## 5 Performance Evaluation
### Simulation
#### 5.2.1 No Population Churn  
In the first set of experiments, we consider the case where we have a stable topology, so there are no new vehicles joining or existing members leaving the communication range. We set the probability \(probResourceRep=0\), so that when RC reaches 0, a UE always reselects a different resource. We divide the CBR into two regimes: 1-5% and 10-90%. To create the CBR from 1% to 5%, we place 25 to 125 vehicles in mutual communication range. To create the CBR from 10% to 90%, we place 250 to 2250 vehicles in mutual communication range. Figure 7 compares the collision probabilities of SPS and SPS/LA. The collision probability plotted in the figure is computed as the total number of collisions divided by the total number of single-subframe resources during the elapsed time. For example, the value at 40 s is obtained by dividing the number of collisions up to that time by the number of single-subframe resources during that time (=\(25\times 40\times 10^{3}=10^{6}\)). Notice that the \(y\)-axis is in log scale. Under very light loads, the standard SPS scheme keeps the collision probability under \(10^{-4}\). However, in the SPS/LA, the probability is even lower, orders of magnitudes lower (compare the \(y\)-axis with SPS). The collision probabilities approach \(10^{-6}\). In particular, there was no collision in 1 and 2% CBR during 100 s of simulated time. It bears out our analysis where the reselection collisions are similarly reduced in SPS/LA. Figure 7: Packet collision rates comparison in **(a)** SPS and **(b)** SPS/LA, light load. As we run ten instances of simulation for each data point, the confidence interval is very narrow, and hard to see with the log scale plots. Table 2 shows the 95% confidence interval at simulation time \(t=100\). Now, we increase the CBR. Figure 8 shows the results. We notice that the collision probability far exceeds \(10^{-4}\) in SPS even for 10% CBR. This number is important because some prominent applications envisioned for 5G eV2X require 99.99% reliability (Table 3) [40]. 5G eV2X will probably use a different radio resource format, but still the SPS performance is disappointing. When the CBR reaches 90%, the collision probability is 12.8%. In SPS/LA, we notice that the collision probability is reduced by a factor of 10 or more compared with the original SPS. Again, this result is in line with the reselection collision probability analysis. In particular, the SPS/LA scheme keeps the probability under \(10^{-4}\) until the CBR exceeds 40%. Even when the CBR increase further, the performance gap between the two algorithms is maintained at more than an order of magnitude. For an extremely high CBR of 90%, the collision probability under SPS/LA is still under 0.6%, compared with 12.8% under SPS. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**CBR** & \(\textbf{Mean}_{\textit{SPS}}\) & \(\textbf{1}\textbf{CI}_{\textit{SPS}}\) & \(\textbf{Mean}_{\textit{SPS/LA}}\) & \(\textbf{1}\textbf{CI}_{\textit{SPS/LA}}\) \\ \hline
1\% & \(3.72\times 10^{-6}\) & \(6.33\times 10^{-6}\) & 0 & 0 \\
2\% & \(1.85\times 10^{-5}\) & \(1.38\times 10^{-5}\) & \(2.40\times 10^{-7}\) & \(1.09\times 10^{-6}\) \\
3\% & \(3.41\times 10^{-5}\) & \(1.34\times 10^{-5}\) & 0 & 0 \\
4\% & \(6.21\times 10^{-5}\) & \(2.31\times 10^{-5}\) & \(3.13\times 10^{-6}\) & \(4.34\times 10^{-6}\) \\
5\% & \(1.04\times 10^{-4}\) & \(1.96\times 10^{-5}\) & \(1.17\times 10^{-6}\) & \(1.63\times 10^{-6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Collision probability at \(t=100\) with 95% confidence interval (CI) width. Figure 8: Packet collision rates comparison in (**a**) SPS and (**b**) SPS/LA, heavy load. Again, we show the mean and the 95% confidence interval widths for each case in Table 4. We again see that the confidence interval width is very small. We obtain the same narrow confidence intervals, so for subsequent results, we omit them.