In this paper the authors presents a new compositional approach providing safe quantitative information about real-time systems. Their method is based on a new model to describe sporadic overload at the input of a system. The authors show how to derive from such a model safe quantitative information about the response time of each task. Experiments demonstrate the efficiency of this approach on a real-life example. In addition they improve the state of the art in compositional performance analysis by introducing execution time models which take into account several consecutive executions and by using tighter bounds for computing output event models.