Optimal Control of Multiclass Fluid Queueing Networks: A Machine Learning Approach

We propose a machine learning approach to the optimal control of multiclass fluid queueing networks (MFQNETs) that provides explicit and insightful control policies. We prove that a piecewise constant optimal policy exists for MFQNET control problems, with segments separated by hyperplanes passing through the origin. We use Optimal Classification Trees with hyperplane splits (OCT-H) to learn an optimal control policy for MFQNETs. We use numerical solutions of MFQNET control problems as a training set and apply OCT-H to learn explicit control policies. Furthermore, we show that both the theoretical results and the proposed algorithm extend to robust MFQNETs with uncertain service and arrival rates. We report experimental results with up to 33 servers and 99 classes that demonstrate that the learned policies achieve 100% accuracy on the test set. While the offline training of OCT-H can take days in large networks, the online application takes milliseconds.