A Metric for Judicious Relaxation of Timing Constraints in Soft Real-Time Systems

For soft real-time systems, timing constraints are not as stringent as those in hard real-time systems: some constraint violations are permitted as long as the amount of violation is within a given limit. The allowed flexibility for soft real-time systems can be utilized to improve system's other quality-of-service (QoS) properties, such as energy consumption. One way to enforce constraint violation limit is to allow an expansion of timing constraint feasible region, but restrict the expansion in such a way that the relaxed constraint feasible region sufficiently resembles the original one. In this paper, we first introduce a new metric, constraint set similarity, to quantify the resemblance between two different timing constraint sets. Because directly calculating the exact value of the metric involves calculating the size of a polytope which is a #P-hard problem, we instead introduce an efficient method for estimating its bound. We further discuss how this metric can be exploited for evaluating trade-offs between timing constraint compromises and system's other QoS property gains. We use energy consumption reduction as an example to show the application of the proposed metric.