The Traffic Assignment Problem is a central problem in transportation systems science and has been widely studied throughout the years. The objective of the TAP objective is to find an optimal allocation of traffic so that an aggregate cost function (e.g., the total travel time) of all users in the transportation network is minimized (social optimum). In real-life transportation networks the flow that travels across a road changes over time and this leads to dynamic formulations of the TAP. In particular, the Dynamic Traffic Assignment (DTA) problem is a optimal control problem that entails optimizing dynamic routing and network flows over given transportation network and time horizon.