In this paper we propose a new method for the analysis of response times in uni-processor real-time systems where task activation patterns may contain sporadic bursts. We use a burst model to calculate how often response times may exceed the worst-case response time bound obtained while ignoring bursts. This work is of particular interest to deal with dual-cyclic frames in the analysis of CAN buses. Our approach can handle arbitrary activation patterns and the static priority preemptive as well as non-preemptive scheduling policies. Experiments show the applicability and the benefits of the proposed method.