大规模批处理系统的吞吐量优化
On the Throughput Optimization in Large-Scale Batch-Processing Systems
摘要：
我们分析了一个数据处理系统与$n$客户端产生的作业，这些作业在\textit{batches}中由$m$并行服务器处理，系统的吞吐量严重依赖于批量大小和相应的子添加剂加速功能。在实践中，吞吐量优化依赖于对最佳批量的数值搜索，在现有的商业系统中，这一过程可能需要多天。在本文中，我们在一个封闭的路由网络的系统建模，一个标准的马尔可夫分析产生的最佳吞吐量在$ω\left(n^4\right)$时间。我们的主要贡献是一个平均场模型的制度，系统的大小是大的。我们表明，平均场模型有一个独特的，全球有吸引力的固定点，可以发现在封闭的形式，其特征在于作为批量大小的函数的系统的渐近吞吐量。使用该表达式，我们找到了$O(1)$时间内的\textit{asymptotically}最佳吞吐量。从一个大型商业系统的数值设置表明，这种渐近最优是准确的，在实际的有限制度。
英文摘要：
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 $ω\left(n^4\right)$ 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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