UNIVERSIDAD OF OVIEDO Computer Science Department Stochastic Analysis of the Steady-State Backlog in Periodic Real-Time Systems

Classical analysis of real-time systems focuses in the study of the “worst-case” scenario, by assuming that all task will require their worst-case execution time, and a critical instant in which the response time will be the longest. Recently, some authors modelled the execution time as a random variable, and developed several techniques in order to obtain the distribution of the response time, from which the probability of deadline misses can be derived. We introduced in Díaz et al. [2002] one of these techniques, which can be ap-plied when the maximum system utilization is not greater than 1. In this report, we show that these techniques can also be applied to systems with maximum utiliza-tion greater than 1, whenever the average system utilization is not greater than 1. For this case, we prove the existence of a steady-state regime, in which the response time of all jobs follow a stationary probability function. The response time distri-butions for that steady-state regime can be derived from the steady-state backlog distribution, using the techniques presented in Díaz et al. [2002], so in this repor