Learning Optimal Admission Control in Partially Observable Queueing
  Networks
Jonatha Anselmi Bruno Gaujal Louis-Sébastien Rebuffi
We present an efficient reinforcement learning algorithm that learns the
optimal admission control policy in a partially observable queueing network.
Specifically, only the arrival and departure times from the network are
observable, and optimality refers to the average holding/rejection cost in
infinite horizon.
  While reinforcement learning in Partially Observable Markov Decision
Processes (POMDP) is prohibitively expensive in general, we show that our
algorithm has a regret that only depends sub-linearly on the maximal number of
jobs in the network, $S$. In particular, in contrast with existing regret
analyses, our regret bound does not depend on the diameter of the underlying
Markov Decision Process (MDP), which in most queueing systems is at least
exponential in $S$.
  The novelty of our approach is to leverage Norton's equivalent theorem for
closed product-form queueing networks and an efficient reinforcement learning
algorithm for MDPs with the structure of birth-and-death processes.