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There is an important class of scheduling strategies that has not been sufficiently covered by the real-time scheduling literature. The new multi-core extensions of the AUTOSAR automotive standard - the dominating automotive design worldwide - uses a combination of partitioned fixed-priority scheduling strategies with preemptive and non-preemptive execution and (potentially) arbitrary deadlines. Since multi-core systems in general use shared resources, this leads to the problem of analyzing preemptive and non-preemptive multiprocessor scheduling with shared resources. While preemptive scheduling has been well investigated in this setup, non-preemptive scheduling analysis is still open and cannot simply be derived. In this paper, we address this subject and present an analysis method which allows the calculation of response-times for tasks with arbitrary activations and deadlines which share resources in multi-core systems scheduled according to the partitioned fixed-priority non-preemptive scheduling. We consider this work an essential building block for the analysis of upcoming multi-core realtime applications where both preemptive and non-preemptive scheduling coexist.