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Optimal Reward-Based Scheduling for Periodic Real-Time Tasks

Summary: Optimal Reward-Based Scheduling
for Periodic Real-Time Tasks
Hakan Aydin, Student Member, IEEE, Rami Melhem, Fellow, IEEE,
Daniel Mosse¬, Member, IEEE, and Pedro Mejű¬a-Alvarez
Abstract–Reward-based scheduling refers to the problem in which there is a reward associated with the execution of a task. In our
framework, each real-time task comprises a mandatory and an optional part. The mandatory part must complete before the task's
deadline, while a nondecreasing reward function is associated with the execution of the optional part, which can be interrupted at any
time. Imprecise computation and Increased-Reward-with-Increased-Service models fall within the scope of this framework. In this
paper, we address the reward-based scheduling problem for periodic tasks. An optimal schedule is one where mandatory parts
complete in a timely manner and the weighted average reward is maximized. For linear and concave reward functions, which are most
common, we 1) show the existence of an optimal schedule where the optional service time of a task is constant at every instance and
2) show how to efficiently compute this service time. We also prove the optimality of Rate Monotonic Scheduling (with harmonic
periods), Earliest Deadline First, and Least Laxity First policies for the case of uniprocessors when used with the optimal service times
we computed. Moreover, we extend our result by showing that any policy which can fully utilize all the processors is also optimal for the
multiprocessor periodic reward-based scheduling. To show that our optimal solution is pushing the limits of reward-based scheduling,
we further prove that, when the reward functions are convex, the problem becomes NP-Hard. Our static optimal solution, besides
providing considerable reward improvements over the previous suboptimal strategies, also has a major practical benefit: Run-time
overhead is eliminated and existing scheduling disciplines may be used without modification with the computed optimal service times.
Index Terms–Real-time systems, imprecise computation, periodic task scheduling, deadline scheduling, reward maximization.


Source: Aydin, Hakan - Department of Computer Science, George Mason University


Collections: Computer Technologies and Information Sciences; Engineering