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This paper studies parallel job scheduling in a distributed system. A simulation model is used to address performance issues associated with scheduling. Five policies are used to schedule parallel jobs over a variety of workloads. Fairness is required among competing jobs. We examine a case where the distribution of the number of parallel tasks per job and also the distribution of task service demand vary with time. Simulated results indicate that although all scheduling methods have merit, one method significantly improves the overall performance and also guarantees fairness in terms of individual job execution.