Optimal Speed Assignment for Probabilistic Execution Times

The problem of reducing energy consumption is dominating the design and the implementation of embedded realtime systems. For this reason, a new generation of processors allow to vary the voltage and the operating frequency to balance computational speed versus energy consumption. The policies that can exploit this feature are called Dynamic Voltage Scheduling (DVS). In real-time systems, the DVS technique must also provide the worst-case computational requirement. However, it is well known that the probability of a task executing for the longest possible time is very low. Hence, DVS policies can exploit probabilistic information about the execution times of tasks to reduce the energy consumed by the processor. In this paper we provide the foundations to integrate probabilistic timing analysis with energy minimization techniques, starting from the simple case of one task.