Recovering scheduling preferences in dynamic departure time models

We aim to infer commuters' scheduling preferences from their observed arrival times, given an exogenous traffic congestion pattern. To do this, we employ a structural model that characterizes how users balance congestion costs against the penalties for arriving early or late relative to an ideal time. In this framework, each commuter selects an arrival time that minimizes her overall trip cost by considering the within-day congestion pattern along with her individual scheduling preference. By incorporating the distribution of these preferences and desired arrival times across the population, we can estimate the likelihood of observing arrivals at specific times. Using synthetic data, we then apply the maximum likelihood estimation (MLE) method to recover the parameters of the joint distribution of scheduling preferences and desired arrival times. Our numerical results demonstrate the effectiveness of the proposed method.