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 time-average 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.
The problem in @cite_11 was extended to a continuous-time formulation with Poisson energy arrivals, finite energy storage (battery) capacity, and random packet errors in the channel in @cite_21 . An age-optimal threshold policy was proposed for the unit battery case, and the achievable AoI for arbitrary battery size was bounded for a channel with a constant packet erasure probability. The concurrent study in @cite_1 , limited to the special cases of unit battery capacity and infinite battery capacity computed the same threshold-type policies under these assumptions. These special cases were investigated also for noisy channels with a constant packet erasure probability in @cite_37 @cite_16 . The case for a battery with 2-units capacity was studied in @cite_29 and the optimal policies for this case characterized as threshold-type policies similar to the optimal policy for unit battery capacity introduced in @cite_21 and @cite_1 . Optimal policies for arbitrary battery sizes were characterized via Lagrangian approach in @cite_25 and using optimal stopping theory in @cite_20 .
@cite_37 @cite_29 @cite_21 @cite_1 @cite_16 @cite_25 @cite_20 @cite_11
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In this paper, we consider a status monitoring system where an energy harvesting sensor continuously sends time-stamped status updates to a destination. With a non-zero probability, each update will be corrupted by noise and result in an updating failure. The destination keeps track of the system status through the successfully delivered updates. We assume that there is a perfect feedback channel between the destination and the source, so that the source is aware of the updating failures once they occur. With the feedback information, our objective is to design the optimal online status updating policy to minimize the expected long-term average Age of Information (AoI) at the destination, subject to the energy causality constraint at the sensor. We propose a status updating policy called Best-effort Uniform updating with Retransmission (BUR), under which the source tries to equalize the delay between two successful updates as much as possible, and retransmits an update immediately if the previous transmission fails. We show that the BUR policy achieves the minimum expected long-term average AoI among a broad class of online policies. A sensor node that is sending measurement updates regarding some physical phenomenon to a destination is considered. The sensor relies on energy harvested from nature to transmit its updates, and is equipped with a finite @math -sized battery to save its harvested energy. Energy recharges the battery incrementally in units, according to a Poisson process, and one update consumes one energy unit to reach the destination. The setting is online, where the energy arrival times are revealed causally after the energy is harvested. The goal is to update the destination in a timely manner, namely, such that the long term average age of information is minimized, subject to energy causality constraints. The age of information at a given time is defined as the time spent since the latest update has reached the destination. It is shown that the optimal update policy follows a renewal structure, where the inter-update times are independent, and the time durations between any two consecutive events of submitting an update and having @math units of energy remaining in the battery are independent and identically distributed for a given @math . The optimal renewal policy for the case of @math energy units is explicitly characterized, and it is shown that it has an energy-dependent threshold structure, where the sensor updates only if the age grows above a certain threshold that is a function of the amount of energy in its battery. Age of Information is a measure of the freshness of status updates in monitoring applications and update-based systems. We study a real-time sensing scenario with a sensor which is restricted by time-varying energy constraints and battery limitations. The sensor sends updates over a packet erasure channel with no feedback. The problem of finding an age-optimal threshold policy, with the transmission threshold being a function of the energy state and the estimated current age, is formulated. The average age is analyzed for the unit battery scenario under a memoryless energy arrival process. Somewhat surprisingly, for any finite arrival rate of energy, there is a positive age threshold for transmission, which corresponding to transmitting at a rate lower than that dictated by the rate of energy arrivals. A lower bound on the average age is obtained for general battery size. In this paper, we consider a scenario where an energy harvesting sensor continuously monitors a system and sends time-stamped status updates to a destination. The destination keeps track of the system status through the received updates. We use the metric Age of Information (AoI), the time that has elapsed since the last received update was generated, to measure the “freshness” of the status information available at the destination. Our objective is to design optimal online status update policies to minimize the long-term average AoI, subject to the energy causality constraint at the sensor. We consider three scenarios, i.e., the battery size is infinite, finite, and one unit only, respectively. For the infinite battery scenario, we adopt a best-effort uniform status update policy and show that it minimizes the long-term average AoI. For the finite battery scenario, we adopt an energy-aware adaptive status update policy, and prove that it is asymptotically optimal when the battery size goes to infinity. For the last scenario where the battery size is one, we first show that within a broadly defined class of online policies, the optimal policy should have a renewal structure. We then focus on a renewal interval, and prove that the optimal policy should have a threshold structure, i.e., if the AoI in the system is below a threshold when an energy arrival enters an empty battery, the sensor should store the energy first and then update when the AoI reaches the threshold; otherwise, it updates the status immediately. Simulation results corroborate the theoretical bounds. An energy-harvesting sensor node that is sending status updates to a destination is considered. The sensor is equipped with a battery of finite size to save its incoming energy, and consumes one unit of energy per status update transmission, which is delivered to the destination instantly over an error-free channel. The setting is online in which the harvested energy is revealed to the sensor causally over time, and the goal is to design status update transmission policy such that the long term average age of information (AoI) is minimized. AoI is defined as the time elapsed since the latest update has reached at the destination. Two energy arrival models are considered: a random battery recharge (RBR) model, and an incremental battery recharge (IBR) model. In both models, energy arrives according to a Poisson process with unit rate, with values that completely fill up the battery in the RBR model, and with values that fill up the battery incrementally, unit-by-unit, in the IBR model. The key approach to characterizing the optimal status update policy for both models is showing the optimality of renewal policies, in which the inter-update times follow a specific renewal process that depends on the energy arrival model and the battery size. It is then shown that the optimal renewal policy has an energy-dependent threshold structure, in which the sensor sends a status update only if the AoI grows above a certain threshold that depends on the energy available. For both the RBR and the IBR models, the optimal energy-dependent thresholds are characterized explicitly, i.e., in closed-form, in terms of the optimal long term average AoI. It is also shown that the optimal thresholds are monotonically decreasing in the energy available in the battery, and that the smallest threshold, which comes in effect when the battery is full, is equal to the optimal long term average AoI. We study the problem of minimizing the time-average expected Age of Information for status updates sent by an energy-harvesting source with a finite-capacity battery. In prior literature, optimal policies were observed to have a threshold structure under Poisson energy arrivals, for the special case of a unit-capacity battery. In this paper, we generalize this result to any (integer) battery capacity, and explicitly characterize the threshold structure. We provide the expressions relating the threshold values on the age to the average age. One of these results, that we derive from these expressions, is the unexpected equivalence of the minimum average AoI and the optimal threshold for the highest energy state. We consider managing the freshness of status updates sent from a source (such as a sensor) to a monitoring node. The time-varying availability of energy at the sender limits the rate of update packet transmissions. At any time, the age of information is defined as the amount of time since the most recent update was successfully received. An offline solution that minimizes not only the time average age, but also the peak age for an arbitrary energy replenishment profile is derived. The related decision problem under stochastic energy arrivals at the sender is studied through a discrete time dynamic programming formulation, and the structure of the optimal policy that minimizes the expected age is shown. It is found that tracking the expected value of the current age (which is a linear operation), together with the knowledge of the current energy level at the sender side is sufficient for generating an optimal threshold policy. An effective online heuristic, Balance Updating (BU), that achieves performance close to an omniscient (offline) policy is proposed. Simulations of the policies indicate that they can significantly improve the age over greedy approaches. An extension of the formulation to stochastically formed updates is considered.