# Congestion-Free Ant Traffic: Jam Absorption Mechanism in Multiple Platoons
## 4 Model Validation
For these \(d\) values, the log-normal distribution appeared to provide the best fit. The above observations related to distance headway and platoon formation were similar to the empirical observations in [14]. On the other hand, we also observed that there were no or very few ants who traveled with intermediate headways, especially for medium \(d\) values [0.2, 0.4]. This can be explained by platooning dynamics, where ants with intermediate or smaller headway accelerate due to the presence of pheromones until they catch up with preceding ants (platooning), whereas ants with a headway greater than an intermediate value do not experience pheromones, thus maintaining their velocity and avoiding joining a platoon ahead. This observation about the intermediate headway indicated that not all ants were converging to form a platoon. We also compared the velocity distribution of ants in ATM with data from [14]. As shown in Figure 5, similar to the empirical data from [14], the distribution became much sharper with an increasing global density, whereas the most probable velocity remained approximately constant. This happened because, as explained earlier, at higher \(d\) values, most of the ants traveled in platoons, where the velocity of an ant was governed by the velocity of the ants ahead, as well as the pheromone concentration in the next cell. At higher \(d\) values (inside the platoon), the maximum velocity of an ant was limited by the velocity of the ant ahead. At the same time, due to a high concentration of pheromones (in a platoon, due to the ants ahead, the given ant experienced a larger pheromone concentration), the \(v_{j}(t)\) of the given ant increased, which led to the scenario where most of the ants in the platoon traveled with a \(v_{j}(t)\) higher than \(v_{min}\) (as most of the ants experienced the pheromone concentration, no ants had deceleration due to a lack of pheromones, which led to a decrease in the overall number of ants who travel with \(v_{min}\)). The above two phenomena resulted in a decrease in the velocity fluctuation. Figure 4: _Cont._  
In conclusion, our model captured all the main features of ant traffic presented in [14]: (1) the absence of jamming for a wide range of \(d\) values, (2) platoon formations, and (3) a decrease in velocity fluctuations with an increase in the \(d\) value, showing that the present model can reasonably replicate empirical data and therefore mimic an AT system under certain limits. Meanwhile, the modeling assumptions from previous physiological studies validated that the agent in our model mimicked ants in real life. Figure 5: The velocity distribution of agents in different densities is plotted: \((\mathbf{a})\quad d\quad\in\quad[0,0.2]\), \((\mathbf{b})\quad d\quad\in\quad[0.2,0.4]\), \((\mathbf{c})\quad d\quad\in\quad[0.4,0.7]\). For all density ranges, the corresponding Gaussian distribution \((Frequency(y))\quad=\quad\frac{1}{\sigma\sqrt{2\pi}}e^{\frac{-(V-y)^{2}}{2\sigma^ {2}}}\) is also shown. Simulation scenarios: \(er=0.02\), \(L=1000\) cells, \(\sigma_{sat}=80\), \(v_{init}=0.15\).