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This paper addresses the schedulability problem of periodic and sporadic real-time task sets with constrained deadlines preemptively scheduled on a multiprocessor platform composed by identical processors. We assume that a global work-conserving scheduler is used and migration from one processor to another is allowed during a task lifetime. First, a general method to derive schedulability conditions for multiprocessor real-time systems will be presented. The analysis will be applied to two typical scheduling algorithms: earliest deadline first (EDF) and fixed priority (FP). Then, the derived schedulability conditions will be tightened, refining the analysis with a simple and effective technique that significantly improves the percentage of accepted task sets. The effectiveness of the proposed test is shown through an extensive set of synthetic experiments.