## 3 MJTAR Protocol
### OMSS Overview  
The optimal multi-junction selection scheme (OMSS) introduced in this study is an algorithm designed to explore 2-hop junctions with highly connected roads using ACOs probabilistically. Figure 9 presents an example scenario to validate the OMSS algorithm's feasibility. In Figure 9, <x,y> denotes the junction location, and [number] indicates the number of vehicles traveling on each road. Let us consider that the source vehicle at J3 initiates the packet and forwards it to the destination vehicle at J14. The subsequent Table 3 illustrates an example of updating the junction ID, the pheromone amount, and the proximity to the destination for a 1-hop candidate junction and a 2-hop candidate junction. These computations are performed using Equations (1)-(8), followed by their update to the CPP management table. Junction Route Probability Procedure  
The source vehicle can compute the probability values for the 1-hop candidate junction and the 2-hop candidate junction using Equation (8). This calculation involves referencing the pheromone amount stored in the CPP management table and the proximity to the destination. \[route\_p_{ij}(t)=\left\{ \begin{array}{l}\frac{\left[\tau_{ij}(t)\right]^{*} \ast\left[\frac{1}{Dp_{j}}\right]^{\beta}}{\sum_{l\in all\text{network}} \left[\tau_{ij}(t)\right]^{*}\ast\left[\frac{1}{Dp_{j}}\right]^{\beta}}&if\ ij\in allowed _{y}\\ \\ 0&Otherwise\end{array} \right. \tag{8}\]  
\(\tau_{ij}(t)\) represents the amount of pheromone collected at time \(t\), and \(\frac{1}{Dp_{j}}\) is the inverse of the proximity to the destination. \(\alpha\) serves as a weighting factor for the pheromone amount, while \(\beta\) functions as a weighting factor for the proximity to the destination. In this study,  
Figure 9: An example scenario of urban streets. the weights of both \(\alpha\) and \(\beta\) are set to 1. Table 4 illustrates an example of the source vehicle updating the probability values for each 1-hop candidate junction and 2-hop candidate junction using Equation (8). The probability value increases with a relatively higher amount of pheromone and a lower distance weight to the destination. The 1-hop candidate junction, J8, has the highest probability of 0.4667. Meanwhile, the 2-hop candidate junction, J9--a neighbor to the 1-hop candidate junction--has the highest probability of 0.1489. However, the location of J9 is opposite from the destination, leading to increased packet latency. To address this issue, we group the probability values of 2-hop candidate junctions that share the same neighborhood relationship as 1-hop candidate junctions. Subsequently, we sum them up and store the result in \(route\_p_{jk}^{group\_sum}\). Then, we calculate the probability average of \(route\_P_{ij}\) and \(route\_p_{jk}^{group\_sum}\), as shown in Equation (9). \[p\_avg_{best}=\frac{selected\_p_{ij}(t)+route\_p_{jk}^{group\_sum}}{2} \tag{9}\]  
The values of the fields \(j_{i}\), \(j_{j}\), \(k_{route}\_P_{ij}\), and \(route\_p_{jk}^{group\_sum}\) are stored separately in the ant metrics table, along with the calculated average (\(p\_avg_{best}\)), as show in the following Table 5. Ultimately, the source vehicle selects the 1-hop junction and the 2-hop junction with the highest probability (\(p\_avg_{best}\)) from the ant metrics table.