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A new technique was recently introduced by Bonifaci et al. for the analysis of real-time systems scheduled on multiprocessor platforms by the global Earliest Deadline First (EDF) scheduling algorithm. In this paper, this technique is generalized so that it is applicable to the schedulability analysis of real-time systems scheduled on multiprocessor platforms by any work-conserving algorithm. The resulting analysis technique is applied to obtain a new sufficient global Deadline Monotonic (DM) schedulability test. It is shown that this new test is quantitatively superior to pre-existing DM schedulability analysis tests; in addition, the degree of its deviation from any hypothetical optimal scheduler (that may be clairvoyant) is quantitatively bounded. A new global EDF schedulability test is also proposed here that builds on the results of Bonifaci et al. This new test is shown to be less pessimistic and more widely applicable than the earlier result was, while retaining the strong theoretical properties of the earlier result.