A theoretical model for uni-directional ant trails

A theoretical model of uni-directional ant traffic, motivated by the motion of ants in trail is proposed. Two different type of ants, one of which smells very well and the other does not, are considered. The flux of ants in this model is investigated as functions of the probability of evaporation rate of pheromone. The obtained results indicate that the mean velocity of the ants varies non-monotonically with their density. In addition, it is observed that phase transition in the flux and the mean velocity vs. density occurs at certain density for a fixed evaporation rate. The effective hopping probability is investigated as well depending on the evaporation rate of pheromone. It is worth to note that the proposed model can be generalized for vehicular traffic on freeways.