Optimal status updating with a finite-battery energy harvesting source

Abstract

We consider an energy harvesting source equipped with a finite battery, which needs to send timely status updates to a remote destination. The timeliness of status updates is measured by a non-decreasing penalty function of the Age of Information (AoI). The problem is to find a policy for generating updates that achieves the lowest possible time-average expected age penalty among all online policies. We prove that one optimal solution of this problem is a monotone threshold policy, which satisfies (i) each new update is sent out only when the age is higher than a threshold and (ii) the threshold is a non-increasing function of the instantaneous battery level. Let τB denote the optimal threshold corresponding to the full battery level B, and p(·) denote the age-penalty function, then we can show that p(τB) is equal to the optimum objective value, i.e., the minimum achievable timeaverage expected age penalty. These structural properties are used to develop an algorithm to compute the optimal thresholds. Our numerical analysis indicates that the improvement in average age with added battery capacity is largest at small battery sizes; specifically, more than half the total possible reduction in age is attained when battery storage increases from one transmission's worth of energy to two. This encourages further study of status update policies for sensors with small battery storage.Index Terms-Age of information; age-energy tradeoff; nonlinear age penalty, threshold policy; optimal threshold; energy harvesting; battery capacity. which implies :Now, consider the case when r = 0 and ℓ = B − 2 for (50):which implies:Suppose that the inequality below is true for j ≥ ℓ + 1:J α (0, j + 1) − J α (0, j + 2) ≤ J α (0, j) − J α (0, j + 1). (53)

Optimized Age of Information Tail for Ultra-Reliable Low-Latency Communications in Vehicular Networks

“…Fig. 9 shows that, when the arrival rate is less than 0.1 Mbps (0.5 Mbps) when K = 80 (20), the network experiences a higher average AoI. It also shows that increasing the arrival rate will lead to a better average AoI, up to a certain point (around 0.8 Mbps when K = 80 and 2 Mbps when K = 20), after which the average AoI starts increasing again.…”

Optimizing Information Freshness in a Multiple Access Channel With Heterogeneous Devices

“…In [22], an EH transmitter is assumed to encode a message into the timings of the status updates. The age-energy tradeoff is explored in [23], where a finite-battery source is charged intermittently by Poisson energy arrivals. The timeliness-distortion tradeoff of an EHpowered system is investigated in [24].…”

Effective age of information in real-time wireless feedback control systems

“…Moreover, there are other studies which consider AoI for source-to-destination link in specific scenarios [24][25][26][27][28][29][30]. For instance, the authors in [24] considered an energy harvesting source and optimized the AoI penalty in status update. In [26], the authors introduced the AoI into content update in a local cache, where they found that update rate in the cache is proportional to the square-root of items' popularity.…”