## 3 MJTAR Protocol
### E-IFTIS Overview
#### 3.3.5. CPP Management Table Update Procedure  
This section presents a method for vehicle V7 to update the value of each field configured in the CPP management table after the timer ends. Initially, the amount of pheromone (\(\tau_{ij}\)) for a 1-hop candidate junction is determined according to Equations (1)-(4). In Equation (1), \(N_{avg}\) represents the average pheromone value in each cell. \(N_{c}\) denotes the number of cells between \(J_{i}\) and \(J_{j}\), while \(N_{i}\) signifies the amount of pheromone in one cell. For this study, it is assumed that the amount in each vehicle is uniform and set to 1.  
\[\left(N_{avg}=\frac{1}{N_{c}}*\sum_{i=1}^{N_{c}}N_{i}\right) \tag{1}\]  
In Equation (2), \(\sigma\) is the standard deviation of the amount of pheromone distributed over all cells between \(J_{i}\) and \(J_{j}\). The standard deviation indicates how far away it is from \(N_{avg}\). A large standard deviation indicates that the cell density is far from the mean, while a small standard deviation indicates that the cell density is clustered closely around the mean.  
\[\sigma=\sqrt{\left(\frac{1}{N_{c}}*\left(\sum_{i=1}^{N_{c}}\left(N_{i}-N_{avg} \right)^{2}\right)\right)} \tag{2}\]  
In Equation (3), \(\tau_{ij}^{v}\) represents the formula for calculating the total pheromone amount between \(J_{i}\) and \(J_{j}\). \(N_{con}\) denotes the theoretical pheromone constant for the cell, set to 12 in this study. \(\phi\) represents an expression mimicking the evaporation effect of pheromone over time, as illustrated in Equation (4). Consequently, when a CPP packet reaches the current junction (\(J_{i}\)), it undergoes a penalty proportional to its experienced delay, reducing the pheromone amount.  
\[\tau_{ij}^{v}=\min\biggl{[}\biggl{\{}(1-\phi)*\frac{1}{\sigma+1}*\frac{\text{ N}_{avg}}{\text{N}_{\text{con}}}\biggr{\}},1\biggr{]} \tag{3}\]  
\[\phi=packet\_recv\_time_{cpp\_master}-packet\_send\_time_{cpp\_master} \tag{4}\]  
The pheromone amount (\(\tau_{jk}\)) for the 2-hop candidate junction is determined using Equations (1)-(4) in a similar manner. The proximity to the next destination (\(Dp_{j}\)) can be computed utilizing Equations (5) and (6). The following notation is defined to facilitate the calculation of the proximity to the next destination.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Notation** & **Description** \\ \hline \(J_{i}\) & Current Junction ID \\ \(J_{j}\) & 1-Hop Neighbor Junction ID \\ \(\tau_{ij}\) & Amount of pheromone scattered between the current junction \\  & and 1-hop junction \\ \(Dp_{j}\) & Closeness of 1-hop junction to destination \\ \(route\_p_{ij}\) & Optimal route probability for neighbor 1-hop junction \\ \(I_{k}\) & 2-Hop Neighbor Junction ID \\ \(\tau_{jk}\) & Amount of pheromone scattered between the current junction \\  & and 2-hop junction \\ \(Dp_{k}\) & 2-hop junction to destination closeness \\ \(route\_p_{ij}\) & Optimal route probability for neighbor 2-hop junction \\ \(route\_p_{k}^{group\_sum}\) & Group and sum the probabilities of 2-hop junctions that are in a neighbor relationship with 1-hop junctions \\ \(d_{j}(x,y)\) & Curve metric distance to destination \\ \(D_{i}\) & Curve metric Distance from the current junction to the destination \\ \(D_{j}\) & Curve metric Distance from 1-hop junction to destination \\ \(D_{k}\) & Curve metric Distance from 2-hop junction to destination \\ \hline \hline \end{tabular}
\end{table}
Table 2: Notation description.  
\(D_{i}\), \(D_{j}\), and \(D_{k}\) can obtain the curve metric [22] distance to the destination using the following Equation (5).  
\[d_{j}(x,y)=\sum_{j=1}^{m}\left|\begin{array}{l}x_{j}-y_{j}\end{array}\right| \tag{5}\]  
\[Dp_{j} =D_{j}/\mathrm{D_{i}} \tag{6}\]  
\[Dp_{k} =D_{k}/\mathrm{D_{i}} \tag{7}\]  
The proximity (\(Dp_{j}\)) between the 1-hop candidate junction and the destination is determined using Equation (6), while the proximity (\(Dp_{k}\)) between the 2-hop candidate junction and the destination is calculated using Equation (7).