Incidents and rolling stock breakdowns are commonplace in rapid transit rail systems and may disrupt the system performance imposing deviations from planned operations. A network design model is proposed for reducing the effect of disruptions less likely to occur. Failure probabilities are considered functions of the amount of services and the rolling stock's routing on the designed network so that they cannot be calculated a priori but result from the design process itself. A two recourse stochastic programming model is formulated where the failure probabilities are an implicit function of the number of services and routing of the transit lines.
Codina, E., Marín, Á., & Cadarso, L. (2014). Robust infrastructure design in rapid transit rail systems. In Transportation Research Procedia (Vol. 3, pp. 660–669). Elsevier. https://doi.org/10.1016/j.trpro.2014.10.045