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50 % upgrades reflect similar runtimes for splits of one, two, and three tasks
per worker, with a small decrease in slope reflecting overhead. Similarly, all four
splits perform better at 75 % Faster and Homogeneous (100 %) Faster upgrade
levels, across all task split granularities, including 4 tasks per node. With the
finest grain split that we tested, performance on the intermediate (25 % and 50 %
upgrade levels) clusters closely matches performance on the 75 % upgrade level.
Thus, an application developer using a traditional coarse-grain split into
1 task per node would not benefit from any incremental upgrades of subsets of
cluster nodes. Only when the entire cluster contains Faster nodes does perfor-
mance increase. Splitting an application into too few tasks (even 2 or 3 per worker
node) similarly does not allow the application to benefit from partial upgrades.
Only when the application splits into 4 tasks per worker does the application
developer benefit from incremental cluster upgrades. Even then, only an upgrade
of the first and last 25 % of nodes improves performance. The upgrade of the first
25 % allows straggler mitigation strategies to become effective, and the upgrade
of the last 25 % helps reduce the appearance of stragglers by turning the cluster
homogeneous.
We plot Fig. 6 's data differently in Fig. 7 . The downward trend across results
within each of the four set of bars depicts the overhead associated with worker
nodes having to retrieve more work, rather than receiving one initial task. In the
two homogeneous clusters (the leftmost and rightmost sets of bars in Fig. 7 ), this
overhead does not pay dividends for any split granularities; the trend continues
Fig. 6. Average number of matrices processed per second; averaged results across all
eight problem sizes. The X-axis displays split granularity in terms of the number of
tasks into which the problem is split. Y-axis displays the number of 33 × 33 matrices
multiplied per second in units of ten thousand. The graph includes sets of bars for six
different cluster configurations.
 
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