Regression-based Statistical Bounds on Software

Our work aims at facilitating the schedulability analysis of non-critical systems, in particular those that have soft real-time constraints, where WCETs can be replaced by less stringent probabilistic bounds, which we call Maximal Execution Times (METs). In our approach, we can obtain adequate probabilistic execution time models by separating the non-random input data dependency from a modeling error that is purely random. To achieve this, we propose to take advantage of the rich set of available statistical model-fitting techniques, in particular linear regression. Although certainly the proposed technique cannot directly achieve extreme probability levels that are usually expected for WCETs, it is an attractive alternative for MET analysis, since it can arguably guarantee safe probabilistic bounds. We demonstrate our method on a JPEG decoder running on an industrial SPARC V8 processor.