Minor incidents such as signal failure and vehicle breakdown are common in day-to-day travel. These incidents cause random link capacity degradations, leading to travel time uncertainty. Over time, commuters take account of the routes' travel time variability and factor it into their route choice decisions. To hedge against this travel time uncertainty, travelers typically add a travel time margin to the expected travel time of a trip to form the travel time budget (i.e., the time set aside for the trip so as to maintain a preferred probability of punctual arrival). Nevertheless, in this learning process, commuters may experience perception variations in the traffic conditions that they actually encounter. To sum up, travelers face two types of uncertainty in their daily commutes: uncertainty in the actual travel time due to random link capacity degradations and perception variations in their travel time budget due to imperfect traffic information. In this study, a stochastic equilibrium was formulated to address both types of uncertainty. With this stochastic formulation as a platform, through a set of numerical studies, the effects of network link strengthening and traffic information provision were studied. The results showed that the provision of quality information was effective only in certain situations, whereas network link strengthening always improved system performance.