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Optimal transport models passenger flow on networks. This study validates its empirical use on the Paris metro, revealing how different coupling functions impact traffic bottlenecks and resilience, offering insights for transportation network design.

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Area of Science:

  • Transportation Engineering
  • Network Science
  • Applied Mathematics

Background:

  • Optimizing passenger routes is essential for efficient transportation networks.
  • Optimal transport (OT) offers a promising alternative to standard optimization methods.
  • Empirical validation of OT on real-world engineering networks is needed.

Purpose of the Study:

  • To assess the empirical validity of optimal transport formulations on engineering networks.
  • To investigate the impact of different passenger interaction functions on network dynamics.
  • To compare OT performance against Dijkstra's algorithm and analyze network resilience.

Main Methods:

  • Implemented optimal transport formulation with two distinct coupling functions for passenger fluxes (sum and sum of squares).
  • Applied the models to the Paris metro network.
  • Analyzed traffic bottlenecks, infrastructure resilience to node removal, and compared with Dijkstra's algorithm.

Main Results:

  • The two coupling functions yield equivalent results in congested transport regimes but differ in branched regimes.
  • One function promotes route consolidation, potentially leading to traffic overload in branched networks.
  • Optimal transport networks demonstrate efficient recovery of shortest-path-like graphs and lie on the Pareto front of energy dissipation and infrastructure cost.

Conclusions:

  • Optimal transport is empirically valid for engineering networks, with coupling functions influencing network behavior.
  • The choice of coupling function significantly impacts traffic flow distribution and bottleneck formation.
  • OT provides a robust framework for analyzing network efficiency, resilience, and trade-offs between operational cost and infrastructure investment.