# Performance Analysis of the IEEE 802.11p Multichannel MAC Protocol in Vehicular Ad Hoc Networks
## 4 Analytical Model and Performance Analysis
### Definitions and Assumptions  
In this paper, the IEEE 802.11p and IEEE 1609.4 protocols work under highway scenario with one lane in each direction, as shown in Figure 4. However, we can easily extend our analysis with the \(M_{ln}\)-lanes in each direction on the highway by multiplying \(M_{ln}\) by the \(N_{tr}\), \(N_{cs}\) and \(N_{int}\), respectively. Since the communication range is much larger than the road's width, we simplify the network in each direction as one-dimensional VANETs. The specific work environment is as follows:  
**Assumption 1** (_Poisson distribution of vehicles on road_). : _Statistic analysis of the empirical data in [31] proves that an exponential distribution is a good fit for highway vehicle traffic according to inter-vehicle distance. Assuming that the vehicle nodes are placed on the line according to a Poisson point process with network density \(\beta\) (in vehicles per meter), the probability of \(j\) vehicles existing within length \(l\), \(P(j,l)\), is given by_  
\[P(j,l)=\frac{(\beta l)^{j}e^{-\beta l}}{j!} \tag{2}\]  
**Definition 1** (_Transmission/receiving range_). : _The transmission/receiving range \(R\) of a node represents the range within which a packet can be successfully received, if there exists no collisions from other nodes. \(R\) mainly depends on the transmission power, the data transmission rate and channel propagation characteristic. The average number of nodes within \(R\) of a tagged node, \(N_{tr}\), can be given by_  
\[N_{tr}=4\beta R \tag{3}\]  
**Definition 2** (_Carrier-sensing range_). : _The carrier-sensing range \(L_{cs}\) denotes the range within which a node can detect other nodes' transmission. It is usually determined by the transmission power and antenna sensitivity. Give the tagged node is in origin, as shown in Figure 4, as long as the nodes in \([-L_{cs},L_{cs}]\) are transmitting, the tagged node will not initiate any transmission at that moment. The average number of nodes within carrier-sensing range of a tagged node, \(N_{cs}\), can be given by_  
\[N_{cs}=4\beta L_{cs} \tag{4}\]  
**Definition 3** (_Interfering range/hidden terminal range_). : _The interfering range \(L_{\text{int}}\) is the range within which nodes in a receiving mode interfere with transmissions from other nodes. The nodes' transmissions in \([-2R,-L_{cs}]\) and \([L_{cs},2R]\) cannot be detected by the tagged node, but interfere with the packets receiving of nodes in \([-R,R]\) from the tagged node. The number of hidden terminal of a tagged node, \(N_{\text{int}}\), can be given by_  
\[N_{\text{int}}=4\beta(2R-L_{cs}) \tag{5}\]  
Figure 4: One-dimensional highway VANETs model. In this paper, the capture effect is not considered, and all nodes have the same \(R\), \(L_{\text{cs}}\) and \(L_{\text{int}}\). **Assumption 2** (_Poisson way of packet arrival rate_). : _The generated packets arrive at the MAC layer in a Poisson way with rate \(\lambda\). According to the IEEE 1609.4 protocol [6], the safety packets and WSA packets are sent on the CCH only during the CCHI. If the packets are generated during the SCHI, they have to wait in the MAC layer queues until the next CCHI to be transmitted. At the beginning of the next CCHI, many nodes contending the CCH, which may lead to synchronized collision [20]. To avoid synchronized collision, the considered application layer has to schedule these packets to arrive at the MAC layer queue by delaying 50 ms (a CCHI). Therefore, in this paper, the synchronized collision issue is not considered. Each node has two queues for each AC: CCHI queue and SCHI queue. CCHI queue is for the packets arriving at the MAC layer during the CCHI, and SCHI queue is for the packets arriving at the MAC layer during the SCHI. For each AC, these two queues have the same arrival rate \(\lambda\). The sum of two independent Poisson processes with rate \(\lambda\) is the Poisson process with rate \(2\lambda\).