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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. 

In this study, we investigate a context-aware status updating system consisting of multiple sensor-estimator pairs. A centralized monitor pulls status updates from multiple sensors that are monitoring several safety-critical situations (e.g., carbon monoxide density in forest fire detection, machine safety in industrial automation, and road safety). Based on the received sensor updates, multiple estimators determine the current safety-critical situations. Due to transmission errors and limited communication resources, the sensor updates may not be timely, resulting in the possibility of misunderstanding the current situation. In particular, if a dangerous situation is misinterpreted as safe, the safety risk is high. In this paper, we introduce a novel framework that quantifies the penalty due to the unawareness of a potentially dangerous situation. This situation-unaware penalty function depends on two key factors: the Age of Information (AoI) and the observed signal value. For optimal estimators, we provide an information-theoretic bound of the penalty function that evaluates the fundamental performance limit of the system. To minimize the penalty, we study a pull-based multi-sensor, multi-channel transmission scheduling problem. Our analysis reveals that for optimal estimators, it is always beneficial to keep the channels busy. Due to communication resource constraints, the scheduling problem can be modelled as a Restless Multi-armed Bandit (RMAB) problem. By utilizing relaxation and Lagrangian decomposition of the RMAB, we provide a low-complexity scheduling algorithm which is asymptotically optimal. Our results hold for both reliable and unreliable channels. Numerical evidence shows that our scheduling policy can achieve up to 100 times performance gain over periodic updating and up to 10 times over randomized policy.