  With the rapid advance of information technology, network systems have become
increasingly complex and hence the underlying system dynamics are often unknown
or difficult to characterize. Finding a good network control policy is of
significant importance to achieve desirable network performance (e.g., high
throughput or low delay). In this work, we consider using model-based
reinforcement learning (RL) to learn the optimal control policy for queueing
networks so that the average job delay (or equivalently the average queue
backlog) is minimized. Traditional approaches in RL, however, cannot handle the
unbounded state spaces of the network control problem. To overcome this
difficulty, we propose a new algorithm, called Reinforcement Learning for
Queueing Networks (RL-QN), which applies model-based RL methods over a finite
subset of the state space, while applying a known stabilizing policy for the
rest of the states. We establish that the average queue backlog under RL-QN
with an appropriately constructed subset can be arbitrarily close to the
optimal result. We evaluate RL-QN in dynamic server allocation, routing and
switching problems. Simulation results show that RL-QN minimizes the average
queue backlog effectively.
