# Cooperation Based Proactive Caching in Multi-Tier Cellular Networks
## 7 Simulations and Results  
In this section, we simulated the cache hit ratio and the user satisfaction ratio of multi-tier caching systems. The popularity matrix for tier 1 and the list of parameter used in this simulation is given in Tables 1 and 2, respectively. The requests for the contents on BS on each tier is different, e.g., some people like one content while others are interested in some different content. Similarly, the number of BS in each tier is different. Each content size is considered to be same and is 1. Each tier has its own data set. The data set compromises of training data and testing data. First, the collaborative filtering is trained by using training data which is the content popularity. Testing data is utilized to predict the missing data in the data set. The popularity matrix of each tier is highly sparse matrix because users have different modes of likeness. Based on the similarities among the data, clusters are formed in each tier. Let the clusters in tier 1 and in tier2 is 2. We have single macro BS. Figure 2(a)-c shows how the cache hit ratio varies as the caching capacity varies in the tier 1, tier 2, and tier 3, respectively. In these figures, we showed that the cluster average popularity with CF (CAP-CF) is far better than other methods such as ground truth method [26; 28] and pure CF. In ground truth methods, only popular contents are cached, based on past requests, but there is no future prediction of the contents. As no clustering is formed in the ground truth method, no similarity between the BSs is observed, which results in poor utilization of the cache memory. On the other hand, in Pure CF method the contents which are not yet requested but hopefully requested in future, are predicted and are cached in descending order based on future popularity predication, without taking into account the present popularity of the contents. The simulations reveal that our proposed algorithm, which is based on the highest average popularity of the contents in the cluster and popularity of the contents to be requested in future, perform well by optimizing the cache hit ratio for each tier and also the average cache hit ratio for the whole multitier caching network. The main achievement in the proactive caching network is to cache the frequent requested content in the limited cache. Figure 3(a),b shows the proposed method 1 for the USR based on intra-tier and cross cooperation for two cluster of tier 1. Similarly, Figure 3(c),d depicts the same method for tier 2. This novel method is compared with other methods such as CF, intra-cluster cooperation, and cross-cluster cooperation methods. In CF there is no cooperation among the BSs for the data sharing, while in intra-cluster cooperation the data sharing take place among the BSs with in cluster and in cross-cluster cooperation the content exchange take place among the clusters with in the tier. On the hand, the proposed scheme performs both intra-tier and cross cooperation in order to maximize the USR. The simulations suggest that the proposed method performs well as compare to all other algorithms \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\mathbf{BS}\) & \multicolumn{3}{c}{**Number of**} & \multicolumn{2}{c}{**Requests**} \\ \hline \(B1\) & F1 & F2 & F3 & F4 \\ \(B2\) & 3 & 6 & 6 & 0 \\ \(B3\) & 3 & 0 & 6 & 8 \\ \(B4\) & 0 & 6 & 0 & 9 \\ \(B5\) & 5 & 5 & 5 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Popularity Matrix. \begin{table}
\begin{tabular}{c c c c} \hline \hline \(\mathbf{Parameters}\) & \multicolumn{1}{c}{**Tier 1**} & \multicolumn{1}{c}{**Tier 2**} & \multicolumn{1}{c}{**Tier 3**} \\ \hline No. of BS & 30 & 20 & 1 \\ \hline No. of past request & 5563 & 7636 & 700 \\ \hline No. of future request & 2000 & 2300 & 500 \\ \hline Caching capacity & 30 & 40 & 50 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: List of parameters. all of the tiers. Figure 5 show the second method which is MITCTC. Simulations show that the novel method MITCTC utilizing CF is better than the ground truth.