Travel time uncertainty is an inevitable part of our daily commutes. Empirical surveys have confirmed that travel time uncertainty/reliability play an important role in travelers' route and departure time choice making process. However, most of the conventional traffic assignment or departure time scheduling studies did not adequately address the stochastic nature of travel time, so as the role of uncertainty in travel decision making. This thesis is proposing a reliability-dependent travel choice model, which assumes travelers' are aware of the chance of punctual arrivals associated with their route and departure time choices. Punctuality-conscious travelers interacts with each other in network equilibrium models, which explicitly considers of travel time uncertainties arising from random capacity degradation, demand fluctuations as well as exogenous sources. By taking into account travel time uncertainty and reliability-dependent travel behavior in network equilibrium models, substantial difference can be found in the predicted link use pattern, network links congestion, time of occurrence of morning peak as well as the congestion profile over time. The equilibrium models developed in this thesis serve as evaluation platforms in analyzing various network optimization strategies under travel time uncertainty, for example network links capacity expansion or reliability enhancement, demand management via road pricing and traffic information provisions. This thesis is expected to make a theoretical contribution to travel behavior modeling by introducing punctuality reliability as a decision criterion. With a proper understanding to travelers' choice behavior, coupled with explicit consideration of stochasticity in travel time, a more realistic representation of transportation system can be formulated. Broadening travel behavior models and equilibrium models with the uncertainty dimension is opening up a theoretically interesting yet practically important area for transportation network studies.