This study aimed to understand demand of park-and-ride (PNR) during different times of day. Surprisingly, there is no significant research in the area of dynamic demand of PNR. To fill this gap, this study of PNR demand was done in three stages. First, to understand why PNR users choose one PNR lot versus another, PNR lot choice models were developed. PNR lot choice behaviour was studied using two decision constructs, random utility maximization (RUM) and random regret minimization (RRM). Second, in order to understand the nature of utilization of PNR lots, a discrete time hazard model was developed based on the car arrival data in the morning period, at PNR lots. Finally, mode choice models (including PNR as one of the modes) were prepared to understand the choice of PNR as a mode. From the developed lot choice models, it is understood that the PNR users' choice of PNR lot could also be explained by the RRM concept. In absence of any applications of RRM in PNR modelling, these new models serve as an important contribution. Further, the lot choice models suggested that the utilization of PNR lots is endogenous in nature. The identification of utilization as an endogenous variable is performed for the first time. The correction of endogeneity is completed using a two-stage control function method. Since the correction of endogeneity in the case of discrete choice transport models is a relatively new area, this work serves as additional evidence of the value of correcting for endogeneity using the control function method. This research modelled the utilisation of parking spaces using a discrete-time logistic regression model and calculated the probability that each parking space is occupied at the end of one of 60 time-intervals between 4:00am and 9:00am on a weekday. The findings from the model suggest that the probability of a parking space to be occupied increases with a larger capacity of the PNR lot, a larger number of public transport services, and a lower walking time to the platforms. Moreover, the results suggest that a parking space is more likely to be occupied in PNR lots farther from the CBD until 8.00am, but it is more probable to be occupied in PNR lots closer to the CBD from 8.00am onwards. Further, to understand the choice of PNR as a mode, mode choice models were prepared. With the aim of capturing a household's long-term decisions (like owing car, motorbike, bicycle etc.) on everyday short-term decision like mode choice, a portfolio-based multinomial logit framework was used to model the mode choice behaviour; where