We illustrate the application of the hyperbolic model, which generalizes standard two-parameter dedicated-link models for communication costs in message-passing environments, to four rather different distributed-memory architectures: Ethernet NOW, FDDI NOW, IBM SP2, and Intel Paragon. We first evaluate the parameters of the model from simple communication patterns. Then over-all communication time estimates, which compare favorably with experimental measurements, are deduced for the message traffic in a scientific application code. For transformational computing on dedicated systems, for which message traffic is describable in terms of a finite number of regular patterns, the model offers a good compromise between the competing objectives of flexibility, tractability, and reliability of prediction.