Kar, Sounak ; Rehrmann, Robin ; Mukhopadhyay, Arpan ; Alt, Bastian ; Ciucu, Florin ; Koeppl, Heinz ; Binnig, Carsten ; Rizk, Amr (2020)
On the Throughput Optimization in Large-Scale Batch-Processing Systems.
38th International Symposium on Computer Performance, Modeling, Measurements and Evaluation (PERF 2020). virtual Conference (02.-06.11.2020)
Conference or Workshop Item

Abstract

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.

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