## 5 Numerical and Simulation Results
### Evaluations of Performance  
Figures 9 and 10 reveal that the exponent partition mechanism is advantageous to the partition latency within a limited value (seen from the curves of \"Proposal without mini\" in Figures 9a and 10a), meanwhile is favorable of a significant gain in terms of the contention latency compared to BPAB and IPES24 (seen from Figures 9b and 10b). Although at high vehicle densities (e.g., 3.0025 vehicles/meter), the gain in partition latency cannot make up the gap in contention latency compared to AMB, the mini-BBM mechanism benefits our proposal to defeat AMB in terms of the sum of partition latency and contention latency.  
As a result, shown in Figure 11a, our proposal achieves more than 18.10%, 15.26% and 19.24% lower two-hop delay than that of BPAB, IPES24 and AMB. In particular in heavy traffic, the enhancement is more significant. Additionally, our proposal attains the second-best performance in terms of message progress, which is only 0.37% worse than the best performing AMB. Consequently, it can be observed in Figure 11b that the message dissemination speed achieved by our proposal outperforms that of BPAB, IPES24 and AMB by at least 21.89%, 17.87% and 23.35%. The improvement even goes up to 125.23%, 123.87% compared to BPAB and IPES24 at the high vehicle density of 3.0025 vehicles/meter, and 63.78% compared to AMB at the relatively low vehicle density of 0.2025 vehicles/meter. It is also observed from Figure 11b that, at the heavy vehicle density, the performance of BPAB and IPES24 in terms of message dissemination speed drops gently, not as drastically as expected. The reason is that when the re-attempt number of CTB contention is over the pre-selected number \(N_{\text{recon}}\), the performance of this case in terms of message dissemination speed does not need to be evaluated, and the contention latency in average one-hop delay is decided by the duration of \(N_{\text{recon}}\) contentions in heavy traffic.  
Figure 12 demonstrates that our proposal presents the second-best performance in terms of PDR, which is over 90% stably. Although our proposal performs worse than the best performing AMB, it can be promoted by choosing a bigger A in dense networks. It is also observed that the performance of BPAB and IPES24 in terms of PDR degrades sharply as the vehicle density increases.  
Figure 10: _Cont._  
Figure 9: Comparison of Latency in Intersection Phase. (**a**) Comparison of partition latency; (**b**) Comparison of contention latency.  
Figure 11: Comparison of efficient performance in whole procedure. (**a**) Comparison of two-hop delay and message progress; (**b**) Comparison of dissemination speed.  
Figure 10: Comparison of Latency in Branch Phase. (**a**) Comparison of partition latency. (**b**) Comparison of contention latency.  
From the results in Figures 9-12 and the above analysis, some conclusions and suggestions can be given as follows: (1) In traffic jams, effective and real-time message dissemination is highly needed. However, the relay-node selection is more likely to fail due to the high collision rate caused by the high number of vehicles, and the performance will deteriorate in terms of message dissemination speed and PDR. In this sense, our proposal provides an effective solution by employing the design of exponent-based partition. It generates thinner final segments and thus improves message dissemination speed and PDR in the dense traffic. (2) From Figure 11b, it is clear to observe that all approaches perform the best message dissemination speed at the density of 0.2025 vehicle/meter. It demonstrates that the relay-node selection method based on the distance has an optimal vehicle density at which the method performs the best in terms of the message dissemination speed. Thus, when considering the real-time dissemination of the message, to select the branch that has the vehicle density closest the optimal value is a good suggestion in the routing design [33; 34; 35; 36; 37; 38].