## 3 Model Validation
### Aggregate System Performance
#### 3.2.1 Synthetic (Vehicular) Mobility Model  
In Figure 7, we compare the model predictions with the simulation outcomes for offloading efficiency \(\epsilon\), average content latency \(\overline{W}\), and number of cached content copies, respectively, as a function of the global content request rate (\(\lambda_{0}\)) and sharing timeout (\(T_{s}\)) for a network with \(N=100\). The results presented in Figure 7a clearly illustrate that, in the considered scenario, the offloading efficiency notably increases with both \(T_{s}\) and \(\lambda_{0}\). In particular, a higher \(T_{s}\) increases content persistence, facilitating a more effective opportunistic diffusion. Similarly, a high \(\lambda_{0}\) means that the content requests are closer in time, which leads to an increase in the number of content copies in the network. Although this latter observation may appear counter-intuitive, it directly results from the fact that \(T_{s}>1/\lambda_{0}\). Indeed, the first nodes generating a content request will most likely receive it from the CDS because there are not sufficient copies of that content in the network. However, the initial set of content copies will quickly boost offloading efficiency. This intuition is confirmed later by plotting the time evolution \(\mathcal{I}(t)\), which rapidly increases after an initial transient phase and then remains constant for most of the system evolution. Finally, we observe that the accuracy of the model predictions increases with \(T_{s}\), but the model slightly overestimates offloading efficiency. This is explained by the fact that similar values of \(T_{s}\) and \(T_{c}\) lead to a more likely occurrence of border cases in which a content copy is discarded when a content timeout is about to expire. Figure 7b shows the content latency under the same conditions, mirroring the trends observed in Figure 7a: higher \(T_{s}\) and \(\lambda_{0}\) values result in lower content latency. This is explained by observing that the higher the offloading efficiency, the greater the probability of receiving content from a nearby node storing a copy of it before the expiration of \(T_{c}\). Interestingly, we can observe that the accuracy of our ODE model in predicting the content latency is very high in all the considered scenarios, even higher than that observed for the offloading efficiency. Figure 6: CCDF of the inter-any-contact time for the synthetic vehicular trace. Finally, Figure 7c illustrates the average number of content copies that are stored in the devices' local caches (also referred to as the number of infected nodes) before all users receive the requested content. It also shows a good agreement between the analytical model and the simulation results. Small model inaccuracies are observed for higher values of both \(\lambda_{0}\) and \(T_{s}\). Interestingly, even when the content request rate is as high as one request per second, the number of copies in the network is less than a quarter of the total number of nodes present. In Section 3.3, we conduct a detailed analysis of the behaviour of the number of infected nodes, demonstrating that the number of infected nodes undergoes a brief initial transient period of rapid growth, then stabilises, and finally experiences a period of rapid decrease. The second set of results aims to investigate the impact of node density on the system performance. In particular, we fix \(\lambda_{0}=0.5\) req/s and vary the number of mobile nodes in the range \([40,100]\). Clearly, the lower the node density, the higher the content request rate per node. Figure 8a, Figure 8b, and Figure 8c show the offloading efficiency, the content latency, and the number of content copies, respectively, for the same combination of \(T_{c}\) and \(T_{s}\) values used in the previous set of figures. The results confirm the accuracy of the proposed modelling approach, which improves for high \(T_{s}\) values.