Research and development of an algorithm for the response time estimation in multiprocessor systems under the interval uncertainty of the tasks execution times

The paper presents an algorithm for the worst case response time (WCRT) estimation for multiprocessor systems with fixed-priority preemptive schedulers and the interval uncertainty of tasks execution times. Each task has a unique priority within its processor, a period, an execution time interval [BCET, WCET] and can have data dependency on other tasks. If a decrease in the execution time of the task A can lead to an increase in the response time of the another task B, then task A is called an anomalous task for task B. According to the chosen approach, in order to estimate a task's WCRT, two steps should be performed. The first one is to construct a set of anomalous tasks using the proposed algorithm for the given task. The paper provides the algorithm and the proof of its correctness. The second one is to find the WCRT estimation using a genetic algorithm. The proposed approach has been implemented software as a program in Python3. A set of experiments have been carried out in order to compare the proposed method in terms of precision and speed with two well-known WCRT estimating methods: the method that does not take into account interval uncertainty (assuming that the execution time of a given task is equal to WCET) and the brute force method. The results of the experiments have shown that, in contrast to the brute force method, the proposed method is applicable to the analysis of the real scale computing systems and also allows to achieve greater precision than the method that does not take into account interval uncertainty.