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In this paper, we present the BandWidth Inheritance (BWI) protocol, a new strategy for scheduling real-time tasks in dynamic systems, which extends the resource reservation framework to systems where tasks can interact through shared resources. The proposed protocol provides temporal isolation between independent groups of tasks and enables a schedulability analysis for guaranteeing the performance of hard real-time tasks. We show that BWI is the natural extension of the well-known priority inheritance protocol to dynamic reservation systems. A formal analysis of the protocol is presented and a guarantee test for hard real-time tasks is proposed that takes into account the case in which hard real-time tasks interact with soft real-time tasks.