Release Offset Bounds for Response Time Analysis of P-FRP Using Exhaustive Enumeration

Functional Reactive Programming (FRP) is a declarative approach to modeling and building reactive systems. Priority-based FRP (P-FRP) is a formalism of FRP that guarantees real-time response. Unlike the classical preemptive model of real-time systems, preempted tasks in P- FRP are aborted and have to restart when higher priority tasks have completed. Due to this abort-restart of nature of preemption, there is no single critical instant of release that leads to Worst-Case Response Time (WCRT) of lower priority P-FRP tasks. At this time, the only method for determining the WCRT is through an exhaustive enumeration of all release offsets of higher priority tasks between the release and deadline of the lower priority task. This makes the computational cost of WCRT dependent on the deadline of a task, and when such deadlines are large the computational costs of this technique make it infeasible even for small task sets. In this paper, we show that the release offsets of higher priority tasks have a lower and upper bound and present techniques to derive these bounds. By enumerating only those release offsets while lie within our derived bounds the number of release scenarios that have to be enumerated is significantly reduced. This leads to lower computational costs and makes determination of the WCRT in P-FRP a practically feasible proposition.