  We analyze a data-processing system with $n$ clients producing jobs which are
processed in \textit{batches} by $m$ parallel servers; the system throughput
critically depends on the batch size and a corresponding sub-additive speedup
function. In practice, throughput optimization relies on numerical searches for
the optimal batch size, a process that can take up to multiple days in existing
commercial systems. In this paper, we model the system in terms of a closed
queueing network; a standard Markovian analysis yields the optimal throughput
in $\omega\left(n^4\right)$ time. Our main contribution is a mean-field model
of the system for the regime where the system size is large. We show that the
mean-field model has a unique, globally attractive stationary point which can
be found in closed form and which characterizes the asymptotic throughput of
the system as a function of the batch size. Using this expression we find the
\textit{asymptotically} optimal throughput in $O(1)$ time. Numerical settings
from a large commercial system reveal that this asymptotic optimum is accurate
in practical finite regimes.
