## 5 Numerical and Simulation Results
### Validations of Analytical Model  
Figures 3-8 show the comparison of the results of analytical models (lines) and the simulation (symbols). These results are a function of vehicle density with varied \(N_{\text{part}}\), \(N_{\text{iter}}\) and \(A\). As can be  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Parameters** & **Default Values** \\ \hline Bit Rate & 18 Mbps \\ Message Packet Size & 500 Bytes \\ RTB Packet Size & 20 Bytes \\ CTB Packet Size & 14 Bytes \\ Slot Time & 13 \(\upmu\)s \\ DIFS & 58 \(\upmu\)s \\ SIFS & 32 \(\upmu\)s \\ Transceiver’s Switching Time & 1 \(\upmu\)s \\ Communication Range & 400 m \\ Confidence Interval & 95\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Major communication parameters.  
seen from these figures, the analytical predictions coincide with simulation results well, showing the validity of the obtained analytical expressions.  
From these figures, some new interesting observations can be got as follows: (1) With one of the three parameters (\(N_{\text{part}}\), \(N_{\text{iter}}\) and \(A\)) decreasing, the partition latency is reduced. In addition, the gain of the partition latency benefited from the decreasing of the three parameters falls as the parameter becomes a smaller value. The similar tendency is also observed for the contention latency, message progress and PDR with the three parameters increasing. (2) The partition latency approaches a constant value when the traffic becomes heavier. This is because when the vehicle density rises over a particular value, at least one node exists in the final segment near the optimal position, then the number of B spent in the partition phase is fixed as \(N_{\text{iter}}-1\). (3) We also find that the bigger values have the three parameters, the smaller the contention latency varies with density, shown as the lowest curve in Figures 4 and 6. The observation is because the bigger values of the parameters can result in a thinner final segment. (4) Increasing these parameters can improve the contention latency but prolong the partition latency, and the influence is different at different vehicle densities. It is confirmed again that there are some optimal values for these three parameters to get a maximum message speed.  
Figure 3: _Cont_.  
Figure 4: _Cont_.  
Figure 3: Validation of the model for partition latency in Intersection Phase. (**a**) When \((N_{\text{iter}},N_{\text{part}})=(2,3)\); (**b**) When \((N_{\text{iter}},A)=(2,2)\); (**c**) When \((N_{\text{part}},A)=(4,2)\).  
Figure 4: Validation of the model for contention latency in Intersection Phase. (**a**) When \((N_{\text{iter}},N_{\text{part}})=(2,3)\); (**b**) When \((N_{\text{iter}},A)=(2,2)\); (**c**) When \((N_{\text{part}},A)=(4,2)\).  
Figure 5: _Cont_.  
Figure 5: Validation of the model for partition latency in Branch Phase. (**a**) When \((N_{\text{iter}},N_{\text{part}})=(2,3)\); (**b**) When \((N_{\text{iter}},A)=(2,2)\); (**c**) When \((N_{\text{part}},A)=(4,2)\).  
Figure 6: _Cont_.  
Figure 7: _Cont_.  
Figure 8: _Cont_.  
Figure 7: Validation of the model for message progress in Branch Phase. (**a**) When \((N_{\text{iter}},N_{\text{part}})=(2,3)\); (**b**) When \((N_{\text{iter}},A)=(2,2)\); (**c**) When \((N_{\text{part}},A)=(4,2)\).