# Congestion-Free Ant Traffic: Jam Absorption Mechanism in Multiple Platoons
## 2 Model and Simulation Scenario  
### Model  
Ants on a trail communicate with each other by chemotaxis: as they move forward on the trail, the ants drop and sense chemical substances known as pheromones [10; 21; 22; 23]. The ants'movements depend on the local pheromone concentration ahead of them, which they detect with their antennae [10; 21]. Physiological studies of ants and other insects show that the antennae-detected pheromone concentration is converted into a self-propelling force [10; 21; 22; 23; 24; 25]. This force increases with the pheromone concentration until the concentration \((\sigma_{sat})\) that saturates the antennae [10; 21; 24; 25]. The antennae cannot detect any further increase in concentration above \(\sigma_{sat}\), and the propulsion force for concentrations beyond saturation remains approximately that at saturation [10; 24; 25]. Based on the aforementioned chemotaxis behavior of ants, we present an agent-based model of the behavior of ants on a unidirectional single-lane ant trail (the ant-trail model (ATM)). As explained earlier, our model is an improvement on the model by [9]. The model in [9] was analyzed using cellular automaton. However, considering that the observations of individual ants are an integral part of our analysis, we chose agent-based modeling. For the simulations, we used NetLogo as the modeling platform, which is a multi-agent programmable modeling environment [28]. The model in NetLogo comprises two types of agent, namely (i) stationary agents representing the cells of the trail (environment in the model) and (ii) moving agents representing the ants. Each cell of our one-dimensional ant trail can accommodate, at most, one ant at any time step (see Figure 1). The cells are labeled by the index \(i\) (\(i=1,2,\ldots,L\)), where \(L\) is the length of the trail. We associate the following three numerical variables with each cell. * The binary variable \(s_{i}(t)\) is either zero or one depending on whether the cell is empty (zero) or occupied (one) by an ant at time step \(t\). * The pheromone concentration \(\sigma_{i}(t)\) is a numerical variable ranging from zero to \(\sigma_{\text{sat}}\). \(\sigma_{i}(t)=0\) means that there is no pheromone in cell \(i\) at time step \(t\), whereas \(\sigma_{i}(t)=\sigma_{\text{sat}}\) means that the cell is saturated with pheromone at that time step. * \(\Omega_{i}\) represents a resistance or drag that the cells present against the ant motion. \(\Omega_{i}\) represents factors related to trail conditions such as obstacle, rough trail, or uphill, which have a negative impact on the motion of ants. In short, \(\Omega_{i}\) provides opposition to the motion in the preferred direction, which is represented in ATM by a negative velocity (velocity in the opposite direction). In a given simulation, \(\Omega_{i}\) is constant for a given cell. To avoid ants moving backwards, \(\Omega_{i}\) is designed to always be positive, but less than the non-zero minimum ant velocity \((v_{min})\) (as explained later, \(\Omega_{i}\) is used while defining the heterogeneous trail.). As shown in Figure 1, the ants are also labeled with a unique number \(j\) (\(j=0,1,2,\ldots,N\)), where \(N\) is the total number of ants in the simulation at the time of measurement (as explained later, the number of ants changes over time). Each ant has the following two associated variables:  
* \(v_{j}(t)\) is the instantaneous velocity of ant \(j\) at time step \(t\). \(v_{j}(t)\) is continuous and ranges from zero to one. * \(p_{j}(t)\) is the position of ant \(j\) on the trail at time step \(t\) and ranges from zero to \(L\). Similar to \(v_{j}(t)\), \(p_{j}(t)\) is also continuous. All the parameters from the model are summarized in Table 1. For the ATM simulations in the paper, we assumed that: (i) ants do not move backwards; (ii) the probability of forward motion is  
Figure 1: Schematic representation of the ant-trail model (ATM), showing a single-lane unidirectional ant trail from left to right. Each cell is indexed by \(i\), and each ant is indexed by \(j\).