Schedulability Analysis of Real-Time Systems with Stochastic Task Execution Times

Systems controlled by embedded computers become indispensable in our lives and can be found in avionics, automotive industry, home appliances, medicine, telecommunication industry, mecatronics, space industry, etc. Fast, accurate and flexible performance estimation tools giving feedback to the designer in every design phase are a vital part of a design process capable to produce high quality designs of such embedded systems. In the past decade, the limitations of models considering fixed (worst case) task execution times have been acknowledged for large application classes within soft real-time systems. A more realistic model considers the tasks having varying execution times with given probability distributions. No restriction has been imposed in this thesis on the particular type of these functions. Considering such a model, with specified task execution time probability distribution functions, an important performance indicator of the system is the expected deadline miss ratio of tasks or task graphs. This thesis proposes two approaches for obtaining this indicator in an analytic way. The first is an exact one while the second approach provides an approximate solution trading accuracy for analysis speed. While the first approach can efficiently be applied to mono-processor systems, it can handle only very small multi-processor applications because of complexity reasons. The second approach, however, can successfully handle realistic multi-processor applications. Experiments show the efficiency of the proposed techniques.