The space of rate monotonic schedulability

Feasibility analysis of fixed priority systems has been widely studied in the real-time literature and several acceptance tests have been proposed to guarantee a set of periodic tasks. They can be divided into two main classes: polynomial time tests and exact tests. Polynomial time tests are used for an online guarantee of dynamic systems, where tasks can be activated at runtime. These tests introduce negligible overhead when executed on a new task arrival, but provide only a sufficient schedulability condition, which may cause poor processor utilization. On the other hand, exact tests, which are based on response time analysis, provide a necessary and sufficient schedulability condition, but are too complex to be executed on line for large task sets. As a consequence, for large task sets, they are often executed offline. This paper proposes a novel approach for analyzing the schedulability of periodic task sets under rate monotonic priority assignment. Using this approach, we derive a new schedulability test which can be tuned through a parameter to balance the complexity vs. acceptance ratio, so that it can be used online to better exploit the processor based on available computational power. Extensive simulations show that our test, when used in its exact form, is significantly faster than current response time analysis methods. Moreover, the proposed approach, for its elegance and compactness, offers an explanation of known phenomena of fixed priority scheduling and could be helpful for further work on rate monotonic analysis.