用神经网络预测多服务器队列的客户分布，速度快且精度高。
Analyzing homogenous and heterogeneous multi-server queues via neural networks
- 输入前四阶到达与服务时间矩，训练神经网络预测稳态分布
- 在GI/GI/c队列中误差低于5%，优于现有方法
- 首次实现异构双服务器队列的稳态分布预测，推理极快
本文采用机器学习方法预测单站多服务器系统中客户数量的稳态分布。考虑两种系统：一是c个同质服务器（即GI/GI/c队列），二是两个异构服务器（即GI/GI_i/2队列）。我们利用前四阶到达和服 务时间矩训练神经网络，实证表明使用第五阶及更高阶矩无法提升精度。相较于现有方法，在GI/GI/c队列的稳态分布和平均客户数预测上达到当前最优。此外，我们是唯一能预测GI/GI_i/2队列中系统客户数稳态分布的方法。通过全面性能评估，验证模型准确性：多数情况下误差低于5%。最后，推理速度极快，可在不足一秒内并行完成5000次预测。
原文摘要 · Abstract (English)
In this paper, we use a machine learning approach to predict the stationary distributions of the number of customers in a single-staiton multi server system. We consider two systems, the first is $c$ homogeneous servers, namely the $GI/GI/c$ queue. The second is a two-heterogeneous server system, namely the $GI/GI_i/2$ queue. We train a neural network for these queueing models, using the first four inter-arrival and service time moments. We demonstrate empirically that using the fifth moment and beyond does not increase accuracy. Compared to existing methods, we show that in terms of the stationary distribution and the mean value of the number of customers in a $GI/GI/c$ queue, we are state-of-the-art. Further, we are the only ones to predict the stationary distribution of the number of customers in the system in a $GI/GI_i/2$ queue. We conduct a thorough performance evaluation to assert that our model is accurate. In most cases, we demonstrate that our error is less than 5\%. Finally, we show that making inferences is very fast, where 5000 inferences can be made in parallel within a fraction of a second.
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