Flow control, Pricing, and Performance under Monopoly Pricing
A fundamental problem in communication networks is the management of congestion
to ensure timely and reliable transmission of information. The traditional
approach is to use optimization methods to achieve the best potential network
performance by adjusting the input flow rates of users and routing the resulting
traffic. However, in many scenarios, it is impossible or impractical to regulate
the traffic in such a centralized manner. Moreover, this approach requires
considerable knowledge about the preferences of all the users in the network,
an increasingly unrealistic assumption in today's large-scale communication
networks.
The recognition of this problem has motivated a recent literature to consider
the selfish flow choice and routing behavior of users in the absence of central
planning. This literature, however, considers mostly situations in which
there are no costs of sending information. In contrast, most networks in
practice are for-profit entities that charge prices for transmission of information.
In this talk, we present a model to analyze traffic in a congested network
where a profit-maximizing service provider sets prices for different routes.
Our objective is twofold. First, we develop a tractable framework
both to analyze the sensitivity of the total flow of information and the
routing choices to prices, and determine the equilibrium of this system,
which we call the monopoly equilibrium (ME). Second, we use this model to
study the performance gap between the monopolized network and the social
optimum, which would be chosen by a network planner that has full information
about the network. In particular, we show that for certain classes of utility
functions (including the pure routing case, where each user has a fixed amount
of data that he or she wants to transmit), the
ME achieves the full-information social optimum despite the selfish behavior
of both users and the service provider. We also show that for general utility
functions, the worst performance of the ME is when the links have a constant
latency, i.e., latency of each link is independent of the congestion.