It is known that the Ant Colony Optimization (ACO) inspired from the collective behavior of real ants, and it is effective to find a better solution for the Traveling Salesman Problem (TSP). Rank based Ant System ASrank has been proposed as a developed version of basic Ant System. In the algorithm of ASrank, each agent in Ant System is ranked from the viewpoint outside the system as to the participation in pheromone update. Then, in spite of the fact that the collective behavior of real ants has inspired in constructing the algorithm of Ant System, ASrank as a developed version includes the viewpoint outside the system that does not exist in the actual ants’ swarm. Furthermore, there is a problem that it tends to be easy to fall into a local solution. In our study, we introduce the behavior observed in real ants’ experiments in order to construct a new algorithm of Ant System. That is, each ant agent in Ant System estimates its own rank by interaction with encountered agents to determine whether it should contribute to pheromone deposition. Therefore, we carried out exploring simulations in several TSP datasets, and we will show some analysis results that indicate the proposed model has superiority than ASrank.