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We develop a workload model based on the observed behavior of parallel computers at the San Diego Supercomputer Center and the Cornell Theory Center. This model gives us insight into the performance of strategies for scheduling moldable jobs on space-sharing parallel computers. We find that Adaptive Static Partitioning (ASP), which has been reported to work well for other workloads, does not perform as well as strategies that adapt better to system load. The best of the strategies we consider is one that explicitly reduces allocations when load is high (a variation of Sevcik's (1989) A+ strategy).