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The hierarchical scheduling framework (HSF) has been introduced as a design-time framework enabling compositional schedulability analysis of embedded software systems with real-time properties. In this paper a system consists of a number of semi-independent components called subsystems. Subsystems are developed independently and later integrated to form a system. To support this design process, our proposed methods allow non-intrusive configuration and tuning of subsystem timing-behaviour via subsystem interfaces for selecting scheduling parameters. This paper considers two methods to handle overruns due to resource sharing between subsystems in the HSF. We present the scheduling algorithms for overruns and their associated schedulability analysis, together with analysis that shows under what circumstances one or the other overrun method is preferred. Furthermore, we show how to calculate resource-holding times within our framework.