# Underlay Loosely Coupled Model for Public Safety Networks Based on Device-to-Device Communication
## 6 Simulation Results
### Effect of Increasing Optimization Intervals on Network Updates and the Average CQI of the Group  
To reduce the number of network updates, a set of simulations is achieved by increasing the optimization interval while the CQI threshold is fixed at 0. Instead of performing the optimization every second, different values of the optimization interval (2, 4, 6, 8, 10, and 20 s) were simulated. Compared with the \"optimized tree\", where optimization is carried out every second, we note from Figure 20, that using an interval of 2 s can reduce the number of network updates by almost 10% when the number of UEs is equal to 70. We also note that, with the variation in the optimization interval, the gap between network updates becomes significant starting at 40 UEs. Moreover, as the number of UEs increases, the reduction in network updates becomes more important.  
Using the same values of the optimization interval, a set of simulations was carried out to verify the effect on the average CQI of the network. In Figure 21, different graphs corresponding to each selected optimization interval value are presented. We notice that the shape of the graph lines in the upper part is almost close to those of the \"optimized network\" approach. However, the difference widens in the lower values of the graph, and we notice that the values of the average CQI drop once the optimization interval increases.  
Figure 21: Average CQI for each optimization frequency.  
Figure 20: Number of network updates generated according to different optimization intervals.  
Effect of the Combination of the CQI Threshold and the Optimization Interval Compared with the \"Optimized Tree\" Approach  
In the series of simulations previously presented, it was possible to note that the use of a CQI threshold equal to 1 or an optimization interval of 2 s made it possible to reduce the number of network updates without significantly affecting the CQI average. Therefore, new simulations were carried out using a new approach that combines the two following parameters: CQI threshold = 1 and optimization interval = 2 s. From the results presented in Figures 22 and 23, we can notice a considerable drop in the number of updates, while the average CQI is slightly degraded. The generated average values, when the number of UEs = 70, are presented in Table 3 and compared with other approaches, i.e., \"optimized tree\", \"less cost\", CQI threshold = 1, and optimized interval = 2 s. The results are also shown as a percentage compared with the optimal values of the \"optimized tree\" approach.  
Figure 23: Comparison of the number of network updates between the “optimized tree” approach and the customized approach (CQI threshold = 1 and optimized interval = 2 s).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Optimized Tree** & **Less Cost** & **CQI Threshold = 1** & **Optimization** & **CQI Threshold = 1 and** \\  & **Approach** & **Approach** & & **Interval = 2 s** & **Optimization Interval = 2 s** \\ \hline Number of network updates & 33,036 & \((-100\%)\) & 24,338 & 29,403 & 21,700 \\  & & \((-100\%)\) & \((-27\%)\) & \((-11\%)\) & \((-35\%)\) \\ \hline Average CQI & 12.03 & 9.25 & 11.89 & 11.77 & 11.6 \\  & & \((-23.11\%)\) & \((-1.16\%)\) & \((-2.16\%)\) & \((-3.57\%)\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Summary of the average results generated using the customized approach (CQI threshold = 1 and optimized interval = 2 s) and compared with some selected other approaches when the number of UEs = 70.  
Figure 22: Comparison of the average CQI between the optimized tree approach and the customized approach (CQI threshold = 1 and optimized interval = 2 s).