## 3 Proposed Methodology
### Estimation of Link Delay
#### 3.3.1 Investigating the Factors Affecting Collision Probability to Formulate an Average  
A collision occurs when multiple transmitting agents contend for the use of the same communication channel. Therefore, the number of neighbors of a given node using the same communication channel should directly contribute to collisions. Accordingly, connectivity of the same communication channel of the network, which we formulate as normalized network per channel link entropy (\(H_{channel}\)), is the first factor affecting collision probability, where the channel is either wireless or wired. Now, let us compute per-channel network link entropy (\(H_{channel}\)). The normalized link entropy of a homogeneous network (\(H_{hom}\)) [62] can be calculated as given in Equation (15):  
\[Homogeneous\ Normalized\ Entropy\ (H_{hom})=\ \frac{\sum_{i=1}^{N}ln\ (N_{i})}{N \times ln(N-1)}\ ;N_{i}\
eq 0 \tag{15}\]  
Equation (15) has two variables: \(N\), which stands for the sum of nodes in the network, and \(N_{i}\), which stands for the degree of node \(i\), or the sum of neighbors of the \(i\)th node. Since homogeneous normalized link entropy (\(H_{hom}\)) is a normalized value, its value falls in the range [0, 1]. In Equation (15), isolated nodes with zero degrees (\(N_{i}=0\)) should not be replaced for \(N_{i}\); nonetheless, those nodes are taken into account when calculating the total number of nodes. However, \(H_{hom}\) is defined for a homogeneous network. The vehicular network is heterogeneous, as there exist mainly two types of links: wireless links and wired links. Thus, homogeneous entropy with respect to each type of link should be separately computed. The contention occurs only in the same communication channel. For example, when a packet is transmitted through Ethernet, it will not collide with a packet transmitted in the DSRC communication channel. The delay parameters also differ between wired and wireless links. If we classify wired and wireless links as identical links and compute normalized network entropy (\(H_{hom}\)), there may be cases where \(H_{hom}\) remains the same (degree or number of neighbors have not altered), but the proximity of nodes has evolved with respect to communication links. Consider, for instance, the network depicted in Figure 7, which consists of four automobile nodes and three RSU nodes. Both of the network examples in Figure 7 have the same homogeneous entropy (\(H_{hom}\)) if we assume that the network is uniform with regard to connections. However, Figure 7 clearly shows that the network's topology has altered in relation to wireless connections. As such, the effect of entropy change on a given type of link should be displayed in the collision probability calculation. Thus, we calculate the normalized homogeneous link entropy with respect to wireless links (\(H_{WL}\)) and wired links (\(H_{WI}\)) separately, as given in Equations (16) and (17), respectively:  
\[H_{WL}=\frac{\sum_{i=1}^{N}ln\ (N_{iWL})}{N\times ln(N-1)}\ ;N_{iWL}\
eq 0 \tag{16}\]  
In Equation (16), \(N\) is the total number of nodes (vehicles and RSUs) and \(N_{iWL}\) is the total number of wireless links in the neighborhood of node \(i\). Note that the denominator of Equation (16) consists of all possible wireless links that exist among vehicles and RSUs (all nodes). \[H_{WI}=\frac{\sum_{i=1}^{N}ln\ (N_{iWI})}{N_{r}\times ln(N_{r}-1)}\ ;N_{iWI}\
eq 0 \tag{17}\]In Equation (17), \(N_{r}\) is the total number of RSU nodes and \(N_{iWI}\) is the total number of wired links in the neighborhood of node \(i\). Note that the denominator of Equation (17) consists of all wired links, which exist only between the RSUs. As evident from the sample calculation for two network instances in Figure 7, the total entropy (\(H_{WL}+H_{WI}\)) is different for the two instances of the network.