Optimal Control of Multiclass Fluid Queueing Networks: A Machine
  Learning Approach
Dimitris Bertsimas Cheol Woo Kim
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 threshold type optimal policy exists for MFQNET
control problems, where the threshold curves are 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. 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.