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The hierarchical scheduling framework (HSF) has been introduced as a design-time framework to enable compositional schedulability analysis of embedded software systems with real-time properties. In this paper, a software 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, in the paper, the proposed methods allow non-intrusive configuration and tuning of subsystem timing-behavior via subsystem interfaces for selecting scheduling parameters. This paper considers three methods to handle overruns due to resource sharing between subsystems in the HSF. For each one of these three overrun methods corresponding scheduling algorithms and associated schedulability analysis are presented together with analysis that shows under what circumstances one or the other is preferred. The analysis is generalized to allow for both fixed priority scheduling (FPS) and earliest deadline first (EDF) scheduling. Also, a further contribution of the paper is the technique of calculating resource-holding times within the framework under different scheduling algorithms; the resource holding times being an important parameter in the global schedulability analysis.