# Performance Analysis of the IEEE 802.11p Multichannel MAC Protocol in Vehicular Ad Hoc Networks
## 4 Analytical Model and Performance Analysis
\begin{table}
\begin{tabular}{l l} \hline \hline
**Symbol** & **Definition** \\ \hline \multirow{3}{*}{\(P_{col}\)} & The probability that a transmission fails due to a collision given that there is at least one station transmits in the considered time slot. \\  & The packet reception rate is the percentage of packets that \\  & successfully received to the number of packets transmitted. \\ \hline \multirow{3}{*}{\(PRR_{i}\)} & The duration for successful transmitting an \(i\) packet. \\  & The duration for a transmission collision caused by \(i\) traffic. \\ \cline{1-1}  & \(SIFS\) \\ \cline{1-1}  & The duration of an SIFS. \\ \cline{1-1}  & \(m^{\prime}\) \\ \cline{1-1}  & The maximum times the CW can be doubled. \\ \cline{1-1}  & \(m\) \\ \cline{1-1}  & The maximum retransmission number. \\ \cline{1-1}  & \(M_{ln}\) \\ \cline{1-1}  & The number of lanes in each direction on the highway. \\ \cline{1-1}  & \(\delta\) \\ \cline{1-1}  & \(\sigma\) \\ \hline \multirow{3}{*}{\(T_{euln}\)} & Vulnerable period during which the transmission \\ \cline{1-1}  & of the tagged node may be subjected to \\ \cline{1-1}  & hidden terminal interference. \\ \hline \multirow{3}{*}{\(T_{eirt}\)} & The average duration of a virtual time slot. \\ \cline{1-1}  & The duration of a synchronization interval. \\ \cline{1-1}  & The duration of CCH interval. \\ \cline{1-1}  & The duration of SCH interval. \\ \cline{1-1}  & The transmission delay of an \(i\) packet. \\ \cline{1-1}  & \(T_{i,suc}\) \\ \cline{1-1}  & The time of successful transmission of an \(i\) packet. \\ \cline{1-1}  & \(T_{i,col}\) \\ \cline{1-1}  & The time of transmission collision of an \(i\) packet. \\ \cline{1-1}  & \(T_{ACK}\) \\ \cline{1-1}  & The header length of MAC-layer of a packet. \\ \cline{1-1}  & \(H_{PHY}\) \\ \cline{1-1}  & The header length of physical-layer of a packet. \\ \cline{1-1}  & \(L_{i}\) \\ \cline{1-1}  & The payload of an \(i\) packet. \\ \cline{1-1}  & \(L_{ACK}\) \\ \cline{1-1}  & \(R_{d}\) \\ \cline{1-1}  & The transmission data rate on the CCH and SCH. \\ \cline{1-1}  & \(W_{e}\) \\ \cline{1-1}  & \(W_{s,i}\) \\ \cline{1-1}  & The GW size for safety packets. \\ \cline{1-1}  & \(W_{s,i}\) \\ \cline{1-1}  & The CW size for WSA packets in the \(i\)th backoff stage. \\ \cline{1-1}  & \(b_{l_{i}}\) \\ \cline{1-1}  & The stationary distribution of idle state for \(i\) traffic. \\ \cline{1-1}  & \(b_{e,k}\) \\ \hline \multirow{3}{*}{\(b_{s,i,k}\)} & The stationary distribution of the backoff state \(k\) \\ \cline{1-1}  & in stage \(i\) for WSA traffic. \\ \cline{1-1}  & The average service time of \(i\) packets. \\ \hline \multirow{3}{*}{\(TQ_{i}\)} & The queuing delay that the duration from the time \\ \cline{1-1}  & instant when an \(i\) packet arrivals at the MAC layer queue \\ \cline{1-1}  & to the time instant when it becomes the head of queue. \\ \hline \multirow{3}{*}{\(TS_{i}\)} & The service time is the duration from the time instant \\ \cline{1-1}  & when an \(i\) packet becomes the head of the queue to the time \\ \cline{1-1}  & instant when this packet is transmitted or dropped. \\ \hline \multirow{3}{*}{\(D_{i}\)} & The transmission delay is the time duration between the time \\ \cline{1-1}  & instant that an \(i\) packet arrives at the queue to the time \\ \cline{1-1}  & instant that this packet is successful transmitted or dropped. \\ \hline \multirow{3}{*}{\(\gamma\)} & The ratio of CCHI to SI. \\ \cline{1-1}  & The number of available SCHs in VAENTS. \\ \cline{1-1}  & \(G_{1}\) \\ \cline{1-1}  & The average number of successful SCHs reservation made on CCH. \\ \cline{1-1}  & \(G_{2}\) \\ \cline{1-1}  & The number of non-safety packets transmitted on all \(N_{sch}\) SCHs. \\ \cline{1-1}  & \(S_{data}\) \\ \hline \hline \end{tabular} Note: \(i\) except \(W_{s,i}\) and \(b_{s,i,k}\) stands for \(e\) and \(s\) which means emergency (safety) and WSA, respectively.  
\end{table} 
Table 3: _Cont._