Optimal control of stochastic networks of $M/M/\infty$ queues with linear costs

We consider an arbitrary network of $M/M/\infty$ queues with controlled transitions between queues. We consider optimal control problems where the costs are linear functions of the state and inputs over a finite or infinite horizon. We provide in both cases an explicit characterization of the optimal control policies. We also show that these do not involve state feedback, but they depend on the network topology and system parameters. The results are also illustrated with various examples.