Response time central-limit and failure rate estimation for stationary periodic rate monotonic real-time systems

Real-time systems consist of a set of tasks, a scheduling policy, and a system architecture, all constrained by timing requirements.

Many everyday embedded systems, within devices such as airplanes, cars, trains, and spatial probes, operate as real-time systems.

To ensure safe failure rates, response times-the time required for the exection of a task-must be bounded.

Rate Monotonic real-time systems prioritize tasks according to their arrival rate.

This paper focuses on the use of the central limit of response times built in \cite{zagalo2022} and an approximation of their distribution with an inverse Gaussian mixture distribution.

The distribution parameters and their associated failure rates are estimated through a suitable re-parameterization of the inverse Gaussian distribution and an adapted Expectation-Maximization algorithm.

Extensive simulations demonstrate that the method is well-suited for the approximation of failure rates.

We discuss the extension of such method to a chi-squared independence test adapted to real-time systems.