# A Swarming Approach to Optimize the One-Hop Delay in Smart Driving Inter-Platoon Communications
## 5 Performance Results
Figure 4: End-to-end delay vs. number of backbone vehicles. mechanism with standard minimum contention window size when the number of backbone vehicles in a multi-platoon is 12 and 24, respectively. It is seen that the one-hop delay and the one-hop throughput of each backbone vehicle with the optimal minimum contention window size is kept around a constant. The end-to-end delay from backbone vehicle 1 to backbone vehicle \(i\) (\(i\) = 2, 3, \(\cdots\), 12/24) with the optimal minimum contention window sizes is reduced by 12%. The end-to-end throughput is increased by around 8% and the transmission probability is increased by about 40%. Figure 8 shows the average improvement ratio of the proposed approach's performance under different number of backbone vehicles. The average decrement ratio \(\eta_{de}\) in Figure 8a-c is calculated by (8)  
\[\eta_{de}=\frac{M_{DCF}-M}{M_{DCF}}, \tag{8}\]  
and the average increment ratio \(\eta_{in}\) in Figure 8d-f is calculated by (9)  
\[\eta_{in}=\frac{M-M_{DCF}}{M_{DCF}}, \tag{9}\]  
where \(M\) and \(M_{DCF}\) are the summation of the metrics with the proposed approach and the DCF mechanism, respectively. Figure 8a shows the average decrement ratio of the contention window size. It is seen that the optimal minimum contention window sizes are reduced by 49.4%, 55.2% and 57.6% as compared to the standard minimum contention window size when the number of backbone vehicles are 6, 12 and 24, respectively. The average decrement ratio of the contention window size increases with the increment of the number of backbone vehicles. Moreover, the decrement ratios of the contention window size under 12 and 24 backbone vehicles are almost the same. This means that the increment of the contention window size with the proposed approach is limited with the increment of the number of backbone vehicles. Figure 5: The performance of inter-platoon communications under six backbone vehicles. (**a**) Minimum contention window size vs backbone vehicle index; (**b**) One-hop delay vs backbone vehicle index; (**c**) End-to-end delay vs backbone vehicle index; (**d**) One-hop throughput vs backbone vehicle index; (**e**) End-to-end throughput vs backbone vehicle index; (**f**) Transmission probability vs backbone vehicle index. Figure 6: The performance of inter-platoon communications under 12 backbone vehicles. (**a**) Minimum contention window size vs backbone vehicle index; (**b**) One-hop delay vs backbone vehicle index; (**c**) End-to-end delay vs backbone vehicle index; (**d**) One-hop throughput vs backbone vehicle index; (**e**) End-to-end throughput vs backbone vehicle index; (**f**) Transmission probability vs backbone vehicle index. Figure 7: The performance of inter-platoon communications under 24 backbone vehicles. (**a**) Minimum contention window size vs backbone vehicle index; (**b**) One-hop delay vs backbone vehicle index; (**c**) End-to-end delay vs backbone vehicle index; (**d**) One-hop throughput vs backbone vehicle index; (**e**) End-to-end throughput vs backbone vehicle index; (**f**) Transmission probability vs backbone vehicle index. Figure 8b,c shows the average decrement ratio of the one-hop delay and the end-to-end delay. It is seen that the one-hop delay and end-to-end delay are reduced by 19.4%, 11.4% and 10.7% as compared to the DCF mechanism when the number of backbone vehicles are 6, 12 and 24, respectively. The average decrement ratio of the one-hop delay and the end-to-end delay increase with the increment of the number of backbone vehicles. Figure 8d,e shows the average increment ratio of the one-hop throughput and end-to-end throughput. It is seen that the one-hop throughput and end-to-end throughput are increased by \(-1.9\%\), \(4.6\%\) and \(7.7\%\) as compared to the DCF mechanism when the number of backbone vehicles are 6, 12 and 24, respectively. Note that the average increment ratio of the one-hop delay and the end-to-end delay is a small negative value when the number of backbone vehicles is 6.