Passenger waiting time at transit stops is an important component of overall travel time and is perceived to be less desirable than in-vehicle travel time or access time. Therefore, an accurate model to estimate waiting time is necessary to better plan for transit and to improve patronage. The majority of previous studies on waiting time have either made very limiting assumptions on the arrival distribution of passengers or lacked a large-scale and high-quality dataset. The smartcard fare collection system in South-East Queensland, Australia, has provided the opportunity of very large-scale and highly accurate data on passenger boarding and alighting times and locations. In this research, all 130,000 daily rail passengers in all 145 stations of a network are considered. First a methodology is developed to match each individual passenger with the most likely rail service he/she boarded. Then, a hazard-based duration modelling approach is adapted to model passenger waiting time as a function of a variety of factors that influence waiting time. Log-logistic accelerated failure time (AFT) models are inferred to be appropriate among the models tested. The results indicate that: (a) the waiting time can be predicted accurately at various confidence levels; (b) the waiting time at all network stations can be predicted with a single model; and (c) a wide range of influencing parameters are statistically significant in the model, which can be categorized to temporal, infrastructure and operation, demographics, and trip characteristics parameters. The results of this study can be used for demand estimation, operational analysis, transit scheduling, and network design through an understanding of the effects of influential variables on waiting time.