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Users of parallel machines need to have a good grasp for how different communication patterns and styles affect the performance of message-passing applications. LogGP is a simple performance model that reflects the most important parameters required to estimate the communication performance of parallel computers. The message passing interface (MPI) standard provides new opportunities for developing high performance parallel and distributed applications. In this paper, we use LogGP as a conceptual framework for evaluating the performance of MPI communications on three platforms: Cray-Research T3D, Convex Exemplar 1600SP, and a network of workstations (NOW). Our objective is to identify a performance model suitable for MPI performance characterization and to compare the performance of MPI communications on several platforms.