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A new feasibility test for preemptive scheduling of periodic or sporadic real-time tasks on a single-queue m-server system allows for arbitrary fixed task priorities and arbitrary deadlines. For the special case when deadline equals period and priorities are rate monotonic, any set of tasks with maximum individual task utilization umax and minimum individual task utilization umin is feasible if the total utilization does not exceed $$m(1-u_{\rm max})/2 + u_{\rm min}$$.