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a cluster configuration, where
p
i
represents the percentage of the cluster that has
a speedup of
s
i
over the slowest node configuration. As a result of this notation, we
can accurately express the heterogeneity of the cluster with respect to
N
classes
of hardware, each represented by one entry in a vector of size
N
. In this vector, the
sum of all
p
i
values is 100. When MARLA configuration causes tasks to sub-divide
into eight subtasks at each node, we observe speedup on Faster nodes to be 1
.
075,
and speedup on Fastest nodes to be 8
010. These numbers reflect performance on
homogeneous clusters of Baseline, Faster, and Fastest nodes when running matrix
multiplication.
This section describes results of experiments on a cluster that includes a third
class of compute nodes, namely the 32-core Fastest nodes described in Sect.
4
.
Figure
8
shows results for an initial split of the matrix multiplication application
into 24 tasks (one per node), and for MARLA configured to split tasks into
eight subtasks at each node. Therefore, even the 32 node cluster uses 8 cores
at a time for each task. When we consider these results, we see two regions
that produce optimal run-times, namely
.
<
(19
,
1
.
0)
,
(65
,
1
.
075)
,
(16
,
8
.
010)
>
and
.
Application runtimes for both of these configurations approximate those for
the Faster homogeneous cluster configuration, which appears in the lower right
corner of Fig.
8
, with 100 % Faster nodes and 0 % Fastest nodes. Even for a coarse
grained task split of one task per node on a cluster configuration that does not
take full advantage of the Fastest nodes, run times improve.
<
(3
,
1
.
0)
,
(65
,
1
.
075)
,
(32
,
8
.
010)
>
Fig. 8.
This contour plot shows the effects of varying two kinds of nodes within a
cluster with respect to computation time. In this case, the effect of 24 tasks in a
24 node cluster that assumes 8 sub-tasks for each task. The X-axis shows the percentage
of the cluster that has been upgraded to Faster nodes, while the Y-axis shows the
percentage of the cluster that has been upgraded to Fastest nodes. Impossible points
have been interpolated. The solid lines indicate the trends in the data.
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