Scheduling the transmission of status updates over an error-prone communication channel is studied in order to minimize the long-term average age of information (AoI) at the destination under a constraint on the average number of transmissions at the source node. After each transmission, the source receives an instantaneous ACK NACK feedback, and decides on the next update without prior knowledge on the success of future transmissions. First, the optimal scheduling policy is studied under different feedback mechanisms when the channel statistics are known; in particular, the standard automatic repeat request (ARQ) and hybrid ARQ (HARQ) protocols are considered. Then, for an unknown environment, an average-cost reinforcement learning (RL) algorithm is proposed that learns the system parameters and the transmission policy in real time. The effectiveness of the proposed methods are verified through numerical simulations.
Most of the earlier work on AoI consider queue-based models, in which the status updates arrive at the source node randomly following a memoryless Poisson process, and are stored in a buffer before being transmitted to the destination @cite_23 @cite_9 . Instead, in the so-called model, @cite_0 @cite_27 @cite_10 @cite_24 @cite_17 , also adopted in this paper, the status of the underlying process can be sampled at any time by the source node.
@cite_9 @cite_0 @cite_24 @cite_27 @cite_23 @cite_10 @cite_17
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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. 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. 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. The Age-of-Information (AoI) has recently been proposed as an important metric for investigating the timeliness performance in information-update systems. Prior studies on AoI optimization often consider a Push model, which is concerned about when and how to "push" (i.e., generate and transmit) the updated information to the user. In stark contrast, in this paper we introduce a new Pull model, which is more relevant for certain applications (such as the real-time stock quotes service), where a user sends requests to the servers to proactively "pull" the information of interest. Moreover, we propose to employ request replication to reduce the AoI. Interestingly, we find that under this new Pull model, replication schemes capture a novel tradeoff between different levels of information freshness and different response times across the servers, which can be exploited to minimize the expected AoI at the user's side. Specifically, assuming Poisson updating process at the servers and exponentially distributed response time, we derive a closed-form formula for computing the expected AoI and obtain the optimal number of responses to wait for to minimize the expected AoI. Finally, we conduct numerical simulations to elucidate our theoretical results. Our findings show that waiting for more than one response can significantly reduce the AoI in most scenarios.