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@article{TRB-18,
  title="Marginal Cost Pricing for System Optimal Traffic Assignment with Recourse under Supply-Side Uncertainty",
  JOURNAL={Transportation Research Part B: Methodological},
  year="2018",
  volume="110",
  pages="104-21",
  issn = "0191-2615",
  doi = "https://doi.org/10.1016/j.trb.2018.02.008",
  url = "https://www.sciencedirect.com/science/article/pii/S0191261516301540",
  author="Tarun Rambha and Stephen D.\ Boyles and Avinash Unnikrishnan and Peter Stone",
  abstract = {Transportation networks are often subject to
              fluctuations in supply-side parameters such as capacity
              and free-flow travel time due to factors such as
              incidents, poor weather, and bottlenecks. In such
              scenarios, assuming that network arcs exist in a finite
              number of states with different delay functions with
              different probabilities, a marginal cost pricing scheme
              that leads to a socially optimal outcome is
              proposed. The suggested framework makes the behavioral
              assumption that travelers do not just choose paths but
              follow routing policies that respond to en route
              information. Specifically, it is assumed that travelers
              are fully- rational and that they compute the optimal
              online shortest path assuming full-reset. However, such
              policies may involve cycling, which is unrealistic in
              practice. Hence, a network transformation that helps
              restrict cycles up to a certain length is devised and
              the problem is reformulated as a convex optimization
              problem with symmetric delay functions. The results of
              numerical tests on the Sioux Falls test network are
              presented using the Frank-Wolfe algorithm.
  },
  wwwnote = {Official version from <a href="https://www.sciencedirect.com/science/article/pii/S0191261516301540">Publisher's Webpage</a>},
}