Decomposition approximation of queueing-network control models with three structures

We devise a decomposition approximation method for a general branching queueing network with service-rate controls. The decomposition method, which reduces and simplifies computation routines considerably, results from the conditions for monotone optimal control policies in induction arguments. We first isolate each branch of connected queues as a subnetwork and then link the subnetworks through branching nodes to approximate the optimal control policies fo the global network. The numerical results for a wide class of cost models show that the approximated optimal policies from the decomposed problems are sufficiently close to the optimal policies of the global problem.