Recently, the bus rapid transit (BRT) systems have been implemented around the world as an efficient and low cost mass public transportation alternative. While studying such systems, a common assumption has been that the user knows and uses the fastest route every time. Therefore, this paper has two main objectives. The first objective is to model the interactions within a BRT system station, modelling the decision making process of each user independently with a cost function in which he is able to take a decision depending on different variables such as the average utilization of a bus or the time arrival of the next scheduled bus. The second objective is incorporating the stochastic nature of input data, such as arrival rates, origin-destination matrix or service time into the model. Using this model logic a complete system can be built. Thereby, investigations that mean to improve the performance of the system can be tested considering the stochastic behavior of the users during the route plan decision making process.