This work deals with the problem to optimise the energy consumption of an embedded system. On system level, tasks are assumed to have a certain CPU-usage they need for completion. Respecting their deadlines, slowing down the task system reduces the energy consumption. For periodically occurring tasks several works exists. But even if jitter comes into account the approaches do not suffice. The event stream model can handle this at an abstract level and the goal of this work is to present and solve the optimisation problem formulated with the event stream model. To reduce the complexity we introduce an approximation to the problem, that allows us a precision/performance trade-off.