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This paper studies parallel job scheduling in adistributed system. A simulation model is used to addressperformance issues associated with scheduling. Fivepolicies are used to schedule parallel jobs over a varietyof workloads. Fairness is required among competing jobs.We examine a case where the distribution of the numberof parallel tasks per job and also the distribution of taskservice demand vary with time. Simulated results indicatethat although all scheduling methods have merit, onemethod significantly improves the overall performanceand also guarantees fairness in terms of individual jobexecution.