Optimal multistage hop-by-hop flow control policies: the multiple sources single destination case

Consideration is given to a flow-control problem involving a treelike network with multiple sources, multiple stages, and a single final destination. Nodes in the stages between the sources and the destination act both as receivers and transmitters. The flow of messages in the network is controlled by the allocation of time slots to the transmitters. The goal is to minimize the number of messages in the network. The authors formulate the problem as a Markovian decision process with an appropriate delayed information structure. They show that the global optimization problem can be decomposed into a set of local optimization problems. The authors also show that the optimal policies of the local problems obey certain structural properties similar to the ones derived in an earlier work of the authors (1988) that analyzes a single-stage network