# Optimal Proactive Caching for Multi-View Streaming Mobile Augmented Reality
## 4 Numerical Investigations
### Simulation Results and Discussion
Figure 7: Preference of View Streams and Embedded AROs with Weight \(\mu\) (6 EC, 30 requests, EC Capacity is 14 and Total Moving Probability is 1). to 9.8% optimality gap compared to the Optim scheme and approaches the Optim scheme better in a non-congested condition. The above aspect can also be seen from Figures 9 and 10. All schemes suffer from an increased delay when fewer ECs are activated or there is less available capacity per EC. However, in all use cases under investigation, the proposed schemes show much better performance in latency than other baseline schemes. Figure 8: Service Delay with Different Number of Requests (6 EC, \(\mu=0.5\), EC Capacity is 14 and Total Moving Probability is 1). CFS [34]; UTIL [35]. Figure 9: Service Delay with Different Number of ECs (30 Requests, \(\mu=0.5\), EC Capacity is 14 and Total Moving Probability is 1). CFS [34]; UTIL [35]. To shed light on the performance, we calculate the _rmse_ (root mean square error), \(\delta\) (relative error) and \(r^{2}\) (determination coefficient) for the LSTM scheme. The predictions from the LSTM network are compared with the optimal solutions, and we have _rmse_\(<2.5\), \(\delta<15\%\) (relative error) and \(r^{2}>0.83\) (determination coefficient) in most cases. Hence, the predictions of the LSTM scheme can be regarded as reliable and closely follow the optimal solutions. Table 3 shows _rmse_ values including the LSTM scheme and greedy baseline schemes for comparison. In simulations, topologically close servers are allocated adjacent indices, and the user mobility is limited to the adjacent server in a period of an MAR session. Hence, indices decided for each server also reveal their location information. Thus, the similarity between the predictions of the LSTM scheme and the optimal solutions reveals the LSTM scheme's competitive edge over other greedy baseline schemes. Noticing that an infeasible prediction might appear and cause a deteriorating quality of service after adjusted in the Feasibility Check Stage. However, according to Figure 11, the LSTM network's validation accuracy is maintained at around 86.3% and is less than 6% worse than its training accuracy, which indicates that the infeasible solutions are rare and the general learning capabilities are effective. \[rmse=\sqrt{\frac{\Sigma_{1}^{n}(YTest_{i}-YPred_{i})^{2}}{n}} \tag{27}\]  
\[\delta=\frac{\Sigma_{1}^{n}|\frac{YTest_{i}}{YPred_{i}}-1|}{n}\times 100\% \tag{28}\]  
\[r^{2}=1-\frac{(YTest_{i}-YPred_{i})^{2}}{YPred_{i}-\frac{1}{n}\sum_{i=1}^{n}Y Pred_{i}} \tag{29}\]  
Figure 10: Service Delay with Different EC Capacities (6 EC, 30 Requests, \(\mu=0.5\) and Total Moving Probability is 1). CFS [34]; UTIL [35]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Scheme** & **Optim** & **LSTM** & **CFS** & **UTIL** & **RandS** \\ \hline
**Delay (ms)** & 25.7 & 27.9 & 30.2 & 31.1 & 37.4 \\ \hline
**RMSE** & - & 2.4 & 8.5 & 3.6 & 5.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: RMSE values and service delay in no mobility event (\(\mu=1\), 6 ECs, 30 requests and EC capacity is 14). Before training the LSTM scheme, it requires a long computational time to create a large number of optimal solutions (\(\sim\)810 s in Figure 12) from the Optim scheme. However, this stage only needs to be executed a few times and is a purely offline task. Similarly, the network training (\(\sim\)70 s in Figure 12) is also offline and does not need to repeat itself if the validation accuracy of the trained LSTM network meets the expectation. As a result, these offline stages do not have a serious detrimental effect on the general computing efficiency. As shown in Table 4, based on a trained LSTM network, the online decision-making stage of the LSTM scheme can generate predictions in an efficient manner for MAR sessions. Because the Optim scheme constructs and solves a complex mixed integer linear problem, it suffers from the longest processing time and is not ideal for a highly dynamic network environment.