# Energy-Optimized Content Refreshing of Age-of-Information-Aware Edge Caches in IoT Systems
## 5 Performance Evaluation
We consider two cases: (i) in the first scenario, ten applications have request periods of the same order of magnitude, e.g., the applications have similar characteristics, and so all the request periods are randomly extracted from a uniform distribution between 1000 and 3000 s; (ii) in the second scenario, five applications have periods uniformly distributed between 50 and 100 s, while the remaining five have periods uniformly distributed between 5000 and 10,000 s, e.g., we consider two different classes of applications. In the first scenario, we consider \(\overline{\beta}=0.95\), in the second scenario we assume \(\overline{\beta}=1\). The optimizer computes the optimum values using \(\lambda\) as the sum of the inverses of the periods and chooses (i) \(w=2\) and \(s=238.1\) s for the first scenario and (ii) \(w=7\) and \(s=66.68\) s for the second scenario. Figure 12 shows the empirical CDFs and the CDFs obtained through the model for the two scenarios: we can notice that the empirical CDFs and the theoretical CDFs are very close to each other, so the optimum values of \(w\) and \(s\) obtained through the model can be applied also in this case. To assess the performance of the cache implemented by the proxy, we compare the case in which the proxy implements the cache against the case in which the proxy does not implement the cache. In the latter case, we consider \(s=AoI_{\alpha}/\alpha\), i.e., the maximum value of \(s\) that satisfies the AoI constraint. In Figure 13 we report the value of \(c_{\overline{\beta}}\) obtained for different types of devices both without the cache and with the cache. We can notice that the optimized cache can significantly reduce the energy cost of devices for which the cost of the transmissions is the prevalent cost because it can significantly reduce the number of transmissions, especially for high values of \(\lambda\). We can also notice that using the cache makes the system less sensitive to higher rates, as the number of exchanged messages depends on the refresh window. Figure 12: AoI CDF with 10 periodic servers: (**a**) first scenario, (**b**) second scenario. Then, we define the service delay as the time between a request sent by the application and the time its response is received. Figure 14 shows the cumulative distribution function of the service delay for \(\lambda=1/180\)s\({}^{-1}\) both for the case in which the proxy does not implement the cache and for the case wherein the proxy implements the cache. For the latter, we consider three values of \(\overline{\beta}\), namely \(\overline{\beta}=0.5\), \(\overline{\beta}=0.97\) and \(\overline{\beta}=1\). All the scenarios satisfy the same AoI requirements: \(AoI_{\kappa}=420\) s and \(\alpha=0.9\). Clearly, we can notice that the cache-enabled proxy always provides quicker responses with respect to the case in which the cache is not implemented, as some responses are taken from the cache, as shown by the CDFs. Indeed, the CDFs obtained with the cache show a bi-modal behavior: some responses are taken from the cache and hence have smaller service delays, while some responses are forwarded to the device and hence have larger service delays. Moreover, we can also notice that the case \(\overline{\beta}=1\) is the configuration that minimizes the service delay. Indeed, \(\overline{\beta}=1\) is the case in which the predominant energy cost is the transmission cost, so it minimizes the number of exchanged messages with the device and hence it is also the configuration that minimizes the service delay.