A Framework to Construct Customized Harmonic Periods for Real-Time Systems

The periodic task model has been widely used in real-time systems due to the periodic behavior of many applications or periodic observation patterns of environmental events as in control applications. While the tasks of some applications have inherent values for periods, many can be defined via ranges of acceptable values. The designer choice of period values has consequences w.r.t. To utilization of the task set and the resulting hyper period. Harmonic task sets are favored, e.g., for their polynomial-time worst case response time analysis or their small hyper periods, which is of major concern e.g., for hyper visors used in virtualization or time triggered systems. In this paper we present a model to describe harmonic relations between ranges of period values, rather than single numbers only. We derive sufficient conditions for the existence of a linear-time solution, as well as a graph representation for the relations between period ranges. We provide utilization bounds of each resulting harmonic range, giving the designer flexibility to select a harmonic task set with high or low utilization. The tightness of the bounds as well as efficiency of our period assignment algorithms have been evaluated by synthetic experiments via system utilization and feasibly constructed harmonic task sets.