Route choice behavior in traffic networks involves users selecting paths between origins and destinations, typically under the assumption of rational and self-interested decision-making. This gives rise to the concept of user equilibrium, where each user chooses the most convenient route for themselves. This equilibrium corresponds to Wardrop’s first principle, stating that travel times on all used routes are equal and no user can improve their travel time by unilaterally switching routes. At equilibrium, all users with the same origin and destination experience equal travel times, ensuring a form of fairness. However, individually optimal route choices may lead to inefficient outcomes at the system level, as the total travel time across the network may not be minimized. The system optimum, aligned with Wardrop’s second principle, represents a centrally coordinated traffic assignment that minimizes total travel time—potentially at the cost of fairness among users. The discrepancy between the efficiency of the system optimum and that of the user equilibrium is quantified by the Price of Anarchy, which measures the loss in overall performance due to selfish behavior in decentralized systems. It makes important both theoretically and practically to study the conditions imposed on the cost functions and the situations when the Wardrop (or Wardrop–Nash) equilibrium coincides with the system optimum. The aim of this paper is to give a survey of recent results on the so-called Wardrop optimal networks and their generalization called Wardrop-Schur optimal networks—networks in which selfish, non-cooperative user behavior leads to flow patterns that are already optimal from a system-wide perspective. In such networks, user equilibrium and system optimum coincide, the Price of Anarchy is equal to one, and traffic congestion is inherently mitigated. Throughout the paper, we also discuss future research and propose some open questions.

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Geometric, Dynamic, and Stochastic Analysis of Wardrop-Schur Optimal Transport Networks: Theory and Applications, and Open Problems

  • Armen Bagdasaryan

摘要

Route choice behavior in traffic networks involves users selecting paths between origins and destinations, typically under the assumption of rational and self-interested decision-making. This gives rise to the concept of user equilibrium, where each user chooses the most convenient route for themselves. This equilibrium corresponds to Wardrop’s first principle, stating that travel times on all used routes are equal and no user can improve their travel time by unilaterally switching routes. At equilibrium, all users with the same origin and destination experience equal travel times, ensuring a form of fairness. However, individually optimal route choices may lead to inefficient outcomes at the system level, as the total travel time across the network may not be minimized. The system optimum, aligned with Wardrop’s second principle, represents a centrally coordinated traffic assignment that minimizes total travel time—potentially at the cost of fairness among users. The discrepancy between the efficiency of the system optimum and that of the user equilibrium is quantified by the Price of Anarchy, which measures the loss in overall performance due to selfish behavior in decentralized systems. It makes important both theoretically and practically to study the conditions imposed on the cost functions and the situations when the Wardrop (or Wardrop–Nash) equilibrium coincides with the system optimum. The aim of this paper is to give a survey of recent results on the so-called Wardrop optimal networks and their generalization called Wardrop-Schur optimal networks—networks in which selfish, non-cooperative user behavior leads to flow patterns that are already optimal from a system-wide perspective. In such networks, user equilibrium and system optimum coincide, the Price of Anarchy is equal to one, and traffic congestion is inherently mitigated. Throughout the paper, we also discuss future research and propose some open questions.