# A Swarming Approach to Optimize the One-Hop Delay in Smart Driving Inter-Platoon Communications
## 5 Performance Results
Figure 5c shows the comparison of the end-to-end delay from backbone vehicle 1 to backbone vehicle \(i\) (_i_ = 2, 3,..., 6) between the proposed approach and the DCF mechanism with the standard minimum contention window size when the number of backbone vehicles is 6. It can be seen that the end-to-end delay from backbone vehicle 1 to backbone vehicle 6 with the optimal minimum contention window sizes is around 16 ms. This is around 5 ms lower than that with the standard minimum contention window size. Moreover, the end-to-end delays from backbone vehicle 1 to other backbone vehicles with the optimal minimum contention window sizes are increased slowly with the increasing of backbone vehicle index. This is because one-hop delay of each backbone vehicle with the optimal minimum contention window size is balanced. Figure 5d shows the comparison of the one-hop throughput of each backbone vehicle between the proposed approach and the DCF mechanism with the standard minimum contention window size \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(CW_{min}\) & 64 & \(a\) & 0.15 \\ \(E[L](bits)\) & 2048 & _P\({}_{e}\)_ & 0.1 \\ \(SIFS(us)\) & 28 & \(m\) & 15 \\ \(DIFS(us)\) & 54 & _c\({}_{1}\)_ & 1.5 \\ \(ACK(bits)\) & 240 & _c\({}_{2}\)_ & 1.5 \\ \(s(us)\) & 13 & \(w\) & 0.8 \\ \(M\) & 5 & \(\Delta cw_{max}\) & 10 \\ \(R(Mbps)\) & 3 & _I\({}_{m}\)_ & 300 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters used in the simulation experiments. when the number of backbone vehicles is 6. It is seen that the one-hop throughput of each backbone vehicle with the optimal minimum contention window size is balanced and kept at around 0.6 Mbp/s. Figure 4(e) shows the comparison of the end-to-end throughput from backbone vehicle 1 to backbone vehicle \(i\) (\(i\) = 2, 3, \(\cdots\), 6) between the proposed approach and the DCF mechanism with the standard contention window size when the number of backbone vehicles is 6. It is seen that the end-to-end throughput from backbone vehicle 1 to backbone vehicle 6 with the optimal minimum contention window sizes are around 3.2 Mbp/s. This is almost the same with the end-to-end throughputs by using the standard minimum contention window size. Moreover, the end-to-end throughputs from backbone vehicle 1 to other backbone vehicles with the optimal minimum contention window sizes are increased by a constant with the increasing of backbone vehicle index. This is because that the one-hop throughput of each backbone vehicle with the optimal minimum contention window size is balanced. Figure 5(f) shows the comparison of the transmission probability of each backbone vehicle between the proposed approach and the DCF mechanism with the standard minimum contention window size when the number of backbone vehicles is 6. It is seen that the transmission probability of each backbone vehicle with the optimal minimum contention window size is larger than that with the standard minimum contention window size. In Figures 6 and 7, the performance metrics with the optimal minimum contention window sizes are discussed under 12 and 24 backbone vehicles, respectively. Figures 6 and 7 compare the performance of inter-platoon communications between the proposed approach and the DCF \begin{table}
\begin{tabular}{c c} \hline \hline \(n\) & **The Optimal Minimum Contention Window Sizes** \\ \hline
4 & [38,49,49,38] \\
6 & [34,43,20,20,43,34] \\
8 & [38,55,24,22,22,24,55,38] \\
10 & [36,51,22,20,18,18,20,22,51,36] \\
12 & [40,54,22,20,18,18,18,18,20,22,54,40] \\
14 & [32,45,18,18,17,20,20,20,20,17,18,18,45,32] \\
16 & [44,56,23,18,16,17,20,21,21,20,17,16,18,23,56,44] \\
18 & [34,45,17,15,14,15,16,17,18,18,17,16,15,14,15,17,45,34] \\
20 & [34,50,21,24,23,30,29,30,27,26,26,27,30,29,30,23,24,21,50,34] \\
22 & [42,55,19,15,13,14,17,19,22,21,21,21,21,22,19,17,14,13,15,19,55,42] \\
24 & [38,50,20,18,17,20,22,23,27,28,31,32,32,31,28,27,23,22,20,17,18,20,50,38] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The optimal contention window sizes.