Exact Polynomial Time Algorithm for the Response Time Analysis of Harmonic Tasks with Constrained Release Jitter

Abstract

In some important application areas of hard real-time systems, preemptive sporadic tasks with harmonic periods and constraint deadlines running upon a uniprocessor platform play an important role. We propose a new algorithm for determining the exact worst-case response time for a task that has a lower computational complexity (linear in the number of tasks) than the known algorithm developed for the same system class. We also allow the task executions to start delayed due to release jitter if they are within certain value ranges. For checking if these constraints are met we define a constraint programming problem that has a special structure and can be solved with heuristic components in a time that is linear in the task number. If the check determines the admissibility of the jitter values, the linear time algorithm can be used to determine the worst-case response time also for jitter-aware systems.

Fuzzy Simultaneous Congruences

“…However, the problem can be solved in polynomial time if a i = 1 [10,15] or if the capacities a i fulfil a harmonic property [5,6,18], i.e. a i+1 /a i is integer for all i < n. Now a recent manuscript in the field of real-time systems by Nguyen et al [16] gives rise to the study of a new problem. They present an exact algorithm for the worst-case response time analysis of harmonic tasks with constrained release jitter running in polynomial time.…”