Optimal Priority Assignments in P-FRP

Priority-based Functional Reactive Programming (P-FRP) has been recently introduced as a new functional programming formalism for real-time systems. P-FRP allows static priority assignment and guarantees real-time response by preempting lower priority tasks. Due to the state-less nature of functional programs, preempted tasks in P-FRP are aborted and restarted after the higher priority tasks have completed execution. In the classical preemptive model † of real-time systems, it has been demonstrated that for fixed priority scheduling, if tasks are schedulable with any priority assignment, they are also schedulable by the rate-monotonic (RM) priority assignment, making this priority assignment optimal for all task sets in the preemptive model. However, the RM priority assignment is not optimal in P-FRP, and it has been unknown if an optimal fixed priority assignment can even exist for such an execution model. In this paper, we formally present the priority assignment characteristics of P-FRP and show that based on task periods, either a combined utilization and rate-monotonic, or only the ratemonotonic priority assignments is optimal for a system with two tasks. Using this result, we formally prove the limitation of optimal priority assignments in a P-FRP system having more than two tasks where, unless arrival periods are integer multiples of each other, no single priority assignment exists which is optimal for all task sets. Experimental results using task sets of different sizes are also presented. † In this paper the classical preemptive model refers to a real-time system in which tasks can be preempted by higher priority tasks and can resume execution from the point they were preempted * This work is supported in part by U.S. National Science Foundation under Award no. 0720856