# Performance Analysis of the IEEE 802.11p Multichannel MAC Protocol in Vehicular Ad Hoc Networks
## 4 Analytical Model and Performance Analysis
### Virtual Collision Handling in EDCA  
According to the specification in IEEE 1609.4 standard [6], each station has four AC queues (virtual queues) acting as four independent virtual stations. Each frame is mapped into an AC queue with a specified priority. When more than one AC queue (virtual queue) of a station initiates a transmission at the same time, the virtual collision occurs. The frame with highest priority is scheduled and transmitted, and the frames with lower priorities enter another backoff stage with doubled CW immediately. If the number of the retransmissions reaches the retry limit, the packet will be dropped. Note that we only discuss two kinds of packets such as safety-related packet with higher priority mapped into AC\({}_{0}\) queue and WSA packet with lower priority mapped into AC\({}_{1}\) queue on the CCH in this paper, as shown in Figure 5. Each virtual queue corresponding to one AC\({}_{i}(i\in[0,1])\), and the packets are coming from two queues: CCHI queue and SCHI queue. Collision may occur among different ACs in the same station (node) called virtual collision, and collision may occur among different nodes called external collision [37]. Let \(P_{i,vc}\) represent the virtual collision probability of an \(i(i\in[e,s])\) (i.e., \(e\) and \(s\) denote safety-related and WSA, respectively, and the following is the same) packet, and \(P_{oc}\) represent external collision probability. Therefore, the collision probability of an \(i(i\in[e,s])\) packet, \(P_{i,c}\), can be expressed as  
\[P_{i,c}=P_{i,vc}+(1-P_{i,vc})P_{oc} \tag{7}\]  
Let \(\tau_{i}\) be the internal transmission probability that the probability of transmission attempt for access class \(i(i\in[e,s])\) in a random time slot observed by the other ACs inside a station. A virtual collision occurs if there are higher priority ACs attempt to transmit in the same station, we have  
\[\left\{ \begin{array}{l}P_{e,vc}=0\\ P_{s,vc}=\tau_{e}\end{array} \right. \tag{8}\]  
Figure 5: Virtual collision inside a station. Let \(\eta_{i}\) be the external transmission probability that the probability of transmission attempt for access class \(i(i\in[e,s])\) observed by other stations. \(\eta_{i}\) can be expressed by  
\[\left\{ \begin{array}{ll}\eta_{e}=\tau_{e}(1-P_{e,yc})&=\tau_{e}\\ \eta_{s}=\tau_{s}(1-P_{s,yc})&=\tau_{s}(1-\tau_{e})\end{array} \right. \tag{9}\]  
Therefore, the total transmission probability of a station, \(\eta_{total}\), is calculated by  
\[\eta_{total}=\eta_{e}+\eta_{s} \tag{10}\]  
For a tagged vehicle, if one of the following conditions is not satisfied, the external collision occurs: (1) when the tagged vehicle is transmitting, no vehicles within its carrier-sensing range delivery packets at the same time slot; and (2) when the tagged vehicle is transmitting, no hidden terminals start transmission during the vulnerable period \(T_{vuln}\)[18; 38; 39], as shown in Figure 6. Each hidden terminal has chance to fail the transmission of the tagged vehicle to the target vehicle: the tagged vehicle starts sending while a hidden terminal is transmitting, or a hidden terminal starts sending while the tagged vehicle is transmitting. The vulnerable period \(T_{vuln}\) is the duration that, during this period, a collision caused by hidden terminals could happen, and it is the interval from the time instance when a hidden terminal is involved in an ongoing communication before the tagged vehicle starts its transmission to the time instance when the tagged vehicle completes its transmission. Therefore, \(T_{vuln}\) consists of two parts: packet transmission time of the hidden terminal and packet transmission time of the tagged vehicle. Let \(T_{e}\) (\(T_{s}\)) and \(E[L_{e}]\) (\(E[L_{s}]\)) denote the transmission delay and the average payload of a safety (WSA) packet, respectively, we have  
\[\left\{ \begin{array}{ll}T_{e}=\frac{H_{PHY}+H_{MAC}+E[L_{e}]}{R_{d}}+\delta \\ T_{s}=\frac{H_{PHY}+E[L_{s}]}{R_{d}}+\delta\end{array} \right.