This paper presents an agent-based model of passenger rail services. It provides an algorithm that is able to find the optimal price and timetable for a service provided by a monopoly train operating company. For testing the efficiency of the algorithm, it presents a simplified setting in which the equilibrium price and timetable can be found analytically using the Salop model of competition. The paper finds that the algorithm approximates well the predicted price and timetable and that an increase in the equilibrium number of trains in the market reduces the efficiency of the algorithm.