Flow Control , Routing , and Performance with a For - profit Service Provider

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 according to the notion of Wardrop equilibrium. We define a monopoly equilibrium (ME) as the equilibrium prices set by the monopolist and the corresponding Wardrop equilibrium. We use this framework to study the performance of the ME relative to the Wardrop equilibrium without 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. We illustrate that ME can improve the performance over the Wardrop equilibrium without prices because the monopolist internalizes the effects of increased congestion on different paths due to lack of coordination among users. We next consider a model for the routing problem, where each user has a fixed amount of data to transmit, under monopoly pricing. Despite nonconvexities in the model, we show that there exists a Wardrop equilibrium under profit-maximizing prices and that the ME always achieves the social optimum.