I propose a series of tools to model travelers’ time-of-day choice in continuous time. The models discussed in this dissertation can help advancing time-of-day modeling of trips or activities and produce demand with fine time resolution. These models are a good fit for dynamic traffic assignment and they can be applied for policy evaluation, travel management, and real-time applications. I first present the Continuous Logit (CL) model as the originator of a variety of discrete and continuous choice models and shed light on the relationship between some of the available choice models and CL by showing how these models can be seen as approximations to the CL. I also demonstrate how different approximation techniques can lead to new forms of choice models. I conduct Monte Carlo experiments to study the magnitude of error in the approximated models. These experiments can help the reader better understand the implications of various approximation and discretization schemes for time-of-day modeling.

Due to the limits of CL in modeling correlations, I introduce and formulate the AutoRegressive Continuous Logit (ARCL) as a novel continuous class of choice models capable of representing correlations across alternatives in the continuous spectrum. I formulate this model by considering two approaches: combining a discrete-time autoregressive process of order one with the CL model, and combining a continuous-time autoregressive process with the CL model. ARCL is the only Random Utility Maximization-based continuous choice model, besides the Continuous Cross-Nested Logit (CCNL), able to handle correlations across alternatives in the continuous spectrum.

I extend the continuous time-of-day modeling to multi-dimensional case by introducing a framework to model the joint choice of arrival to an activity and departure from the activity. Each choice is modeled in continuous time using CCNL. I use Copula to capture the correlation between the two dependent choices. Copula can model the correlation structure without knowing the actual bivariate distribution function. With its multidimensionality and ability to capture different sorts of correlations and model demand in fine time resolution, the introduced framework can provide a sufficient tool for the time-of-day component of various travel demand models.