Departure Time Choice Models in Congested Transportation Systems Based on Mean Field Games

Mostafa Ameli, Mohamad Sadegh Shirani Faradonbeh, Jean-Patrick Lebacque, Hossein Abouee-Mehrizi, Ludovic Leclercq

Published 2021-01-06Version 1

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.