Title: Performance Limits of Solutions to Network Utility Maximization Problems,
Abstract: We study performance limits of solutions to utility maximization problems
(e.g., max-min problems) in wireless networks as a function of the power budget
$\bar{p}$ available to transmitters. Special focus is devoted to the utility
and the transmit energy efficiency (i.e., utility over transmit power) of the
solution. Briefly, we show tight bounds for the general class of network
utility optimization problems that can be solved by computing conditional
eigenvalues of standard interference mappings. The proposed bounds, which are
based on the concept of asymptotic functions, are simple to compute, provide us
with good estimates of the performance of networks for any value of $\bar{p}$
in many real-world applications, and enable us to determine points in which
networks move from a noise limited regime to an interference limited regime.
Furthermore, they also show that the utility and the transmit energy efficiency
scales as $\Theta(1)$ and $\Theta(1/\bar{p})$, respectively, as
$\bar{p}\to\infty$.