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This paper introduces the circulating processor model for parallel computer systems. Models of parallel systems tend to be computationally complex due to synchronization constraints such as task forking and joining. However, product form queuing network models remain computationally efficient as the size of the system grows by calculating only the mean performance metrics of the system. The circulating processor model is a product form queuing network model that differs from more traditional models in that the processors circulate among the parallel applications. In traditional models, the tasks of the parallel application circulate among the processors. Behaviors such as forking and joining of tasks and barrier synchronizations are better captured using this new approach. The circulating processor model may be load-dependent or load-independent. For systems that contain a single parallel application, the load-dependent circulating processor model is exact, while the load-independent model is not. In the latter case, an exact error can be calculated. For systems that contain multiple parallel applications, the load-dependent circulating processor model is a good approximation to the actual system, while the load-independent model is not. A case study using Parallel Virtual Machine (PVM) on a network of workstations illustrates the applicability of the circulating processor model.