ADAPTIVE DECENTRALIZED CONTROL UNDER NONUNIQUENESS OF THE OPTIMAL-CONTROL

We study the problem of decentralization of flow control in packet-swi tching networks under the isarithmic scheme. An incoming packet enters the network only if there are permits available at the entry port whe n it arrives. The actions of the controllers refer to the routing of p ermits in the network and the control variables are the corresponding probabilities. We study the behavior of adaptive algorithms implemente d at the controllers to update these probabilities and seek optimal pe rformance. This problem can be stated as a routing problem in a closed queueing network. The centralized version of a learning automaton is a general framework presented along with the proof of asymptotic optim ality. Decentralization of the controller gives rise to non-uniqueness of the optimal control parameters. Non-uniqueness can be exploited to construct asymptotically optimal learning algorithms that exhibit dif ferent behavior. We implement two different algorithms for the paralle l operation and discuss their differences. Convergence is established using the weak convergence methodology. In addition to our theoretical results, we illustrate the main results using the flow control proble m as a model example and verify the predicted behavior of the two prop osed algorithms through computer simulations, including an example of tracking.