for task sets under realistic fault and error assumptions is an essential requirement, though complex and tricky to achieve. An important factor to be considered in this context is the random nature of occurrences of faults and errors, which, if addressed in the traditional schedulability analysis by assuming a rigid worst case occurrence scenario, may lead to inaccurate results. In this paper we first propose a stochastic fault and error model which has the capability of modeling error bursts in lieu of the commonly used simplistic error assumptions in processor scheduling. We then present a novel schedulability analysis that accounts for a range of worst case scenarios generated by stochastic error burst occurrences on the response times of tasks scheduled under the fixed priority scheduling (FPS) policy. Finally, we describe a methodology for the calculation of probabilistic schedulability guarantees as a weighted sum of the conditional probabilities of schedulability under specified error burst characteristics.