Optimal Control for Traffic Flow Networks

Gugat, Martin; Herty, Michaël; Klar, Axel; Leugering, Günter

doi:10.1007/s10957-005-5499-z

Cited by 117 publications

(66 citation statements)

References 16 publications

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“…Various optimization problems for traffic flow, based on the Lighthill-Whitham conservation law model, have been considered in [9,10,11,12]. Global optima and equilibria for a different kind of transport problem were recently studied in [5], also providing results on the asymptotic stability of Nash equilibria.…”

Section: Introductionmentioning

confidence: 99%

Optima and Equilibria for a Model of Traffic Flow

Bressan¹,

Han²

2011

SIAM J. Math. Anal.

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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 time and on the arrival time 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 solution. The analysis also yields a strategy for optimal toll pricing.

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Section: Introductionmentioning

confidence: 99%

Optima and Equilibria for a Model of Traffic Flow

Bressan¹,

Han²

2011

SIAM J. Math. Anal.

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“…Various optimization problems for traffic flow, based on the Lighthill-Whitham conservation law model, have been considered in [8,9,10,11]. For an introduction to differential games and for recent applications to traffic flow on networks we refer to [6] and [7], respectively.…”

Section: Introductionmentioning

confidence: 99%

Nash equilibria for a model of traffic flow with several groups of drivers

Bressan

Han

2012

ESAIM: COCV

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Traffic flow is modeled by a conservation law describing the density of cars. It is assumed that each driver chooses his own departure time in order to minimize the sum of a departure and an arrival cost. There are N groups of drivers, The i-th group consists of κ i drivers, sharing the same departure and arrival costs ϕ i (t), ψ i (t). For any given population sizes κ 1 , . . . , κ n , we prove the existence of a Nash equilibrium solution, where no driver can lower his own total cost by choosing a different departure time. The possible nonuniqueness, and a characterization of this Nash equilibrium solution, are also discussed.

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“…Traffic congestion leads to a strong degradation of the network infrastructure and accordingly reduced throughput, which can be countered via suitable control measures and strategies. Some optimization problems for road networks modeled by fluid-dynamic approach have been already studied: Helbing et al (2005) is devoted to traffic light regulation, while Gugat et al (2005) and Herty et al (2003) are more related to our analysis but focus on the case of smooth solutions (not developing shocks) and boundary control. A specific traffic regulation problem is addressed in Chitour & Piccoli (2005).…”

Section: Introductionmentioning

confidence: 99%