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

On the Throughput Optimization in Large-Scale Batch-Processing Systems