## 5 Simulation Results and Performance Evaluation
### Simulations Results and Discussion  
The system performance is evaluated by the trade-off relationship between the total user interest and transmission delay. First of all, Figure 6 compares the performance between our proposed algorithm and two standard meta heuristic algorithms: the simulated annealing (SA) and genetic algorithm (GA) [47; 48]. The simulated annealing algorithm can find a high-quality solution that does not strongly depend on the choice of the initial solution. It has been theoretically proved to converge to the optimum solution as long as the cooling process is slow enough [49]. On the other hand, the basic rationale of the genetic algorithm is to maintain a population of solutions to the problem and select the next generation solution according to the principle of survival of the fittest. The specific steps for SA and GA could be found in [50]. The simulation settings used in our paper for SA and GA are summarized in Table 2. It is shown in Figure 6 that our proposed algorithm outperforms the SA and GA algorithms, especially when the transmission delay is small. In addition, for comparison purposes, we also show the performance of the traditional content delivery protocol based on, e.g., the \"pull-type\" http protocol. Because the traditional protocol does not include the \"user-in-the-loop\" procedure, it yields a static performance regardless of the delay \begin{table}
\begin{tabular}{l l} \hline \hline
**Simulation Parameter** & **Parameter Value** \\ \hline Number of users \(U\) & 10 \\ \hline Number of contents \(F\) & 500 \\ \hline Number of channels \(K\) & 256 \\ \hline Recommended form length \(N\) & 50 \\ \hline System bandwidth \(B\) & 10 MHz \\ \hline Noise power spectral density \(N_{0}\) & \(-\)174 dBm/Hz [45] \\ \hline Bit error rate BER & \(1\times 10^{-4}\)[46] \\ \hline Macrocell path loss model & 128.1 + 37.6 log\({}_{10}d\) (\(d\) in km) [45] \\ \hline Inter-site distance \(d\) & 330 m \\ \hline Channel gain \(\alpha_{nk}^{2}\) & Exponential distribution of parameter 1 \\ \hline File distribution \(L\) & Logarithmic normal distribution with location parameter of 9.357 and scale parameter of 1.318 [33] \\ \hline Interest matrix \(\mathbf{R}\) & Zipf distribution with parameter 1 [38]; Truncated Gaussian distribution between 1 and 5 with a mean of 3 and a variance of 2 [40]. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. constraint. The static performance, shown as a single star sign in Figure 6, represents the case where the transmission delay is relaxed to an extreme to obtain the highest user interest. The above comparisons show that our heuristic algorithm not only offers greater trade-off flexibility than traditional protocols, but also outperforms standard meta-heuristic algorithms in solving the complicated NP-hard problem. Figure 7 investigates the impact of arrival rate \(\lambda\) on the system performance. The arrival rate represents the probability for a user to request a file from the central server at a time slot. It can be observed in Figure 7 that a lower arrival rate leads to a higher user interest. This is because a lower arrival rate means less competition for the limited radio resource, so that each user can be allocated with a higher capacity. It is interesting to see that a four times increase on the arrival rate (from 0.2 to 0.8) only causes less than 15% percent of reduction on the total interest. This means our system is robust to traffic congestion, such that it can cope well with increasing traffic demand per user or increasing number of users. We note that such a robustness essentially comes from our joint content recommendation and delivery design: when the per user capacity is reduced, content recommendation can choose to recommend small-size files with high user interests, so that the traffic demand can be effectively reduced while maintaining a high user interest level.