The marginal user principle for resource allocation in wireless networks

We consider the problem of resource allocation in a wireless network operated by a single service provider. The motivating model is the downlink in a cellular network where the provider sets the price of entry into the wireless network and then allocates power levels (and transmission rates) to the participating users as a function of the users' channel conditions according to a pre-specified policy. The provider's goal is to design the power allocation policy that maximizes its revenue, recognizing the effects of his decisions on the choice of users to join the network. We show that the power allocation policy chosen by the service provider satisfies the following marginal user principle: the network allocates power levels such that the utility of the marginal user, who is indifferent to joining the network or not, is maximized. While the motivation is drawn from power allocation, the marginal user principle also generalizes to other resource allocation problems.