Rational Interpolation for Real-Time System Analysis

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Real-time systems in embedded application have proliferated over the past few years. Many such systems are being used in life-critical and other important applications, where the failure of the computer to meet some deadlines can have disastrous consequences. The need therefore exists to accurately evaluate the reliability of such computers. Failure in a real-time system can occur due to timing as well as to traditional causes such as hardware failure. Timing overruns are often the consequence of a complicated series of interactions between various elements of the computer, such as individual application tasks, the operating system, the scheduling algorithm, the system architecture, component transient and permanent failure characteristics among other things. It is hard to take account of such interactions in analytical models without resorting to simplifying assumptions which raise questions about the models' accuracy and validity. Furthermore, traditional simulation to validate analytical models is very difficult because the failure rates that are being validated tend to be very low: system failure rates as low as .000000001 are involved. An earlier NSF-funded project developed the Rational Interpolation technique, and showed its usefulness in may compute applications. It created a framework in which various difficult modeling, control, and optimization issues can be attacked. The results indicate that Rational Interpolation is a powerful tool that can be used to complement other mechanisms of reliability and performance evaluation, especially in predicting very low failure rates. This project will involve the development of techniques and tools based on Rational Interpolation for real-time systems. While the focus will be on real-time systems, the results are expected to be useful in evaluating computers in other applications as well, such as random algorithms.