Optimal Status Update for Age of Information Minimization with an Energy Harvesting Source (1706.05773v3)

Abstract: 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. We assume energy arrives randomly at the sensor according to a Poisson process, and each status update consumes one unit of energy. 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, i.e., the status update epochs form a renewal process, and the length of each renewal interval depends on the first energy arrival over that interval only. We then focus on a renewal interval, and prove that if the AoI in the system is below a threshold when the first energy arrives, the sensor should store the energy and hold status update until the AoI reaches the threshold, otherwise, it updates the status immediately. We analytically characterize the long-term average AoI under such a threshold-based policy, and explicitly identify the optimal threshold.

• The paper’s main contribution is the development of three status update policies that minimize AoI in energy harvesting systems across different battery scenarios.
• It introduces a uniform update policy for infinite battery capacity and an adaptive strategy for finite batteries to uphold energy causality while approaching the AoI lower bound.
• A threshold-based policy for unit battery capacity achieves an optimal AoI near 0.9012, with simulations confirming robustness under non-Poisson energy arrivals.

Optimal Status Update for Age of Information Minimization with an Energy Harvesting Source

The paper investigates the problem of optimizing Age of Information (AoI) in a setting where an energy harvesting sensor transmits time-stamped status updates to a destination. AoI is a critical metric for evaluating the timeliness of information in network systems. The challenge of minimizing AoI is particularly significant in scenarios involving energy harvesting (EH), where the energy resources are inherently variable and restricted.

The authors explore three specific battery capacity scenarios and focus on deriving optimal or near-optimal status update policies:

1. Infinite Battery Size: For systems with infinite battery capacity, the authors propose a best-effort uniform status update policy. The policy schedules updates at regular intervals, specifically once per unit time, addressing the AoI minimization without violating energy causality constraints. This policy is proven to achieve the minimum long-term average AoI of 0.5, providing an exact solution within this setup.
2. Finite Battery Size: For cases where the battery has finite capacity, the authors describe an energy-aware adaptive status update policy. This policy dynamically adjusts the inter-update duration inversely to the sensor’s energy level—employing longer update intervals for low energy levels and shorter ones for higher energy levels—to mitigate the effects of potential energy overflow and ensure feasibility of scheduled updates. The authors demonstrate that this policy is asymptotically optimal as battery capacity increases, approaching the lower bound of AoI achieved with infinite battery capacity.
3. Unit Battery Capacity: When considering the limiting case of a battery that can only store energy for one update (i.e., a unit capacity), the authors advance a distinct threshold-based policy that waits for the AoI to surpass a certain threshold before executing an update. This results from showing that for a specific threshold value (approximately 0.9012), the AoI can be minimized given the constraints.

The paper's theoretical developments are substantiated by rigorous stochastic analyses, ensuring that the policies indeed meet the specified goals under varying conditions. The policy structures—uniform, adaptive, and threshold-based—reflect strategic balancing between the freshness of the received data (minimal AoI) and the constraints of energy availability.

Numerical Results and Implications

The authors present simulation results that corroborate theoretical findings across the scenarios. Significantly, the adaptive status updating policy is shown to be effective even under non-Poisson energy arrival processes, indicating the policy's robustness. This facet suggests potential real-world applicability to a wider spectrum of systems beyond those modeled with Poisson processes, such as those influenced by Markov-based energy harvesting fluctuations.

The implications of this research are impactful:

• Practical Applications: This framework and its underlying strategies for AoI minimization can be crucial for designing sustainable IoT and sensor networks, potentially leading to improved operational efficiency in systems where data freshness is paramount.
• Theoretical Insights: The results also advance the theoretical understanding of AoI as it relates to energy harvesting systems, providing pathways for more refined models that take into account diverse error-prone channels or multi-hop network scenarios.

Future work could explore extensions to these policies in broader network configurations, incorporating more complex energy management strategies, multi-source extensions, or the exploration of AoI with newer performance metrics in mind. This would further consolidate the understanding and practical application of AoI optimization in energy harvesting contexts.