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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. 

This paper studies a remote sensing system where multiple wireless sensors generate possibly noisy information updates of various surveillance fields and delivering these updates to a control center over a wireless network. The control center needs a sufficient number of recently generated information updates to have an accurate estimate of the current system status, which is critical for the control center to make appropriate control decisions. The goal of this work is then to design the optimal policy for scheduling the transmissions of information updates. Through Brownian approximation, we demonstrate that the control center’s ability to make accurate real-time estimates depends on the averages and temporal variances of the delivery processes. We then formulate a constrained optimization problem to find the optimal means and variances. We also develop a simple online scheduling policy that employs the optimal means and variances to achieve the optimal system-wide performance. Simulation results show that our scheduling policy enjoys fast convergence speed and better performance when compared to other state-of-the-art policies. 

This paper considers a wireless network where multiple flows are delivering status updates about their respective information sources. An end user aims to make accurate real-time estimations about the status of each information source using its received packets. As the accuracy of estimation is most impacted by events in the recent past, we propose to measure the credibility of an information flow by the number of timely deliveries in a window of the recent past, and say that a flow suffers from a loss-of-credibility (LoC) if this number is insufficient for the end user to make an accurate estimation. We then study the problem of minimizing the system-wide LoC in wireless networks where each flow has different requirement and link quality. We show that the problem of minimizing the system-wide LoC requires the control of temporal variance of timely deliveries for each flow. This feature makes our problem significantly different from other optimization problems that only involves the average of control variables. Surprisingly, we show that there exists a simple online scheduling algorithm that is near-optimal. Simulation results show that our proposed algorithm is significantly better than other state-of-the-art policies.