# Performance Analysis of the IEEE 802.11p Multichannel MAC Protocol in Vehicular Ad Hoc Networks
## 5 Model Validation and Numerical Analysis
We give the reference curves with parameters: safety-related packet: AIFSN[0] = 3, \(W_{e}\) = 8 and WSA packet: AIFSN[1] = 6, \(W_{s,0}\) = 16, \(m^{\prime}\) = 2, \(m\) = 4. It can be observed that bigger CW size and bigger AIFSN help improve the reliability and also increase the packet transmission delay. This is because that bigger CW size and bigger AIFSN generate fewer contentions and reduce the collision probability, and also increase packet service time. Figure 10f,g gives the comparison of probabilities of external collision, virtual collision, collision and transmission failure under unsaturated condition (\(\lambda_{e}=\lambda_{s}\) = 2 packets/s) and saturated condition (\(\lambda_{e}=\lambda_{s}\) = 500 packets/s. Note that the real packets arrival rate for safety traffic and WSA traffic are 2\(\lambda_{e}\) (1000 packets/s) and 2\(\lambda_{s}\) (1000 packets/s) on the CCHI, respectively. It can be observed that the virtual collision probabilities are very small under both conditions. Although the safety-related packet has higher priority than WSA packet, the probabilities of collisions of safety-related packets almost are equal to the probabilities of collisions of WSA packets. This is due to that the external collision probability has a primary impact on PRR. In the figure, it can be seen that the transmission failure probabilities of safety-related packets are slightly bigger than that of WSA packets since a safety-related packet size is bigger than that of a WSA packet which incurs the safety-related packet having higher packet error probability. In this case, we need to decrease the packet error probability due to bit error rate, especially in dynamic mobile networks, and this is our future work. Figure 10h gives the comparison of throughout on the SCH: IEEE 1609.4 standard versus \(\gamma\)-varying multichannel scheme. In order to facilitate the comparison between IEEE 1609.4 standard and \(\gamma\)-varying multichannel scheme, we set \(p_{ber}=0\). It can be observed that, in the IEEE 1609.4 standard, the throughput rises at first and then reduces (or keep maximum values for a small segment length and then reduces) when the vehicle density rises further. The reason is that, taking \(\lambda_{e}=\lambda_{s}\) = 5 packets/s for example, when the vehicle density is less than 0.04 vehicles/m, due to the longer CCHI and the shortage of WSA packets, the CCH is idle for a while, and then the throughput is lower. When the vehicle density is more than 0.04 vehicles/m, higher vehicle density generates more contentions and requires more CCHI to make SCH reservations. Under the above two conditions, the SCHs are starved state, and the SCHs is under utilized. From Figure 10h, it can be seen when the ratio of CCHI to SI, \(\gamma\), increases within the range of 0.7, the maximum throughput vales of \(\gamma\)-varying multichannel scheme also increases. While when \(\gamma\) increases from 0.7 to 1, the throughput of \(\gamma\)-varying multichannel scheme deceases. This is because that, when \(\gamma\leq 0.7\), due to the effect of factors such as virtual collision, channel fading and hidden terminals, the number (\(G_{1}\) in Equation (52)) of successful SCH reservations is smaller, and then the SCHs are idle for a long time. Therefore, the SCH throughput is lower and the SCHs are under utilized, and the CCH is the performance bottleneck. On the other hand, when \(\gamma>0.7\), due to the shortage of SCHI, the number (\(G_{2}\) in Equation (53)) of non-safety packets which can be allowed to be transmitted on the SCHs is smaller (\(G_{2}<G_{1}\)). Under this condition, SCH is the  
performance bottleneck, and the CCH is under utilized. In these cases, we need to determine the \(\gamma\) dynamically based on the vehicle density so as to obtain an efficient and optimal throughput.