Decentralized dynamic routing as a Markov chain optimization problem

The routing of customers in a network of queues (e.g., packets in a communication network) is considered as a decentralized (team) control problem. By a suitable information exchange among the network nodes, a partially nested information structure with a common past is obtained, which allows the existence of a sufficient statistic and the exploitation of a non-classical dynamic programming decomposition. Based on these, an infinite horizon optimization problem can be defined, and some existing results in the centralized control of Markov chains can be extended in order to seek stationary decentralized strategies. Some implications arising in this respect, due to the peculiar nature of the sufficient statistic, are discussed.