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In this paper, we consider fair scheduling of soft real-time applications on multiprocessors using the earliest pseudo deadline first (EPDF) Pfair algorithm. Our main contributions are twofold. First, we establish a condition for ensuring a tardiness of at most one quantum under EPDF. This condition is very liberal and should often hold in practice. Second, we present simulation results involving randomly-generated task sets, including those that do not satisfy our condition. In these experiments, deadline misses were rare, and no misses by more than one quantum ever occurred.