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 $G/G/c$).
Optimal Control of Multiclass Fluid Queueing Networks: A Machine Learning Approach
Sloan School of Management, Massachusetts Institute of Technology（麻省理工学院斯隆管理学院）；Operations Research Center, Massachusetts Institute of Technology（麻省理工学院运筹学中心）
A High-fidelity, Machine-learning Enhanced Queueing Network Simulation Model for Hospital Ultrasound Operations
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Shenzhen Research Institute of Big Data（深圳市大数据研究院）；Shanghai University of Finance and Economics（上海财经大学）；Fudan University（复旦大学）；Cornell University（康奈尔大学）；McGill University（麦吉尔大学）；Purdue University（普渡大学）；Luohu Hospital System（罗湖医院集团）
A Queueing-Theoretic Framework for Vehicle Dispatching in Dynamic Car-Hailing [technical report]
East China Normal University（华东师范大学）；The Hong Kong University of Science and Technology（香港科技大学）；The University of New South Wales（新南威尔士大学）；Sun Yat-sen University（中山大学）
Rotman school of management, University of Toronto（多伦多大学罗特曼管理学院）；Ariel University（阿里尔大学）；The Hebrew University Business School, Hebrew University（希伯来大学商学院）
The Catechol Benchmark: Time-series Solvent Selection Data for Few-shot Machine Learning
Department of Computing, Imperial College London（计算系，帝国理工学院伦敦分校）；Department of Chemistry, Imperial College London（化学系，帝国理工学院伦敦分校）；SOLVE Chemistry（SOLVE化学）
PETScML: Second-order solvers for training regression problems in Scientific Machine Learning
Extreme Computing Research Center, King Abdullah University of Science and Technology（阿卜杜拉国王科技大学极端计算研究中心）；Mathematical Institute, University of Oxford（牛津大学数学研究所）
