Gradient descent algorithm for the optimization of fixed priorities in real-time systems

This paper considers the offline assignment of fixed priorities in partitioned preemptive real-time systems where tasks have precedence constraints. This problem is crucial in this type of systems, as having a good fixed priority assignment allows for an efficient use of the processing resources while meeting all the deadlines. In the literature, we can find several proposals to solve this problem, which offer varying trade-offs between the quality of their results and their computational complexities. In this paper, we propose a new approach, leveraging existing algorithms that are widely exploited in the field of Machine Learning: Gradient Descent, the Adam Optimizer, and Gradient Noise. We show how to adapt these algorithms to the problem of fixed priority assignment in conjunction with existing worst-case response time analyses. We demonstrate the performance of our proposal on synthetic task-sets with different sizes. This evaluation shows that our proposal is able to find more schedulable solutions than previous heuristics, approximating optimal but intractable algorithms such as MILP or brute-force, while requiring reasonable execution times.