On the nature and impact of self-similarity in real-time systems

Abstract

In real-time systems with highly variable task execution times simplistic task models are insufficient to accurately model and to analyze the system. Variability can be tackled using distributions rather than a single value, but the proper charac- terization depends on the degree of variability. Self-similarity is one of the deep- est kinds of variability. It characterizes the fact that a workload is not only highly variable, but it is also bursty on many time-scales. This paper identifies in which situations this source of indeterminism can appear in a real-time system: the com- bination of variability in task inter-arrival times and execution times. Although self- similarity is not a claim for all systems with variable execution times, it is not unusual in some applications with real-time requirements, like video processing, networking and gaming. The paper shows how to properly model and to analyze self-similar task sets and how improper modeling can mask deadline misses. The paper derives an analyti- cal expression for the dependence of the deadline miss ratio on the degree of self- similarity and proofs its negative impact on real-time systems performance through system¿s modeling and simulation. This study about the nature and impact of self- similarity on soft real-time systems can help to reduce its effects, to choose the proper scheduling policies, and to avoid its causes at system design time.