论文标题
机器可以解决一般排队系统吗？
Can machines solve general queueing systems?
论文作者
论文摘要
在本文中，我们分析了机器能够解决排队理论中的一般问题。为了回答这个问题，我们使用深度学习模型来预测$ m/g/1 $ queue的固定队列长度分布（泊松到达，一般服务时间，一台服务器）。据我们所知，这是机器学习模型首次应用于一般排队理论问题。我们选择了本文的$ m/g/1 $队列，因为它位于分析边界的“尖端”：一方面，该模型的精确解决方案可以使用，这在计算和数学上都是复杂的。另一方面，问题（特别是服务时间分布）是一般的。这使我们能够比较分析解决方案的深度学习方法的准确性和效率。 将机器学习应用于此问题的两个关键挑战是（1）生成各种培训示例，这些培训示例可很好地表示“通用”正值分布，以及（2）服务时间连续分配作为输入的表示。我们展示了如何克服这些挑战。 我们的结果表明，我们的模型确实能够非常准确地预测$ m/g/1 $队列的固定行为：在整个测试集中，我们的度量的平均值为$ 0.0009 $。此外，我们的机器学习模型非常有效，在一秒钟的一小部分中计算非常准确的固定分布（基于仿真建模的方法将需要更长的时间才能收敛）。我们还提出了一个模仿现实生活环境的案例研究，并表明我们的方法更强大，并且与现有方法相比提供了更准确的解决方案。这表明了将我们的方法扩展到可解决的系统（例如$ g/g/g/1 $或$ g/g/c $）之外的希望。
In this paper, we analyze how well a machine can solve a general problem in queueing theory. To answer this question, we use a deep learning model to predict the stationary queue-length distribution of an $M/G/1$ queue (Poisson arrivals, general service times, one server). To the best of our knowledge, this is the first time a machine learning model is applied to a general queueing theory problem. We chose $M/G/1$ queue for this paper because it lies "on the cusp" of the analytical frontier: on the one hand exact solution for this model is available, which is both computationally and mathematically complex. On the other hand, the problem (specifically the service time distribution) is general. This allows us to compare the accuracy and efficiency of the deep learning approach to the analytical solutions. The two key challenges in applying machine learning to this problem are (1) generating a diverse set of training examples that provide a good representation of a "generic" positive-valued distribution, and (2) representations of the continuous distribution of service times as an input. We show how we overcome these challenges. Our results show that our model is indeed able to predict the stationary behavior of the $M/G/1$ queue extremely accurately: the average value of our metric over the entire test set is $0.0009$. Moreover, our machine learning model is very efficient, computing very accurate stationary distributions in a fraction of a second (an approach based on simulation modeling would take much longer to converge). We also present a case-study that mimics a real-life setting and shows that our approach is more robust and provides more accurate solutions compared to the existing methods. This shows the promise of extending our approach beyond the analytically solvable systems (e.g., $G/G/1$ or $G/G/c$).
