This paper presents a study based on the probabilistic dynamic model PDM / MDP with application in TCAS. The algorithm for solving PDM is analysed and also it presents the first step focused by discretizing the state space model. The MDP is evaluated to predict the state space at the next time step for the adequate set of operations. The conformity with the least expected cost criterion allows a better action from that state space. The DP algorithm involve all potential trajectories in the state space and features the selection of the most probable trajectory from the global set. The number of potential trajectories increases exponentially in the time horizon, and hence in case of mathematical models, it is not proposed to string each potential trajectory. In the collision avoidance MDP, the number of predictable trajectories exceeds the number of particles in the universe, however DP can establish all the required data in quick numerical computations. If an aircraft equipped with TCAS receives a traffic alert from other aircraft with TCAS, it will broadcast a coordination message report to the other aircraft instructing it to neither descend nor climb, as being most acceptable. If both aircraft will choose conflicting actions simultaneously, the aircraft with the higher rank from identification number needs to turn out the direction of its advisory. In the case study when an aircraft is receiving instructions from another aircraft not to descend or climb it is powerfully advised to o level off. The results of the analysis carried on in this study are consistent with the real time operations.