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On the Throughput Optimization in Large-scale Batch-processing Systems

Sounak Kar; Robin Rehrmann; Arpan Mukhopadhyay; Bastian Alt; Florin Ciucu; Heinz Koeppl; Carsten Binnig; Amr Rizk
In: Performance Evaluation, Vol. 144, Pages 0-10, Elsevier, 2020.


We analyze a data-processing system with $n$ clients producing jobs which are processed in textitbatches 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 $omegaleft(n^4right)$ 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 textitasymptotically optimal throughput in $O(1)$ time. Numerical settings from a large commercial system reveal that this asymptotic optimum is accurate in practical finite regimes.