# Performance Analysis of the IEEE 802.11p Multichannel MAC Protocol in Vehicular Ad Hoc Networks
## 4 Analytical Model and Performance Analysis
### Performance Analysis
#### 4.4.3 Throughput Analysis  
In this section, we analyze the throughput of non-safety packets on the SCHs. According to the specification in IEEE 1609.4 standard, a dedicated CCH is used to provide a unique rendezvous for nodes to transmit, gather, and share information such as safety-related messages and SCH reservation information through exchange WSA/ACK messages. The nodes rendezvous on the CCH only during the CCHI. Note, we assume that nodes can determine the starting time of their transmissions on SCHs after their negotiations on the CCH. However, the fixed switch mechanism between CCH and SCH defined in IEEE 1609.4 standard may come with a drawback: When a larger number of nodes is present to communicate with each other under a density vehicular environment, the single CCH can be highly congested and limited CCHI makes nodes having no enough time to performance SCH reservations, and thus CCH becomes a performance bottleneck. Beside, considering the delivery of non-safety packets only during SCHI and the unique feature of multichannel operation in the IEEE 1609.4 standard such as periodical and synchronous fixed switching between CCH and SCH, the throughput of SCHs is thus lower and the SCHs are not fully utilized. We first calculate the number of successful exchange the WSA/ACK packets on the CCH, and then discuss the control channel bottleneck and the SCHs utilization issue. Let \(N_{sch}\) denote the number of SCHs available under the vehicular environments. According to the specification defined in the IEEE 1609.4 standard, we have  
\[T_{SYNC}=T_{CCHI}+T_{SCHI} \tag{50}\]  
Let \(G_{1}\) represent the average number of successful exchange WSA/ACK packets during the CCHI on the CCH. To observe how the length of CCHI affects \(G_{1}\) which in turn affects the throughput of SCHs, we define a variable \(\gamma\) to represent the ratio of CCHI to SI, and we call this scheme \(\gamma\)-varying multichannel scheme. Thus, the \(\gamma\) is defined as  
\[\gamma=\frac{T_{CCHI}}{T_{SYNC}},\quad 0<\gamma<1 \tag{51}\]According to the fixed switch scheme defined in the IEEE 1609.4 standard, \(\gamma\) is equal to 1/2. We derive the expression of \(G_{1}\) as  
\[ \begin{split} G_{1}&=\frac{T_{CCHI}\times(P_{busy}P_{ s,suc}^{v})}{T_{virt}}\\ &=\frac{\gamma T_{SYNC}\times(P_{busy}P_{s,suc}^{v})}{T_{virt}}, \quad 0<\gamma<1\end{split}  \tag{52}\]  
Let \(G_{2}\) be the number of non-safety packets which can be transmitted on all \(N_{sch}\) SCHs during the SCHI, we have  
\[G_{2}=\frac{(1-\gamma)T_{SYNC}}{T_{data}}N_{sch},\quad 0<\gamma<1 \tag{53}\]  
where \(T_{data}\) be the duration of successful transmission of a non-safety packet, and it is calculated by  
\[ \begin{split} T_{data}&=DIFS+\frac{H_{PHY}+H_{MAC} +E[L_{data}]}{R_{d}}\\ &\quad+SIFS+T_{ACK}+2\delta\end{split}  \tag{54}\]  
where \(DIFS\) and \(E[L_{data}]\) represent the duration of a DIFS and the payload of a non-safety packet. Note, we still use \(DIFS\) instead of AIFS for clarity and simplicity when calculating \(T_{data}\). On the one hand, when \(G_{1}\leq G_{2}\), it means when a sender and a receiver are performing SCH reservation, there are always free SCHs. Thus, the SCH reservation is successful as long as the transmission of WSA/ACK packet is successful. In other words, a successful transmission of WSA/ACK means a successful transmission of non-safety message. Under this circumstance, the CCH becomes a performance bottleneck and the SCHs are under utilization. On the other hand, when the available \(N_{sch}\) or SCHI is limited, \(G_{1}\) is greater than \(G_{2}\), and thus the successful transmission of WSA/ACK packets cannot perform successfully transmission of non-safety packets on the SCHs. The throughput of SCHs also decreases. Under this circumstance, the SCHs becomes a performance bottleneck. Therefore, based on the above analysis, the average total throughput of SCHs can be expressed as  
\[