  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 system level of service. 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 apply
our framework to a standard test case and observe that the solutions obtained
based on our model are 5.6\% better in terms of relative cost compared to the
solutions determined based on models in the literature. Moreover, our proposed
model converges with less number of iterations than the reference solution
method in the literature. Finally, the model is scaled up to the real test case
corresponding to the whole Lyon Metropolis with real demand pattern. The
results show that the proposed framework is able to tackle much larger test
case than usual to includes multiple preferred travel times and heterogeneous
trip lengths more accurately than existing models in the literature.
