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This paper studies task scheduling in a distributed system. A simulation model is used to address performance issues associated with scheduling. Three policies are employed to schedule parallel jobs over a variety of workloads. Their performance is studied and compared under time varying workloads. Simulated results indicate that all scheduling methods have merit, and that the choice of a policy depends on whether the performance goal is to achieve only good overall performance or to provide also some guarantee for fairness in terms of individual job service.