Flow Control , Routing , and Performance from Service Provider Viewpoint

We consider a game theoretic framework to analyze traffic in a congested network, where a profit-maximizing monopolist sets prices for different routes. Each link in the network is associated with a flow-dependent latency function which specifies the time needed to traverse the link given its congestion. Users have utility functions defined over the amount of data flow transmitted, the delays they incur in transmission, and the expenditure they make for using the bandwidth. Given the prices of the links, each user chooses the amount of flow to send and the routes to maximize the utility he receives. We define an equilibrium of user choices given the prices, show its existence and essential uniqueness, and characterize how this equilibrium changes in response to changes in prices. We then define a monopoly equilibrium (ME) as the equilibrium prices set by the monopolist and the corresponding user equilibrium, and characterize this equilibrium. We also study the performance of the ME relative to the user equilibrium at zero prices and the social optimum, which would result from the choice of a network planner with full information and full control over the flow and routing choices of users. Although equilibria for a given price vector or without prices are typically inefficient relative to the social optimum, we show that the ME achieves full efficiency for the routing problem (i.e., where each user has a fixed amount of data to transmit).