Sequential Composition of Execution Time Distributions by Convolution

Embedded real-time systems are increasingly being assembled from software components. This raises the issue how to find the timing properties for the resulting system. Ideally, these properties can be inferred from the properties of the components: this is the case if the underlying timing model is compositional. However, compositional timing models tend to provide a simplified view. An important question is then: when is a compositional model accurate enough to meet the requirements for an analysis that is based on the model?In this paper we consider a simple, statistical compositional model for execution time distributions of sequentially composed components, which assumes that the distributions of the underlying random variables are independent. This assumption is only approximately correct in general, as dependencies can appear due to both software and hardware effects. We have made an experimental investigation of how hardware features affect the validity of the timing model. The result is that for the most part, the effect of hardware features on the validity of the model is small. The hardware feature with the strongest influence in the experiment was the reorder buffer, followed by branch table associativity, L2 cache size, and out-of order execution.