Polynomial Time Schedulability Test for Periodic Non-Preemptive 2-Task System

Abstract

Non-preemptive scheduling of tasks is often preferred in safety-critical systems because of its simplicity in implementation. But, one of the major issues with non-preemptive scheduling is that no known polynomial time schedulability condition exists. The general problem of schedulability of a set of tasks on a single processor under such scheme is known to be NP-Hard [1]. People have attempted to propose different sufficient or necessary conditions for schedulability of a set of tasks under various constrained scenarios. In this work, we explore schedulability condition for 2-task systems when the tasks are scheduled non-preemptively and periodically using work conserving model of execution. We assume that the tasks are released at the same point of time initially. We show that the proposed condition for 2-task systems can be evaluated in polynomial time.