Towards Efficient Probabilistic Scheduling Guarantees for Real-Time Systems Subject to Random Errors and Random Bursts of Errors

Real-time computing and communication systems are often required to operate with prespecified levels of reliability in harsh environments, which may lead to the exposure of the system to random errors and random bursts of errors. The classical fault-tolerant schedulability analysis in such cases assumes a pseudo-periodic arrival of errors, and does not effectively capture any underlying randomness or burst characteristics. More modern approaches employ much richer stochastic error models to capture these behaviors, but this is at the expense of greatly increased complexity. In this paper, we develop a quantile-based approach to probabilistic schedulability analysis in a bid to improve efficiency whilst still retaining a rich stochastic error model capturing random errors and random bursts of errors. Our principal contribution is the derivation of a simple closed-form expression that tightly bounds the number of errors that a system must be able to tolerate at any time subsequent to its critical instant in order to achieve a specified level of reliability. We apply this technique to develop an efficient 'one-shot' schedulability analysis for a simple fault-tolerant EDF scheduler. The paper concludes that the proposed method is capable of giving efficient probabilistic scheduling guarantees, and may easily be coupled with more representative higher-level job failure models, giving rise to efficient analysis procedures for safety-critical fault-tolerant real-time systems.