# Performance Analysis of the IEEE 802.11p Multichannel MAC Protocol in Vehicular Ad Hoc Networks
## 4 Analytical Model and Performance Analysis
### Definitions and Assumptions
Therefore, the packets arrival rate for safety traffic and WSA traffic during the CCHI are \(2\lambda_{e}\) and \(2\lambda_{s}\), respectively._  
**Assumption 3** (_Unlimited length of queue_). : _Each AC has two independent queues (CCHI queue and SCHI queue) at the MAC layer with unlimited length for each, which means that the packet dropping caused by the queue overflow is not taken into consideration. These two queues can be considered one virtual queue with rate \(2\lambda\). Therefore, each node have two virtual M/G/1 queues with a common server: one virtual queue for safety packets and the other virtual queue for WSA packets, as shown in Figure 5. To simplify, the following queues refer to virtual queues._  
**Assumption 4** (_Erroneous channel Bit Error Rate (BER)_). : _In VANETs, V2V communications present environment with unfavorable characteristic of channel fading, i.e., multiple reflecting objects able to degrade the strength and quality of the received signal. In addition, high mobility makes worse Doppler spread on Orthogonal Frequency Division Multiplex (OFDM), which leads to higher BER. To simply the discuss, we follow the similar assume in [32] that control packet such as Acknowledgement (ACK) packet and frame headers (the header of both physical layer and MAC layer) of both safety and WSA packet are error free. The channel fading leads to packet error probability \(P_{e,err}\) and \(P_{s,err}\) for a safety packet and a WSA packet, respectively, which can be given by_  
\[\left\{ \begin{array}{l}P_{e,err}=1-(1-p_{ber})^{E[L_{e}]}\\ P_{s,err}=1-(1-p_{ber})^{E[L_{e}]}\end{array} \right. \tag{6}\]  
_where \(p_{ber}\), \(E[L_{e}]\) and \(E[L_{s}]\) denote the probability of BER, the average payload of a safety packet and the average payload of a WSA packet, respectively. \(p_{ber}\) can be numerically evaluated for a Rician fading channel [33] or Nakagami-m fading channel [34]._  
**Assumption 5** (_Neglecting the impact of vehicle mobility on the performance_). : _The impact of vehicle mobility on reliability, timeliness and throughput are not considered in the model. In fact, it is illustrated in [35] that the high mobility of vehicles (up to 120 km/h) has a very small impact on the performance of the direct packet transmission with high data rate (e.g., \(\geq\) 12 Mbps/s). In addition, the number of one-hop neighboring nodes of a tagged node does not significantly change in the short time span of our interest (a CCH interval) [36]. For example, in 50 ms, when vehicles travel in the same direction, vehicles move a very few meters forward (typically, less than 1 m in a city and less than 2 m on a highway). Even considering vehicles moving in opposite directions, for example, on a highway, vehicles travelling at 130 km/h move 3.6 m apart in 50 ms._  
We also assume that transmission rate on the CCH and SCHs are constant and are the same. The non-safety messages on the SCHs have the same size, which means that all the non-safety messages occupy the same length of transmission time.