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We consider an important tradeoff between processor and memory allocation in distributed parallel processing systems. To study this tradeoff, we formulate stochastic models of parallel program behavior, distributed parallel processing environments and memory overheads incurred by parallel programs as a function of their processor allocation. A mathematical analysis of the models is developed, which includes the effects of contention for shared resources caused by paging activity. We conduct a detailed analysis of real large-scale scientific applications and use these results to parameterize our models. Our results show that memory overhead resulting from processor allocation decisions can have a significant effect on system performance in distributed parallel environments, strongly suggesting that memory considerations must be incorporated in the resource allocation policies for parallel systems. We also demonstrate the importance of the inter-locality miss ratio, which is introduced in this paper and analyzed for the first time.