# Congestion-Free Ant Traffic: Jam Absorption Mechanism in Multiple Platoons
## 5 Analysis of Jam-Free Ant Traffic  
### Intra-Platoon Analysis  
In the early studies, it was argued that individual ants on a trail have convergent behavior, which leads to the formation of multiple platoons [26]. However, the more recent studies argued that not just individual ants, but also platoons have convergent behavior, and if given sufficient time, all the platoons merge to form a single platoon [5; 12; 14; 27]. It is also argued that ants inside a platoon march together (move with the same \(v_{j}(t)\)) [14]. As explained earlier, in the paper, the above two arguments--platoon formation and marching ants--are collectively called the marching platoon hypothesis. In the case of the marching platoon scenario, all the ants in the same platoon should have the same \(v_{j}(t)\). Therefore, to test the hypothesis, we observed the \(v_{j}(t)\) of different ants from the same platoon in an ATM simulation. For this analysis, we chose three ants (\(ant_{0}\), \(ant_{50}\), and \(ant_{100}\)) from the same notional platoon: \(ant_{0}\) was the leader of the platoon, while \(ant_{100}\) was the last ant in the platoon. The environment of the selected ants was kept undisturbed, and a simulation was carried out on a heterogeneous trail. In this scenario, \(L\) was 1000 units, of which the section from \(cell_{400}\)-\(cell_{800}\) was the high-resistance part (\(\Omega=0.1\)). Therefore, the junction between \(cell_{399}\) and \(cell_{400}\) marked the beginning of a bottleneck, and the junction between \(cell_{800}\) and \(cell_{801}\) marked its downstream end. Because the value of \(\Omega\) for the high-resistance section (\(\Omega=0.1\)) was higher than that for the low-resistance part (\(\Omega=0\)), we expected the \(v_{j}(t)\) of an ant in the high-resistance part to be lower than that of one in the other part of the trail. Therefore, changes in the velocities of different ants were observed with respect to the position of an ant on the trail. As shown in Figure 6, the velocity of the leading ant in the platoon decreased suddenly at the bottleneck (\(cell_{399}\)), whereas those of the other ants in the platoon decreased well before the bottleneck. This decrease in velocity before the bottleneck demonstrated queuing. At the same time, as shown in Figure 6, near the upstream of the bottleneck, ants showed a large velocity fluctuation, where the velocity fluctuated between zero (stop) and high velocity (go) due to the queuing effect. The fluctuation due to the queuing effect indicated stop-and-go motion upstream of the bottleneck. This happened because the flow out of the bottleneck (i.e., the flow from \(cell_{399}\)) was lower than the flow into it (i.e., the flow towards \(cell_{399}\)). This led to the formation of a queue, which forced incoming ants to reduce their velocity as they approached the bottleneck. For a given ant in a platoon, the more ants in front there were, the longer the queuing experienced. This means that ants in a platoon (other than the leader) do experience stop-and-go motion. It is also interesting to note that different ants in the platoon showed differing velocity variation: \(ant_{0}\) had a meager velocity variation where the velocity depended only on the trail conditions (\(\Omega\)), whereas the variations for \(ant_{50}\) and \(ant_{100}\) were much larger and far from identical. Contrary to previous perceptions, the above dissimilarity of velocity variation indicated that ants in a platoon do not march in sync. This desynchronizing behavior is consistent with the notion that the movements of ants on a trail is based on the pheromone concentration in the next cell, which depends on the flow of ants in the recent past. Therefore, ants cannot have real-time information about other ants in a platoon and so cannot synchronize their actions as a group. Figure 6: The instantaneous velocities of (**a**) \(ant_{0}\), (**b**) \(ant_{50}\), and (**c**) \(ant_{100}\) in the intra-platoon analysis plotted against the positions of the same ants.