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
[10][8]. 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
.