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Historically, the need to solve large-scale scientific problems has provided the motivation for the design and construction of large computing systems. The traditional methods for providing greater computational capacity--that of developing faster logic technology--cannot continue indefinitely. The alternative approach for meeting the demands for greater computational power appears to be the development of machines capable of performing significant numbers of operations concurrently in time. Such machines are expensive, and development by trial and error is not economically viable. In order to develop efficient high-performance concurrent computer systems, some sort of design tool is necessary which will permit the prediction of the performance of hypothetical system organizations. A limited theory of concurrent computations is developed for concurrent systems based on a requestor/server concept. By use of the Petri-Net concurrent control system model, it is shown that this theory is easily implemented and is capable of predicting the performance of scientific programs running on complex concurrent computer systems. The performance of this type of model is discussed in the light of the requirements for a computer architectural design tool. A number of examples are given to demonstrate the inherent correctness or accuracy. A large-scale computer system design example is presented where this model is used to predict performance. The questions of ease of use, efficiency, and accuracy are discussed, and the problems in the use of this type of approach for predicting performance of software--hardware ensembles are examined. 35 figures, 119 references. (ERA citation 04:014943)