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  1. We consider the problem of timely exchange of updates between a central station and a set of ground terminals V , via a mobile agent that traverses across the ground terminals along a mobility graph G = (V;E). We design the trajectory of the mobile agent to minimize peak and average age of information (AoI), two newly proposed metrics for measuring timeliness of information. We consider randomized trajectories, in which the mobile agent travels from terminal i to terminal j with probability Pi;j . For the information gathering problem, we show that a randomized trajectory is peak age optimal and factor-8H average age optimal, where H is the mixing time of the randomized trajectory on the mobility graph G. We also show that the average age minimization problem is NP-hard. For the information dissemination problem, we prove that the same randomized trajectory is factor-O(H) peak and average age optimal. Moreover, we propose an age-based trajectory, which utilizes information about current age at terminals, and show that it is factor-2 average age optimal in a symmetric setting. 
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  2. measuring information freshness. AoI measures the time that elapsed since the last received update was generated. We consider the problem of minimizing average and peak AoI in wireless networks under general interference constraints. When fresh information is always available for transmission, we show that a stationary scheduling policy is peak age optimal. We also prove that this policy achieves average age that is within a factor of two of the optimal average age. In the case where fresh information is not always available, and packet/information generation rate has to be controlled along with scheduling links for transmission, we prove an important separation principle: the optimal scheduling policy can be designed assuming fresh information, and independently, the packet generation rate control can be done by ignoring interference. Peak and average AoI for discrete time G/Ber/1 queue is analyzed for the first time, which may be of independent interest. 
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