Passenger transportation planning is important to reduce the emission of contaminants and expenses involved in the operation of vehicles used for this purpose. Determining the optimal number of vehicles to provide an efficient transportation service is required. While transportation logistics currently supports advanced and complex methods to address this situation, an alternative method can be more appropriate for interurban passenger transportation.  In this paper a mathematical model is presented for fast estimation of (a) the number of transportation services to be scheduled per hour, (b) the number of transportation services to be performed by each vehicle, and (c) the number of vehicles to perform all transportation services. Factorial analysis and computer simulation were considered for static and dynamic assessment of the mathematical model. Experiments with numerical examples showed that the parameters estimated with the model are reliable if variability is already considered within the main variables of the model such as transportation time and number of incoming passengers.