Evaluate and Compare Two Utilization-Based Schedulability-Test Frameworks for Real-Time Systems

This report summarizes two general frameworks, namely k2Q and k2U, that have been recently developed by us. The purpose of this report is to provide detailed evaluations and comparisons of these two frameworks. These two frameworks share some similar characteristics, but they are useful for different application cases. These two frameworks together provide comprehensive means for the users to automatically convert the pseudo polynomial-time tests (or even exponential-time tests) into polynomial-time tests with closed mathematical forms. With the quadratic and hyperbolic forms, k2Q and k2U frameworks can be used to provide many quantitive features to be measured and evaluated, like the total utilization bounds, speed-up factors, etc., not only for uniprocessor scheduling but also for multiprocessor scheduling. These frameworks can be viewed as "blackbox" interfaces for providing polynomial-time schedulability tests and response time analysis for real-time applications. We have already presented their advantages for being applied in some models in the previous papers. However, it was not possible to present a more comprehensive comparison between these two frameworks. We hope this report can help the readers and users clearly understand the difference of these two frameworks, their unique characteristics, and their advantages. We demonstrate their differences and properties by using the traditional sporadic realtime task models in uniprocessor scheduling and multiprocessor global scheduling.