# Energy-Optimized Content Refreshing of Age-of-Information-Aware Edge Caches in IoT Systems
## 2 Related Work  
Energy-efficient IoT solutions and IoT-network life span are the key challenges for enhanced smart cities, smart grids, smart transport systems, etc. [14]. So, energy management is a critical issue in designing IoT networks, since many IoT devices can rely only on limited battery power and it is often unfeasible to replace or recharge their batteries. Therefore, efficient energy management strategies should be implemented in IoT devices to prolong their lifetime; for example, in [15] [PERSON] et al. propose an energy-efficient routing protocol to enhance network lifespan, or in [16] [PERSON] et al. optimize energy utilization through an optimal cluster head selection. In general, IoT devices consume energy, especially in sensing the environment and processing the acquired data, and transmitting their updates. However, the energy management strategies must guarantee the freshness of data, which is typically quantified using the AoI metrics. For example, in [17] [PERSON] et al. devise a discrete-time Markov chain model to predict the values of AoI and the probability of packet drops in status update systems, investigating the effects of the arrival rates of the packets, the number of nodes, and the queue length of each node. In [18] [PERSON] et al. propose a discrete-time queueing model to derive the distributions of AoI and Peak AoI in multisource IoT-based status update systems under the assumption of Bernoulli information packet arrivals and a general discrete phase-type service time distribution across all the sources. So, several works studied the problem of designing an optimum sampling and updating policy for the device. For example, in [2], [PERSON] et al. designed an optimal status sampling and updating policy for an IoT device to minimize the AoI of the data at the destination, under an average energy cost constraint at the device. As another example, in [19] [PERSON] et al. face the problem of keeping the status updates of the sources as timely as possible to all their monitors; they consider the first-come-first-served queue policy and show the existence of an optimal rate at which a source should generate its updates. In [20], [PERSON] et al. investigated an optimal sampling policy that minimizes a long-term weighted sum-AoI. In [21], [PERSON] et al. proposed the Age of Information at Query (QAoI) measure to characterize the AoI available to the receiver when it needs it; they considered a sensor that needs to schedule transmissions over a link with limited availability and they maximize the freshness of the data at query time, considering that the sensor needs to limit the number of transmissions to prolong its lifetime. Since IoT devices use near-range technologies, they cannot communicate directly with applications usually deployed in the cloud: for this reason, IoT networks are typically accessed through gateways/proxies acting as intermediaries between IoT devices and IoT applications. So, these intermediary nodes can be leveraged to also provide better performance in terms of energy consumption. For this purpose, caching the data generated by the devices can be very effective because it can lower the power consumption, reducing the frequency of environmental sensing and the frequency of data transmissions. So, for example, in [22] [PERSON] et al. introduced the use of a cache for an IoT sensing service with energy harvesting. Indeed, since the IoT sensor has a limited and random energy supply, caching can help to reduce the number of requests sent to the sensor and, therefore, can lower its energy consumption. The cache is deployed at a gateway and its refreshing scheme is a timer threshold mechanism: a cached item has a timer and, if the timer is larger than the threshold, the cache assumes that the item is expired, activates the sensor, and obtains a fresh sensing result. In [23], [PERSON] et al.