Utilization bound for periodic task set with composite deadline

Due to polynomial time complexity, utilization based tests are desired for online feasibility analysis of periodic task systems. However, the associated disadvantage with these tests is that they propose a bound on system utilization, which trade processor utilization for performance. On the contrary, response time based tests share pseudo-polynomial time complexity, which are very expensive in terms of analysis time and therefore, impractical for analyzing feasibility of online systems. Realizing the advantage of utilization based tests over response time tests, attempts are being made to propose utilization based exact tests that achieve 100% CPU utilization for the system by modifying task parameters such as restricting task periods to be harmonic. We show that in systems where task deadlines are large, better results are obtained by making the task deadlines harmonic. The paper proposes a novel solution to feasibility problem of periodic task system under the assumption of composite deadline by providing a utilization based exact test with an upper bound of 1 and complexity O(n)O(n).