# Performance Analysis of the IEEE 802.11p Multichannel MAC Protocol in Vehicular Ad Hoc Networks
## 4 Analytical Model and Performance Analysis  
In this section, we propose an analytical model. The proposed analytical model takes two kinds of messages with different priorities, different packet arrival rate, unsaturated conditions, hidden terminal problem, channel switch, channel fading into account. The main symbols together with their significances used in our analytical model are given in Table 3.  
To give a tractable yet reasonable model to characterize the performance of the IEEE 802.11p multichannel MAC protocol, we give some definitions and assumptions. \begin{table}
\begin{tabular}{c p{284.5 pt}} \hline \hline
**Symbol** & **Definition** \\ \hline \(\beta\) & The vehicle density on the highway (vehicles/m). \\ \(R\) & The transmission range of a node. \\ \(L_{cs}\) & The carrier-sensing range of a node. \\ \(L_{int}\) & The interfering range of a node. \\ \hline \(N_{tr}\) & The number of nodes within the transmission/receiving range of tagged node. \\ \hline \(N_{cs}\) & The number of nodes within the carrier-sensing range of tagged node. \\ \(N_{int}\) & The number of nodes within the interfering range of tagged node. \\ \hline \(P(j,l)\) & The probability that \(j\) vehicles exist within \\  & length \(l\) of the highway. \\ \hline \(P_{i,arr}\) & The arrival probability of \(i\) packets. \\ \(P_{i,emp}\) & The probability that the type of \(i\) queue is empty. \\ \(\rho_{i}\) & The probability that at least one packet waits in the type of \(i\) queue. \\ \(P_{i,suc}\) & The probability that a transmission attempt of an \(i\) packet is successful. \\ \hline \(P_{i,b}\) & The backoff blocking probability that other nodes \\  & or other ACs in the same node is occupying the channel. \\ \hline \(P_{i,f}\) & The probability that transmission of an \(i\) packet is failing. \\ \hline \(P_{oc}\) & The external collision probability that an \(i\) packet collides with other nodes while accessing the channel. \\ \hline \(P_{i,vc}\) & The virtual collision probability that an \(i\) packet collides with the higher priorities inside a node. \\ \hline \(P_{i,c}\) & The collision probability of an \(i\) packet. \\ \(P_{i,err}\) & The \(i\) packet error probability caused by channel fading. \\ \(p_{ber}\) & The bit error rate. \\ \hline \(\tau_{i}\) & The internal transmission probability that the probability of transmission attempt for access class \(i\) in a random time slot \\  & observed by the other ACs of the same station. \\ \hline \(\eta_{i}\) & The external transmission probability that the probability of transmission attempt for access class \(i\) observed by other node. \\ \hline \(\eta_{total}\) & The total transmission probability of a station. \\ \hline \(P_{s,drop}\) & The probability that a WSA packet is dropped due to more than retransmission limit. \\ \hline \(P_{busy}\) & The probability that the channel is busy in a time slot. \\ \hline \(P_{i,suc}^{p}\) & The probability that the transmission attempt of an \(i\) packet is successful, conditioned on the fact that at least one station transmits in the considered time slot. \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of important symbols.