# Multi-Connectivity-Based Adaptive Fractional Packet Duplication in Cellular Networks
## 5 Simulation Results
### Distribution-Based Packet Duplication  
We selected exponential random variables to decide the rates of enabling and disabling the PD. We turned the PD ON and OFF randomly based on our exponential rates [23]. If both BS and UE agree on the random number generator and seed, then, theoretically, there would be no signaling overhead to turn ON and OFF the PD. This can also be termed as a zero-signaling mechanism. An advantage of our method is that the UE and BS would be more aware of the event occurrences since random ON and OFF choices can always be studied, and required resources can always be made available beforehand. As shown in Figure 22, the exponential random rate of starting duplication is plotted on the \(x\)-axis, and the exponential random rate of stopping duplication is plotted on the \(z\)-axis.  
The 3D plot shows how the packet duplication is impacted due to the coordination on these two exponential random variables impacting the PD ON and OFF rates. A 100% PD is achieved when the log of the starting duplication rate is about 2.5 (rate equals \(10^{2.5}=316\) starts per second) and corresponding log of the stopping duplication rate is at \(-0.5\) (rate equals \(10^{-0.5}=0.32\) stops per second). The reverse is for the 0% PD where the log of the starting duplication rate is about \(-0.5\) and the corresponding log of the stopping duplication rate is at 2.5.  
The corresponding corrupt packets are shown in Figure 23. Similar to the above plot, a lower starting duplication rate along with a higher stopping duplication rate yields over 9% corrupt packets. Furthermore, a maximum starting duplication rate with a lower stopping duplication rate provides a corrupt packet percentage close to 2%. Lastly, Figure 24 shows the number of times PD is triggered in the entire communication. It can be clearly seen that,  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Fade Threshold (dB)** & **500 Samples** & **50 Samples** \\ \hline
5 & \(-8.42\%\) & \(-7.96\%\) \\
10 & \(-1.08\%\) & \(-4.56\%\) \\
15 & \(6.82\%\) & \(3.91\%\) \\
20 & \(5.20\%\) & \(5.17\%\) \\
25 & \(3.31\%\) & \(5.35\%\) \\
50 & \(20.67\%\) & \(19.9\%\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Relative decrease in the % corrupt packets vs. % increase in Packet Duplication.  
Figure 22: Packet Duplication based on exponential random variable.  
when both the starting duplication and stopping duplication rates are high, the number of switches is also high.  
The PD switches are the lowest when both these rates are at their lowest. This study can be used to understand and analyze the RF channel, and the actual amount of PD can be determined. In this study, we used the same mean starting and stopping rates throughout the simulation. However, as seen Figure 7, the mean SINR values change over the course of a simulation when affected by buildings and distance. In [23], the best starting and stopping rates are based on the average SINR. Thus, it would be advantageous in practical applications to have some adjustment of the starting and stopping rates over time; however, these would change infrequently.  
Figure 23: Corrupt Packet Duplication based on an exponential random variable.  
Figure 24: Actual number of times that Packet Duplication is triggered.