k2Q: A Quadratic-Form Response Time and Schedulability Analysis Framework for Utilization-Based Analysis

TL;DR

k2Q is a versatile framework that provides quadratic bounds for response time and schedulability analysis in real-time systems, applicable across various task models and platforms, improving efficiency and accuracy.

Contribution

The paper introduces the k2Q framework, enabling automatic quadratic bounds for response time and schedulability analysis across diverse real-time task models.

Findings

k2Q yields better schedulability tests for uniprocessor and multiprocessor systems.

It applies effectively to traditional and expressive task models like generalized multi-frame and acyclic models.

Exponential-time tests can be transformed into efficient polynomial-time tests using k2Q.

Abstract

In this paper, we present a general response-time analysis and schedulability-test framework, called k2Q (k to Q). It provides automatic constructions of closed-form quadratic bounds or utilization bounds for a wide range of applications in real-time systems under fixed-priority scheduling. The key of the framework is a $k$-point schedulability test or a $k$-point response time analysis that is based on the utilizations and the execution times of $k-1$ higher-priority tasks. The natural condition of k2Q is a quadratic form for testing the schedulability or analyzing the response time. The response time analysis and the schedulability analysis provided by the framework can be viewed as a "blackbox" interface that can result in sufficient utilization-based analysis. Since the framework is independent from the task and platform models, it can be applied to a wide range of applications. We show the generality of k2Q by applying it to several different task models. k2Q produces better uniprocessor and/or multiprocessor schedulability tests not only for the traditional sporadic task model, but also more expressive task models such as the generalized multi-frame task model and the acyclic task model. Another interesting contribution is that in the past, exponential-time schedulability tests were typically not recommended and most of time ignored due to high complexity. We have successfully shown that exponential-time schedulability tests may lead to good polynomial-time tests (almost automatically) by using the k2Q framework.