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In this paper, we study schedulability analysis problems for multi-processor real-time systems. Assume a set of real-time tasks whose execution times and deadlines are known. We use timed automata to describe the non-deterministic arrival times of tasks. The schedulability problem is to check whether the released task instances can be executed within their given deadlines on a multi-processor platform where each processor has a task queue to buffer task instances scheduled to run on the processor. On the positive side, we show that the problem is decidable for systems with non-preemptive schedulers or tasks with fixed execution times. A surprising negative result is that for multi-processor systems with variable task execution times and a preemptive scheduler, the schedulability analysis problem is undecidable, which is still an open problem in the single-processor setting.