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

TL;DR

This paper introduces a novel statistical method using inverse Gaussian mixtures and EM algorithms to estimate response times and failure rates in stationary periodic rate monotonic real-time systems, enhancing safety analysis.

Contribution

It presents a new approach for approximating response time distributions and failure rates in real-time systems using inverse Gaussian mixtures and adapted EM algorithms.

Findings

Effective approximation of failure rates demonstrated through extensive simulations.

Method suitable for real-time system safety analysis.

Potential extension to independence testing in real-time contexts.

Abstract

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.