Response Time Stochastic Analysis for Fixed-Priority Stable Real-Time Systems

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.

Automated summary

In this paper, it is proven that a mean system utilization smaller than one is a necessary condition for the feasibility of real-time systems. Stable systems, which have two distinct states, a transient state and a steady-state, are defined as systems where the same distribution of response times is repeated infinitely for each task. The Liu and Layland theorem is proved to hold for stable probabilistic real-time systems with implicit deadlines, and an analytical approximation of response times for each of those two states is provided, along with a bound of the instant when a real-time system becomes steady.