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.

翻译：本文采用机器学习方法预测单站点多服务台系统中顾客数量的稳态分布。我们考虑两种系统：第一种是包含c个同构服务台的系统，即$GI/GI/c$队列；第二种是包含两个异构服务台的双服务台系统，即$GI/GI_i/2$队列。我们针对这些排队模型训练神经网络，输入特征为前四阶到达间隔时间与服务时间的矩。实验表明，使用第五阶及更高阶矩并不能提升预测精度。与现有方法相比，在$GI/GI/c$队列的稳态分布及平均顾客数预测方面，我们的方法达到了当前最优水平。此外，我们是首个能够预测$GI/GI_i/2$队列中系统顾客数稳态分布的方法。通过全面的性能评估，我们验证了模型的准确性：在多数情况下，预测误差低于5%。最后，我们证明该方法具有极高的推理速度，可在零点几秒内并行完成5000次推理。