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We describe a new, non-FCFS policy to schedule parallel jobs on systems that may be part of a computational grid. Our algorithm continuously monitors the system (i.e., intensity of incoming jobs and variability of their resource demands) and continuously adapts its scheduling parameters to sudden workload fluctuations. The proposed policy is based on backfilling which permits job rearrangement in the waiting queue. By exploiting otherwise idle processors, this rearrangement reduces fragmentation of system resources, thereby providing higher system utilization. We propose to maintain multiple job queues that effectively separate jobs according to their projected execution time. Our policy supports different job priority classes as well as job reservations, making it appropriate for scheduling jobs on parallel systems that are part of a computational grid. Detailed performance comparisons via simulation using traces from the Parallel Workload Archive indicate that the proposed policy consistently outperforms traditional scheduling approaches.