A hyperbolic model for communication in layered parallel processing environments

We introduce a model for communication costs in parallel processing environments, called the hyperbolic model, which generalizes two-parameter dedicated-link models in an analytically simple way. The communication system is modeled as a directed communication graph in which terminal nodes represent the application processes and internal nodes, called communication blocks (CBs), reflect the layered structure of the underlying communication architecture. A CB is characterized by a two-parameter hyperbolic function of the message size that represents the service time needed for processing the message. Rules are given for reducing a communication graph consisting of many CBs to an equivalent two-parameter form, while maintaining a good approximation for the service time. We demonstrate a tight fit of the estimates of the cost of communication based on the model with actual measurements of the communication and synchronization time between end processes. We compare the hyperbolic model with other two-parameter models and, in appropriate limits, show its compatibility with the LogP model.