Pricing Network Resources : A New Perspective

Abstract

The aim of the work is to examine the issue of pricing network resources so as to ensure fair and efficient resource-sharing among users. The basic question we address is: Do there exist simple pricing schemes such that fair and efficient resource-sharing is ensured, even though (i) individ-ual users are concerned with maximizing their own net benefits, and (ii) a user alternates between data-limited and infinite-data phases? The Internet provides congestion control through the Transport Control Protocol TCP). TCP congestion control is dependent on voluntary participation of cooperative end users. If everyone uses TCP, congestion could be managed. However, it can be mathematically shown that it is economically more favorable for users to violate TCP rules. The published literature suggests pricing as a mechanism to control congestion. The context of operation is as follows. Each user is assumed to have a utility function which is a concave in-creasing function of the rate at which she sends data through the network. The problem is to find the vector of users' rates such that the sum of all users' utility functions is maximized, subject to resource capacity constraints. This constrained optimization problem can be solved in a central-ized manner if all the utility functions are known. In practice, however, the utility functions are not known and there is no central authority. In the literature this optimization problem has been decomposed into two sub-problems such that the knowledge of utility functions is not required. These problems are solved independently by the network and the users. It has been shown that at system optimum, the network computed vec-tor of rates and users’ choice of prices are in equilibrium and they also solve the system optimi-zation problem of maximizing sum of utilities of all users. But in all related work, the authors as-sume that users have infinite amount of data to sustain the system-optimal data rates indefinitely. In practice, however, users may run out of data at times. We propose a pricing scheme in which, under certain conditions, the following is possible. If some users run out of data, and hence are not able to inject traffic at their respective system op-timal data rates, it is possible for others with plenty of data to transmit above their system opti-mal rates. This allows efficient utilization of the resource at all times. Further, it is possible to compel users above optimal rates to back down when, at a later point of time, data-limited users are back with enough data. This ensures that fairness is maintained.