# A Swarming Approach to Optimize the One-Hop Delay in Smart Driving Inter-Platoon Communications
## 5 Performance Results  
In this section, we compare the performance in terms of the transmission probability, one-hop delay, end-to-end delay, one-hop throughput, end-to-end throughput and transmission probability of the inter-platoon communications under the optimal minimum contention window sizes and the standard minimum contention window size defined in the IEEE 802.11 DCF mechanism through simulation experiments. The simulation experiments were conducted using MATLAB (R2015a-academic use, 64 bit, MathWorks, Natick, MA, USA). The simulation codes are available in the supplementary material. The simulation scenario is described in Section 3. Let \(CW_{min}\) be the standard minimum contention window size defined in the IEEE 802.11 DCF mechanism, \(E[L]\) be the size of each packet, \(s\) be the duration of a slot, \(M\) be the retransmission limit, \(R\) be the channel bit rate, \(P_{e}\) be transmission error probability caused by channel, and \(I_{m}\) be the iteration limit. Table 1 gives the parameters used in the simulation experiments. Figure 4 shows the relationship between the end-to-end delay from the first backbone vehicle to the last backbone vehicle and the number of backbone vehicles in a multi-platoon when the standard minimum contention window size is used. In [24], European Telecommunications Standard Institute  
Figure 3: The flow chart of the swarming approach. (ETSI) defined that a packet should be ensured to be accepted successfully within a maximum delay limit 100 ms. In [25], it also claimed that the maximum highway platooning end-to-end delay required for the ETSI and the 3 rd Generation Partnership Project (3 GPP) is 100 ms. In [26; 27], they indicated that the most stringent required end-to-end latency is less than 100 ms and in the case of the small latency (less than 100 ms) the longitudinal and lateral error between the vehicles are low. In [28], the results show that most of the vehicle Central Address Memories (CAMs) have a delay of less than 2 ms when only inter-platoon communications exists. However, the corresponding experiments in [28] did not consider the backoff procedure of the IEEE 802.11 MAC protocol. As mentioned above, _in most related work_, the maximum end-to-end delay is 100 ms. Figure 4 illustrates that that the maximum number of backbone vehicles in a multi-platoon is 24 when the maximum delay is 100 ms. The optimal minimum contention window sizes under the different number of backbone vehicles are given by Table 2. As there are two backbone vehicles in each platoon, the number of backbone vehicles varies from 4 to 24. In Figure 5a, the performance metrics such as the optimal minimum contention window size, the one-hop delay, end-to-end delay, one-hop throughput, end-to-end throughput and transmission probability with the optimal minimum contention window sizes are discussed respectively under six backbone vehicles. Figure 5a shows the comparison between the optimal minimum contention window size of each backbone vehicle and the standard minimum contention window size when the number of backbone vehicle is 6. It is seen that all optimal minimum contention window sizes are smaller than the standard minimum contention window size, thus it can guarantee a relatively low one-hop delay. Moreover, the minimum contention window size of each backbone vehicle is different to get the one-hop delay of each backbone vehicle balanced. Figure 5b shows the comparison of the one-hop delay 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 can be seen that the one-hop delays of backbone vehicles with the standard minimum contention window size are unbalanced. The one-hop delays of backbone vehicles of the proposed approach are balanced and kept at around a small value 3.2 ms.