A Schedulability Test for Sporadic Task DM Scheduling Based on Density Upper Bound

Abstract

Due to low runtime overhead and simple implementation of DM (Deadline Monotonic) scheduling, it is widely used in real-time systems. Aiming at the schedulability test problem of the sporadic task DM scheduling under uniprocessor, a density upper bound of 0.693 is analyzed, which can determine the schedulability of a task set in linear time. The theoretical analysis process is carried out in three steps. Firstly, the case is considered where the task set contains only two tasks and the deadline ratio between the tasks is less than 2. Secondly, the case is considered where the task set contains multiple tasks and the deadline ratio between any two tasks is still less than 2. Finally, the case is considered where the task set contains multiple tasks and the deadline ratio between tasks is an arbitrary value. The experimental results show that the upper bound of density is higher than related methods and the run time overhead is much lower than that of other available exact schedulability tests. The time complexity is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(1)$ </tex-math></inline-formula> when a task is dynamically added to a task set, while that of other methods increases rapidly along with the number of tasks. In addition, we combined this upper bound and other tests to further propose an exact schedulability test, which effectively reduces the running time overhead by 30.8% compared with the state-of-the-art schedulability test. Due to the high efficiency of our schedulability test, an online schedulability test can be implemented in open real-time systems.