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Response Time Stochastic Analysis for Fixed-Priority Stable Real-Time Systems
Abstract
In this paper, we prove that a mean system utilization smaller than one is a necessary condition for the feasibility of real-time systems. Such systems are defined as stable. Stable systems have two distinct states: a transient state, followed by a steady-state where the same distribution of response times is repeated infinitely for each task. We prove that the Liu and Layland theorem holds for stable probabilistic real-time systems with implicit deadlines, we provide an analytical approximation of response times for each of those two states and a bound of the instant when a real-time system becomes steady.
Versions
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BibTeX
@misc{zagalo2026response,
title = {{Response Time Stochastic Analysis for Fixed-Priority Stable Real-Time Systems}},
author = {Kevin Zagalo and Yasmina Abdeddaïm and Avner Bar-Hen and Liliana Cucu-Grosjean},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21760},
eprint = {2609.21760},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21760},
}
RIS
TY - UNPB
TI - Response Time Stochastic Analysis for Fixed-Priority Stable Real-Time Systems
AU - Kevin Zagalo
AU - Yasmina Abdeddaïm
AU - Avner Bar-Hen
AU - Liliana Cucu-Grosjean
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21760
UR - https://arxiv.org/abs/2609.21760
AB - In this paper, we prove that a mean system utilization smaller than one is a necessary condition for the feasibility of real-time systems. Such systems are defined as stable. Stable systems have two distinct states: a transient state, followed by a steady-state where the same distribution of response times is repeated infinitely for each task. We prove that the Liu and Layland theorem holds for stable probabilistic real-time systems with implicit deadlines, we provide an analytical approximation of response times for each of those two states and a bound of the instant when a real-time system becomes steady.
ER -