  This paper introduces a new theoretical framework for optimizing second-order
behaviors of wireless networks. Unlike existing techniques for network utility
maximization, which only consider first-order statistics, this framework models
every random process by its mean and temporal variance. The inclusion of
temporal variance makes this framework well-suited for modeling Markovian
fading wireless channels and emerging network performance metrics such as
age-of-information (AoI) and timely-throughput. Using this framework, we
sharply characterize the second-order capacity region of wireless access
networks. We also propose a simple scheduling policy and prove that it can
achieve every interior point in the second-order capacity region. To
demonstrate the utility of this framework, we apply it to an unsolved network
optimization problem where some clients wish to minimize AoI while others wish
to maximize timely-throughput. We show that this framework accurately
characterizes AoI and timely-throughput. Moreover, it leads to a tractable
scheduling policy that outperforms other existing work.
