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A method to perform exact worst case response time analysis for fixed priority tasks with offsets and release jitter is described. Available methods are either pessimistic or inefficient as they incorporate numerous time consuming schedule simulations in order to find the exact response times of tasks. The method presented here is based on the creation of the worst case conditions for the execution of each individual task instance within a hyperperiod. The worst case is built by choosing release jitter of higher priority tasks appropriately. Given these conditions, the corresponding task instance response time is calculated using partly iterative algorithms. Experiments comparing the efficiency of the proposed method to an alternative exact method based on schedule simulation show that the new method outperforms the latter. The analysis is expected to be particularly useful when analysing response times and schedulability of tasks that form transactions in distributed systems.