Response Time Central-Limit and Failure Rate Estimation for Stationary Periodic Rate Monotonic Real-Time Systems
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.
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BibTeX
@article{zagalo2026response,
title = {{Response Time Central-Limit and Failure Rate Estimation for Stationary Periodic Rate Monotonic Real-Time Systems}},
author = {Kevin Zagalo and Avner Bar-Hen},
journal = {IEEE Transactions on Computers},
year = {2026},
month = oct,
doi = {10.1109/tc.2026.3742489},
eprint = {2211.01720},
archivePrefix = {arXiv},
url = {https://inria.hal.science/hal-03839408v4},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Response Time Central-Limit and Failure Rate Estimation for Stationary Periodic Rate Monotonic Real-Time Systems
AU - Kevin Zagalo
AU - Avner Bar-Hen
PY - 2026
DA - 2026/10/27
JO - IEEE Transactions on Computers
DO - 10.1109/tc.2026.3742489
UR - https://inria.hal.science/hal-03839408v4
AB - 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.
SN - 0018-9340
ER -