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In computer architecture investigations a major interest is in the analysis of organizations which explore parallelism, and therefore, may have multiple instruction and multiple data streams (MIMD). In this paper, a MIMD structure with one shared resource is analyzed for both synchronous and asynchronous request arrivals. Although the analysis is somewhat restricted, it appears that a similar approach can be used to extend the model to more general MIMD cases. Results presented for one particular set of parameters indicate that an optimum resource replication is possible such that an optimum cost performance is achieved.