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This paper introduces a new theoretical framework for optimizing second-orderbehaviors of wireless networks. Unlike existing techniques for network utilitymaximization, which only considers first-order statistics, this frameworkmodels every random process by its mean and temporal variance. The inclusion oftemporal variance makes this framework well-suited for modeling stateful fadingwireless channels and emerging network performance metrics such asage-of-information (AoI). Using this framework, we sharply characterize thesecond-order capacity region of wireless access networks. We also propose asimple scheduling policy and prove that it can achieve every interior point inthe second-order capacity region. To demonstrate the utility of this framework,we apply it for an important open problem: the optimization of AoI overGilbert-Elliott channels. We show that this framework provides a very accuratecharacterization of AoI. Moreover, it leads to a tractable scheduling policythat outperforms other existing work.

A Theory of Second-Order Wireless Network Optimization and Its Application on AoI