## 4 Performance Comparison with Benchmarks  
A model is justified not only by its ability to replicate the behaviour of the system it represents but, more importantly, by its capacity to provide actionable insights that can improve protocol performance. In this section, we demonstrate how the model can be applied to optimally tune key protocol parameters of OORS. Through this analysis, we aim to show that the proposed model serves as a practical tool for both understanding and improving protocol performance in realistic scenarios. To this end, we also compare the performance of the optimally tuned OORS scheme with Push-and-track [6] and SNSNI [15], two state-of-the-art data offloading schemes that ensure guaranteed delays but rely on unlimited caching. The main difference between PAT and SNSNI is that the former randomly selects the initial set of seed nodes, while the latter leverages a node influence metric. We also point out that the goal of this performance comparison is not to show that OORS outperforms Push-and-track (PAT) or SNSNI in terms of offloading efficiency, but to show that a mobile data offloading scheme with time-limited caches, if optimally configured, can approximate the offloading efficiency of a mobile data offloading scheme with unlimited caching while using fewer resources. First, we investigate the impact of the weight parameters \(\alpha_{1}\), \(\alpha_{2}\), and \(\alpha_{3}\) on the optimisation problem **P** for determining the optimal \(T_{s}\) value. To this end, we compute (17) across the three scenarios outlined in Table 3 for the synthetic mobility model, considering different node densities. Setting \(A\) models the scenario where offloading efficiency, content latency, and memory usage are assigned equal weights. The other two scenarios model cases in which either offloading efficiency or content latency is considered for the optimisation process. In Figure 14, we illustrate the utility function \(U(T_{s})\) across some values of \(N\). The graphs clearly show that \(U(T_{s})\) exhibits a different behaviour before and after \(T_{s}^{*}\), the solution of the optimisation problem **P**. In particular, the utility function rapidly increases with \(T_{s}\) for \(0\leq T_{s}\leq T_{s}^{*}\), and then slowly decreases for \(T_{s}>T_{s}^{*}\). Notably, settings \(B\) and \(C\) lead to very similar utility functions. This result can be explained by considering that the utilities associated with offloading efficiency and content lat  
Figure 13: Real-world mobility model: time evolution of the number of copies with \(T_{c}=2\) min, \(T_{s}=20\) min, and \(\lambda_{0}=0.5\) req/min. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Setting** & \(\mathbf{\kappa_{1}}\) & \(\mathbf{\kappa_{2}}\) & \(\mathbf{\kappa_{3}}\) \\ \hline \(A\) & \(1/3\) & \(1/3\) & \(1/3\) \\ \(B\) & \(1/2\) & \(0\) & \(1/2\) \\ \(C\) & \(0\) & \(1/2\) & \(1/2\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Settings for the weight parameters in the optimisation problem **P**. To emphasise the importance of determining the optimal \(T_{s}\) value, in Figure 15 we plot the utility value versus the number of nodes in the network across three scenarios: (i) the \(T_{s}\) value is dynamically adjusted based on the network size and set equal to \(T_{s}^{*}\); (ii) \(T_{s}=20\) s, independently of \(N\); and (iii) \(T_{s}=80\) s, independently of \(N\). The results suggest that, from a utility perspective, a short \(T_{s}\) value is preferable in sparse networks (small \(N\)), while a long \(T_{s}\) is preferable in dense networks (large \(N\)). However, only \(T_{s}^{*}\) consistently delivers the highest utility across all conditions. In the following, we compare the performance of the optimally tuned OORS and Push-and-track in terms of utility and total number of cached content copies versus traffic intensity, for both the synthetic and real-world mobility models. We consider setting \(B\), as we have previously shown that settings \(B\) and \(C\) lead to very similar results.