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

TL;DR

This paper introduces an exact polynomial-time algorithm for calculating worst-case response times of harmonic tasks with release jitter in real-time systems, improving efficiency over previous methods.

Contribution

It presents a new linear-time algorithm for response time analysis of harmonic tasks with jitter, incorporating a specialized constraint programming approach for jitter admissibility.

Findings

Algorithm reduces computational complexity compared to previous methods.

Efficient jitter constraint checking with linear time heuristic.

Applicable to jitter-aware real-time system analysis.

Abstract

In some important application areas of hard real-time systems, preemptive sporadic tasks with harmonic periods and constraint deadlines running upon a uni-processor 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.