The BLAS processes communicate with each other via calls to the BLACS. For the sake of simplicity, we model a restricted subset of the possible BLACS operations, namely point-to-point communication and broadcast/combine operations along a row or column of the mesh. It is customary to model the time for sending a message of items between two processes by
where denotes the latency, and the inverse of the bandwidth. The broadcast/combine operations are more complicated since the BLACS allow the user to specify a topology argument . We estimate the cost of broadcasting items using a split-ring topology to processes by .
Similarly, the cost of a 1-tree combine operation of items involving processes is estimated by .
At this level of the model, it is not possible to determine the values of because no assumption has been made so far on the physical network to model. This justifies the introduction of these functions .