Optima and equilibria for a model of traffic flow

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

The paper is concerned with the Lighthill-Whitham model of traffic flow, where the density of cars is described by a scalar conservation law. A cost functional is introduced, depending on the departure and arrival times of each driver. Under natural assumptions, we prove the existence of a unique globally optimal solution, minimizing the total cost to all drivers. This solution contains no shocks and can be explicitly described. We also prove the existence of a Nash equilibrium solution, where no driver can lower his individual cost by changing his own departure time. A characterization of the Nash solution is provided, establishing its uniqueness. Some explicit examples are worked out, comparing the costs of the optimal and the equilibrium solutions. The analysis also yields a strategy for optimal toll pricing.

Original languageEnglish (US)
Pages (from-to)2384-2417
Number of pages34
JournalSIAM Journal on Mathematical Analysis
Volume43
Issue number5
DOIs
StatePublished - Nov 21 2011

Fingerprint

Traffic Flow
Driver
Equilibrium Solution
Costs
Scalar Conservation Laws
Time of Arrival
Nash Equilibrium
Model
Pricing
Shock
Conservation
Railroad cars
Uniqueness
Optimal Solution

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

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Optima and equilibria for a model of traffic flow. / Bressan, Alberto; Han, Ke.

In: SIAM Journal on Mathematical Analysis, Vol. 43, No. 5, 21.11.2011, p. 2384-2417.

Research output: Contribution to journalArticle

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