Response-Time Analysis of tasks with offsets

This article presents some results about schedulability analysis of tasks with offsets also known as transactions, in the particular case of monotonic transactions. The impact of a transaction on the response time of a lower priority task under analysis is computed with the interference implied by the transaction. In the general context of tasks with offsets (general transactions), only exponential methods are known to calculate the exact worst-case response time of a task. However, in this case, Maki-Turja and Nolin have proposed an efficient approximation method. A monotonic pattern in a transaction (regarding the priority of the task under analysis), occurs when, by rotation of the higher priority tasks in a transaction, it is possible to find a pattern of tasks such that the processor demand of the transaction is monotically decreasing during a period of the transaction. We have shown in our previous work that if a task under analysis is such that all the interfering transactions are monotonic, then it is possible to evaluate its exact response time in a pseudo-polynomial time. This article presents in detail how to apply this method. Then, it compares our results to the multiframe model proposed by Mok and Chen in (1996) (AM "accumulatively monotonic" pattern). We show that the multiframe model is a particular instance of tasks with offsets but the results presented for AM multiframe cannot be applied on monotonic transactions. Finally, we show that the approximation method proposed by Maki-Turja and Nolin computes an exact response time in the case of monotonic transactions, even if its complexity is higher than the one of the test that we proposed.