No abstract

In noncooperative networks users make control decisions that optimize their own performance measure. Focusing on routing, we devise two methodologies for architecting noncooperative networks, that improve the overall network performance. These methodologies are motivated by problem settings arising in the provisioning and the run time phases of the network. For either phase, Nash equilibria characterize the operating point of the network. The goal of the provisioning phase is to allocate link capacities that lead to systemwide e cient Nash equilibria. In general, the solution of such design problems is counterintuitive, since adding link capacity might lead to a degradation of user performance. We show that, for systems of parallel links, such paradoxes cannot occur and the optimal solution coincides with the solution in the single-user case. We derive some extensions to general network topologies. During the run time phase, a manager controls the routing of part of the network ow. The manager is aware of the noncooperative behavior of the users and makes its routing decisions based on this information while aiming at improving the overall system performance. We obtain necessary and su cient conditions for enforcing an equilibrium that coincides with the global systemwide optimum, and indicate that these conditions are met in many cases of interest.

The capacity allocation problem in a network that is to be shared by noncooperative users is considered. Each user decides independently upon its routing strategy so as to optimize its individual performance objective. The operating points of the network are the Nash equilibria of the underlying routing game. The network designer aims to allocate link capacities, so that the resulting Nash equilibria are efficient, according to some systemwide performance criterion. In general, the solution of such design problems is complex and at times counterintuitive, since adding link capacity might lead to degradation of user performance. For systems of parallel links, we show that such paradoxes do not occur and that the capacity allocation problem has a simple and intuitive optimal solution that coincides with the solution in the single-user case.

Abstract. The existence of Nash equilibria in noncooperative flow control in a general productform network shared by K users is investigated. The performance objective of each user is to maximize its average throughput subject to an upper bound on its average time-delay. Previous attempts to study existence of equilibria for this flow control model were not successful, partly because the time-delay constraints couple the strategy spaces of the individual users in a way that does not allow the application of standard equilibrmm existence theorems from the game theory literature.To overcome this difficulty, a more general approach to study the existence of Nash equilibria for decentralized control schemes is introduced. This approach is based on directly proving the existence of a fixed point of the best reply correspondence of the underlying game. For the investigated flow control model, the best reply correspondence is shown to be a function, implicitly defined by means of K interdependent linear programs. Employing an appropriate definition for continuity of the set of optimal solutions of parametrized linear programs, it is shown that, under appropriate conditions, the best reply function is continuous. Brouwer's theorem implies, then, that the best reply function has a fixed point.

In noncooperative networks users make control decisions that optimize their own performance measure. Focusing on routing, we devise two methodologies for architecting noncooperative networks, that improve the overall network performance. These methodologies are motivated by problem settings arising in the provisioning and the run time phases of the network. For either phase, Nash equilibria characterize the operating point of the network. The goal of the provisioning phase is to allocate link capacities that lead to systemwide e cient Nash equilibria. In general, the solution of such design problems is counterintuitive, since adding link capacity might lead to a degradation of user performance. We show that, for systems of parallel links, such paradoxes cannot occur and the optimal solution coincides with the solution in the single-user case. We derive some extensions to general network topologies. During the run time phase, a manager controls the routing of part of the network ow. The manager is aware of the noncooperative behavior of the users and makes its routing decisions based on this information while aiming at improving the overall system performance. We obtain necessary and su cient conditions for enforcing an equilibrium that coincides with the global systemwide optimum, and indicate that these conditions are met in many cases of interest.