  Departure time choice models play a crucial role in determining the traffic
load in transportation systems. This paper introduces a new framework to model
and analyze the departure time user equilibrium (DTUE) problem based on the
so-called Mean Field Games (MFGs) theory. The proposed framework is the
combination of two main components including (i) the reaction of travelers to
the traffic congestion by choosing their departure times to optimize their
travel cost; and (ii) the aggregation of the actions of the travelers, which
determines the congestion of the system. The first component corresponds to a
classic game theory model while the second one captures the travelers'
interactions at the macroscopic level and describes the system dynamics. In
this paper, we first present a continuous departure time choice model and
investigate the equilibria of the system. Specifically, we demonstrate the
existence of the equilibrium and characterize the DTUE. Then, a discrete
approximation of the system is provided based on deterministic differential
game models to numerically obtain the equilibrium of the system. To examine the
efficiency of the proposed model, we compare it with the departure time choice
models in the literature. We observe that the solution obtained based on our
model is 5.6\% closer to the optimal ones compared to the solutions determined
based on models in the literature. Moreover, our proposed model converges much
faster with 87\% less number of iterations required to converge. Finally, the
model is applied to the real test case of Lyon Metropolis. The results show
that the proposed framework is capable of not only considering a large number
of players but also including multiple preferred travel times and heterogeneous
trip lengths more accurately than existing models in the literature.
