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In this paper, the Multiprocessor Bandwidth Inheritance (M-BWI) protocol is presented, which constitutes an extension of the Bandwidth Inheritance (BWI) protocol to symmetric multiprocessor and multicore systems. Similarly to priority inheritance, M-BWI reduces priority inversion in reservation-based scheduling systems, it allows the coexistence of hard, soft and non-real-time tasks, it does not require any information on the temporal parameters of the tasks, hence, it is particularly suitable to open systems, where tasks can dynamically arrive and leave, and their temporal parameters are unknown or only partially known. Moreover, if it is possible to estimate such parameters as the worst-case execution time and the critical sections length, then it is possible to compute an upper bound to the task blocking time. Finally, the M-BWI protocol is neutral to the underlying scheduling scheme, since it can be implemented both in global and partitioned scheduling schemes.