## 6 Numerical Results
### Verification of the Analytical Model  
We verify the analytical model by comparing it with simulation results over the case studies whose parameters are reported in Table 2. We consider a network topology (similar to the one depicted in Figure 1) consisting of one MCEN, four metro nodes, 32 AMENs and 96 ANs distributed over four different access rings. VoD content requests originate uniformly from all 96 ANs with probabilities 0.5, 0.25 and 0.25 of choosing bit-rates of 3 Mbps, 6 Mbps or 12 Mbps, respectively. Consequently, the average bit-rate of all requests is 6 Mbps. We consider that all 32 AMENs, 16 AMENs or 8 AMENs host caches. Note that the number of AMENs which host caches differs from one case study to another. Moreover, note that if all AMENs are equipped with caches (\(n_{access}=32\)), the average hop-distance from the AMEN caches \(h_{access}\) is equal to 1, whereas if half of the AMENs are equipped with caches, (\(n_{access}=16\)), meaning that not all ANs are directly connected to an AMEN which hosts a cache, the average hop-distance \(h_{access}\) becomes equal to 1.5. Moreover, the average hop-distance from users to the MCEN, \(h_{metro}\), in this case is 4.5, whereas \(h_{server}\), the average hop-distance from users to the remote data center, is 8. To find the optimal storage distribution for each case study, we perform an extensive set of simulations considering all possible storage distributions for a given cache deployment. Specifically, in each simulation, we vary the number of items stored in caches deployed at AMENs, \(k\). \(k\) ranges from 0 (the case where all the storage capacity is utilized in the cache located at the MCEN), to the  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Case Study \#** & \(\mathbf{\alpha}\) & \(\mathbf{S_{a}}\) (GB) & **T** & \(AMENs\) & \(\mathbf{n_{access}}\) & \(\mathbf{h_{access}}\) \\ \hline
1 & 0.9 & 8 & 160,000 & 32 & 32 & 1 \\
2 & 1 & 6 & 120,000 & 32 & 16 & 1.5 \\
3 & 1.1 & 8 & 160,000 & 32 & 32 & 1 \\ \hline \maximum possible number of items to be stored in each of the AMEN caches \(\frac{T}{n_{access}\cdot S_{a}}\). We refer to these cache deployments as _Only MCEN_ and _Only AMENs_, respectively. Note that when a certain amount of storage capacity is deployed in caches of AMENs, only the remaining amount of the available storage capacity can be deployed in the cache located at the MCEN. We simulate the arrival of 500,000 VoD requests for each case; i.e., for each value of \(k\) considered. The VoD requests are Poisson-distributed. Specifically, we set an arrival rate guaranteeing negligible blocking probability to provide a fair comparative analysis between the different cache deployment strategies. Figure 4 shows \(RO_{avg}/req\) (i.e., the average resource occupation per VoD request) as a function of \(k\), for all the three case studies considered. Results show that \(RO_{avg}/req\) initially decreases as \(k\) increases (as more items being stored in the caches located at AMENs enables serving more requests from locations near end-users) until a certain value of \(k\), at which \(RO\) increases again (as it becomes less-advantageous to deploy more storage capacity in the caches of the AMENs and more-advantageous to deploy the storage capacity in the MCEN cache). One might argue: why is the optimal solution not deploying all available storage capacity at AMENs? This is due to the fact that, when the storage capacity is limited, it becomes more-advantageous not to store duplicates of a number of popular items at AMENs, but rather store one copy of a larger set of items, thereby pulling more items from the origin server into the network. Certainly, in a scenario when the storage capacity is not limited, deploying more caches in proximity to end users and/or increasing their capacity allows one to significantly decrease the amount of network resources occupied to perform VoD content caching.