  In 2002, Chowdhury et al. introduced a simplified model aimed at depicting
the dynamics of single-lane unidirectional ant traffic. Despite efforts, an
exact solution for the stationary state of this ant-trail model remains
elusive. The primary challenge arises from inherent fluctuations in the total
amount of pheromone along the ant-trail. These fluctuations significantly
influence ant movement. Consequently, unlike conventional models involving
driven interacting particles, the average velocity exhibits non-monotonic
behavior with ant density. In this study, we propose an exactly solvable model
for ant traffic whose dynamics is based on the one in Chowdhury et al.'s model,
and then discuss the circumstances under which the non-monotonic trend of
average velocity arises.
