DescriptionThis dissertation investigates different aspects of the reliability of a transportation system subject to random events by means of applied queueing theory. We use queueing models and fundamental principles of stochastic analysis, to shine light on the behavior and properties of a traffic system that is subject to random deteriorations of the quality of service as indicated by vehicular travel time. For this, we discuss stationary and transient analytical solutions for the number of customers and service-time distributions of Markov-modulated service rates queues. We also study analytically the effect that different random components of the system have in the completion time of a single trip. We are able to give closed form solutions to accommodate a number of different combinations of random variables as inputs of the system, as well as to give analytical insights on the asymptotic behavior when abnormally slow customers show up. We validate and calibrate the analytical models using incident reports and weather conditions as sources of traffic deterioration. We generate measures of the performance of the system with explicit dependencies on traffic and incident parameters, avoiding the use of costly simulation. We make use of these measures for optimizing risk-averse route choice problems. We expect our models contribute to the design and operation of management tools for roadway traffic and incident mitigation that can lead to safer and more efficient movement of people, goods, and other resources.