# Junction Selection Based on Optimal-Weighted Multiple Attributes for VANETs
## 2 System Model  
For the proposed model, the MADAM-based junction selection algorithm and mathematical model are used [15]. It considers the distance, traffic density, and angle between the candidate junction to the destination junction in the path selection process [16]. Note that the distance is the geographical distance from the candidate junction to the destination junction [17], the traffic density is defined as the number of vehicles on the road segment, and the angle is defined as the angle between the current junction and the candidate junction towards the destination junction [16]. The main goal of the proposed protocol is to guarantee that the routing path has more connectivity within city environments, which ensures an increase in the packet delivery ratio and a significant decrease in the end-to-end delay. The early version of the manuscript with the title \"Intelligent junction selection considering multiple attributes in position-based VANET routing\" is submitted to IET Technical Review. The proposed technique considered the static weights for distance and speed [18]. The assumptions of the proposed protocol are  
* Every vehicle is supported with a GPS device to obtain its position. * The sending node is aware of the current location of the destination node via the hierarchical location system (HLS). * Each vehicle knows its direction and velocity. * Every vehicle knows the traffic density between two junctions by using a traffic sensor. The optimal junction selection process is explained below:  
_Step 1: Create the standardized decision matrix \(D\)._  
In Equation (1); \(1,2,...,n\) represents all of the candidate junctions, and \(P1,P2,P3\) represent the distance, traffic density, and angle, respectively. \(\alpha,\beta,\gamma\) is the original data of distance, traffic density, and angle that the forwarding vehicle obtains from each candidate junction. \(N\in N1,N2,...,Nn\), whereas N represents the junction number. The decision matrix is shown below in Equation (1):  
\[D_{(x_{ij})}= \begin{bmatrix}P_{1}&P_{2}&P_{3}\\ \alpha_{1}&\beta_{1}&\gamma_{1}\\ \alpha_{2}&\beta_{2}&\gamma_{2}\\...&...&...\\ \alpha_{n}&\beta_{n}&\gamma_{n}\end{bmatrix}\begin{bmatrix}N1\\ N2\\ N3\end{bmatrix}  \tag{1}\]  
_Step 2: Create the normalized matrix \(D^{*}\)._  
Let \(P_{j}^{*}=\max_{l\leq i\leq m}(x_{ij})\) and \(P_{j}^{\circ}=\min_{l\leq i\leq m}(x_{ij})\) denote the maximum and minimum values in matrix D, respectively. x represents the attributes \(\alpha,\beta\), or \(\gamma\) in matrix D, whereas i represents a row and j represents a column in matrix D. This computation is done using the following equation. Here, \(\overline{X_{ij}}\) represents the normalized value of Equations (2) and (3). \[BenefitCriteria:\overline{X_{ij}}=\frac{x_{ij}}{\sqrt{\sum_{j=1}^{n}x_{ij}^{2}}} \tag{2}\]  
\[CostCriteria:1-\overline{X_{ij}}=\frac{x_{ij}}{\sqrt{\sum_{j=1}^{n}x_{ij}^{2}}} \tag{3}\]Then, the normalized matrix \(D^{*}\) of Equation (4) is calculated as below; the \(\alpha^{*}\), \(\beta^{*}\), \(\gamma^{*}\) are the normalized attribute value:  
\[D^{*}(x_{ij})= \begin{bmatrix}\alpha_{1}^{*}&\beta_{1}^{*}&\gamma_{1}^{*}\\ \alpha_{2}^{*}&\beta_{2}^{*}&\gamma_{2}^{*}\\...&...&...\\ \alpha_{m}^{*}&\beta_{m}^{*}&\gamma_{m}^{*}\end{bmatrix}  \tag{4}\]  
_Step 3: The normalized matrix should be weighted in this step._  
\(w_{1}\), \(w_{2}\), \(w_{3}\) are optimized weight values for each attribute in matrix \(Z\), as shown in Equation (5). We obtain this optimal weight value from the simulation. In the original TOPSIS, users can determine the optimal weight value for each parameter. If an on-road user is not available to allocate weight to the selected parameters, then the default weights value is applied. This means that the forwarding vehicle has to determine the weight value whenever it selects the next junction. Otherwise, the default value is applied. However, the default weight may have a certain impact on the accuracy. So, it is worth paying attention to the weight value assignment for each parameter.