Determining rate monotonic schedulability of real-time periodic tasks using continued fractions

Fixed-priority scheduling algorithms are widely used for real-time systems with a single processor because of their implementation simplicity and relatively low run-time overheads. However, determining whether a task set is schedulable by a fixed-priority scheduling algorithm has been shown to be NP-hard. There are few exact schedulability test methods such as the time demand analysis or the worst-case response time analysis for Rate Monotonic scheduling, while much research has been done to find a tighter sufficient condition for the fixed-priority schedulability. In this paper, a new approach to analyze the schedulability of fixed-priority scheduling using well-known mathematical tool called continued fractions is presented. With continued fractions, a new schedulability test for Rate Monotonic algorithm is derived. The schedulability test condition is an exact condition that can be applied tasks with total utilization less than 1.