Optimal Decentralized Flow Control of Markovian Queueing Networks with Multiple Controllers

Hsiao, M.-T.T. and A.A. Lazar, Optimal decentralized flow control of Markovian queueing networks with multiple controllers, Performance Evaluation 13 (1991) 181-204. A Markovian queueing network model is used to derive decentralized flow control mechanisms in computer communication networks with multiple controllers. Under the network optimization criterion, finding the optimal decentralized flow control that maximizes the average network throughput under an average network delay bound becomes a team decision problem. It is shown that the network optimization problem depends on the parameters of the network only through the conditional estimates of the total arrival and departure rates. Using linear programming, the network optimal control is demonstrated to be a set of window-type mechanisms. Under the user optimization criterion, each individual user maximizes its average throughput subject to a constraint on its average time delay. Finding the optimal decentralized flow control under the individual user's performance results in a multiple objective optimization problem and leads to a game theoretic formulation. Structural results which simplify the problem are presented. It is shown that the user optimization problem depends on the parameters of the network and the action of the other users only through the conditional estimate of the user service rate. The Nash equilibrium solution under the game theoretic formulation is demonstrated to be a set of window-type mechanisms. Finally, the class of decentralized flow control problems with Nash equilibrium solutions is characterized.