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

TL;DR

This paper develops a mean-field model for large-scale batch-processing systems to efficiently determine the optimal batch size for maximizing throughput, significantly reducing computation time compared to traditional methods.

Contribution

It introduces a mean-field approach that provides a closed-form solution for asymptotic throughput optimization in large systems, enabling rapid and accurate parameter tuning.

Findings

Mean-field model accurately predicts system throughput.

Optimal batch size can be computed in constant time.

Asymptotic solutions are effective in practical finite systems.

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.