Exact best-case response time analysis of fixed priority scheduled tasks

We present a solution for exact calculation of the best-case response times of a periodic task set with fixed priorities. The solution is based on the identification of the best-case phasing of a low priority task compared to the higher priority tasks. This phasing occurs when the low priority task is released such that it finishes simultaneously with the releases of all the higher priority tasks, when these have experienced their maximum release jitter. A recurrence equation is applied to find the best-case response time. The dualism between worst-case and best-case response time calculation is characterized. The most important application of the solution is in the analysis of response jitter.