# Proactive Service Caching in a MEC System by Using Spatio-Temporal Correlation among MEC Servers
## 5 Performance Evaluation
### Hit Rate Comparison  
In Figure 7, we show the variations of a cache hit rate in different MECSs with different cache sizes over time. To facilitate the comparison, the ranges of the y-axis in all subfigures are shown to be the same. We observe that the hit rates obtained by our method are higher than those acquired by the LSTM method, regardless of the MECS locations and \(\eta\).  
To further verify our method, we compare the distribution of a cache hit rate in each MECS. Specifically, for each MECS, we investigate the difference between the maximum cache hit rate that can be obtained when \(S_{m}^{T}(t)\) is used and that acquired when \(S_{m}^{P}(t)\) is used. We denote the cache hit rate when \(S_{m}^{T}(t)\) is used as \(h_{m}^{T}(t)\). We also denote the cache hit rate obtained by a popularity prediction method as \(h_{m}^{P}(t)\). For each time slot, we calculate the relative hit rate \(\rho_{m}(t)=h_{m}^{P}(t)/h_{m}^{T}(t)\) and show its distribution in Figure 8. This figure has four subfigures. In each subfigure, the x-axis is a MECS index \(m\) and the y-axis is \(\rho_{m}(t)\). Each subfigure shows the distribution of \(\rho_{m}(t)\) in each MECS as a box plot.  
In this figure, we observe that the proposed method outperforms the LSTM method in terms of \(\rho_{m}\) in all MECSs and \(\eta\)s. When \(\eta=8\), the average \(\rho_{m}(t)\) is 82.13% when our method is used, while it is 76.78% when the LSTM method is used. In other words, our method improves the average cache hit rate by 6.97%. In the case of \(\eta=16\), the proposed method enhances the average cache hit rate by 8.48%. The average \(\rho_{m}(t)\) is 81.08% when our method is used, while the average \(\rho_{m}(t)\) obtained by the LSTM method is 74.74%. We  
Figure 7: Comparison of a cache hit rate over time in different MECSs.  
also observe that our method decreases the variance in the cache hit rate. When \(\eta=8\), the average IQR resulted by the proposed method is 14.19%, while the LSTM method produces an average IQR of 15.88%. In the case of \(\eta=16\), the proposed method achieves an average IQR of 11.76%, while it is 13.55% when the LSTM method is used. By decreasing the average IQR by more than 10%, our method makes the cache hit rate in a MEC system stabler than the LSTM method.  
We also note that the proposed method needs only one ConvLSTM model to predict the popularity of each service in each MECS. On the contrary, since each MECS needs at least one LSTM model to predict the popularity of each service within only its service area, the LSTM method needs the \(M\) LSTM model to predict the service popularity in a MEC system. As we show in Table 4, we use a total of 746,689 parameters for the ConvLSTM model and 121,301 parameters for a single LSTM model. Since the LSTM method uses a total of \(M\times 121,301\) model parameters, the proposed method reduces the total model parameters by 32.15%. Therefore, when we consider these facts along with the results observed in Figure 8 in an integrated manner, our method can achieve a higher cache hit rate with a smaller amount of model parameters compared to the LSTM method.