| Abstract: |
| In this talk, I will present a recursive algorithm developed to solve stationary critical congestion mean-field games (MFGs) on networks. These games model scenarios where a large number of agents move through a network -- such as transportation systems -- seeking to minimize costs based on their actions and the congestion created by others. The MFG formulation leads to an algebraic system consisting of linear equations, inequalities, and complementarity conditions.
The algorithm I will discuss handles the complexity of the problem. We implement preprocessing steps that reduce the system`s size and complexity, along with a custom approach for managing the combinatorial challenges at key network nodes. However, the recursive nature of the algorithm introduces some limitations, particularly with regard to scalability.
I will illustrate the algorithm`s performance using several case studies, including road merges and forks, and a real-world scenario inspired by the Jamarat bridge during the Hajj pilgrimage. Finally, if time permits, I will discuss the challenges posed by non-critical congestion cases and explore future directions for improving the algorithm`s efficiency and applicability. |
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