In recent empirical studies on values of time and reliability, many have suggested that travelers are interested not only in travel time saving but also in reduction in travel time variability. Variability introduces uncertainty for travelers such that they do not know exactly when they will arrive at their destination. Thus, it is considered as a risk (or an added cost) to a traveler making a trip. Continuing research is reported on route choice models and the effect on travel time reliability in an uncertain environment caused by demand and supply variations. The goal is to examine what the aggregate impact of changes in variability might be on network assignment and how travelers with different risk-taking behaviors respond to these changes.