## 3 Proposed Methodology
### Estimation of Link Delay
Thus, by substituting \(t_{control,ij}\) into Equation (7), Equation (10) can be derived, which shows the total one-hop delay of the \(i\)th node using the wired communication channel (\(\mathcal{D}_{iW1}\)) when CSMA-CD is implemented, which does not have flow control:  
\[ \begin{split}\mathcal{D}_{iW1}&=\sum_{j=1}^{K}(t_{ trans,ij}+t_{cont,ij}+t_{proc,ij}+t_{control,ij}+t_{prop,ij})\\ &=\sum_{j=1}^{K}(t_{trans,ij}+t_{cont,ij}+t_{proc,ij}+0+t_{prop,ij})\\ &=\sum_{j=1}^{K}(t_{trans,ij}+t_{cont,ij}+t_{prop,ij}+t_{proc,ij}) \end{split}  \tag{10}\]  
As the propagation delay is independent of packet size and for the special case of equal packet size, Equations (9) and (10) can be simplified further to obtain the delay Equations applicable for routing in this research, as given in Equation (11) for CSMA-CA and Equation (12) for CSMA-CD:  
\[\mathcal{D}_{iWL}=K\times(t_{trans,i}+4t_{proc,i}+t_{trs}+t_{tts}+t_{ack})+\sum _{j=1}^{K}(t_{cont,ij}+4t_{prop,ij}) \tag{11}\]  
Equation (11) computes the delay in the DSRC communication channel (IEEE 802.11p) as it implements a stop-and-wait with RTS-CTS flow control for CSMA-CA. \[\mathcal{D}_{iW1}=K\times(t_{trans,i}+t_{proc,i})+\sum_{j=1}^{K}(t_{cont,ij}+ t_{prop,ij}) \tag{12}\]  
Equation (12) computes the delay in the Ethernet communication channel that exists between the RSUs, as it implements a stop-and-wait without RTS-CTS flow control for CSMA-CD. Contention delay occurs in vehicular networks due to simultaneous transmission attempts by multiple nodes to send a packet to a particular destination using the same communication channel. In such a scenario, transmission will be delayed by a random back-off time determined by the minimum and maximum contention window sizes. The contention delay for the \(j\)th packet in the queue of the \(i\)th node (\(t_{cont,j}\)) is given by Equation (13):  
\[t_{cont,ij}=t_{frame\ space}+BO_{ij}+t_{collision,ij} \tag{13}\]  
In Equation (13), \(t_{frame\ space}\) is Distributed Inter-Frame Space (DIFS) (which is a constant in CSMA-CA) or \(t_{frame\ space}\) is Inter-Frame Gap (IFG) in CSMA-CD, \(BO_{ij}\) refers to the total back-off time for transmitting the \(j\)th packet in the queue of node \(i\), and \(t_{collision,ij}\) is the total time during which collision occurs during the transmission of the \(j\)th packet. However, it is not possible to exactly predict \(t_{cont,ij}\), as it causes nodes to back off for a random amount of time for a given packet \(j\) (due to \(BO_{ij}\)) before the channel is inspected again for transmission. Therefore, when there is high contention, it is difficult to predict the exact total delay, as the contention delay that occurs at routing time is random in nature. However, [PERSON] et al. in [61] approximated an average theoretical value for contention delay by modeling it as a function of collision probability. Using Equation (13), the average value of contention delay of the node \(i\) (\(\overline{t_{cont,i}}\)) for transmitting the \(j\)th packet in the queue can be written as given in Equation (14):  
\[\overline{t_{cont,ij}}=t_{frame\ space}+\overline{BO_{ij}}+\overline{t_{ collision,ij}} \tag{14}\]Work in [61] derived \(\overline{t_{cont,ij}}\) by modeling average back-off time (\(\overline{BC_{ij}}\)) as a function of collision probability (\(\rho\)). Even though they computed an average theoretical value using collision probability, such work fails to present how exactly the collision probability is found practically. In this research, we investigate factors contributing to collision probability, use these to model collision probability, and then compute collision probability, as explained in the following subsections.