Optima and
equilibria for traffic flow on networks
with backward propagating queues

Alberto Bressan; Khai T. Nguyen; Alberto Bressan; Khai T. Nguyen

doi:10.3934/nhm.2015.10.717

Networks and Heterogeneous Media

2015, Volume 10, Issue 4: 717-748. doi: 10.3934/nhm.2015.10.717

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Optima and equilibria for traffic flow on networks with backward propagating queues

Alberto Bressan ^{1
,},
Khai T. Nguyen ^{2
,}

1.
Department of Mathematics, Penn State University, University Park, Pa.16802
2.
Department of Mathematics, Penn State University, University Park, PA 16802

Received: 01 January 2015 Revised: 01 April 2015
Primary: 49K35, 35L65; Secondary: 90B20.

This paper studies an optimal decision problem for several groups of drivers on a network of roads. Drivers have different origins and destinations, and different costs, related to their departure and arrival time. On each road the flow is governed by a conservation law, while intersections are modeled using buffers of limited capacity, so that queues can spill backward along roads leading to a crowded intersection. Two main results are proved: (i) the existence of a globally optimal solution, minimizing the sum of the costs to all drivers, and (ii) the existence of a Nash equilibrium solution, where no driver can lower his own cost by changing his departure time or the route taken to reach destination.
- Traffic flows,
- network of roads,
- scalar conservation laws,
- global optima,
- Nash equilibria
Citation: Alberto Bressan, Khai T. Nguyen. Optima andequilibria for traffic flow on networkswith backward propagating queues[J]. Networks and Heterogeneous Media, 2015, 10(4): 717-748. doi: 10.3934/nhm.2015.10.717

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Abstract

This paper studies an optimal decision problem for several groups of drivers on a network of roads. Drivers have different origins and destinations, and different costs, related to their departure and arrival time. On each road the flow is governed by a conservation law, while intersections are modeled using buffers of limited capacity, so that queues can spill backward along roads leading to a crowded intersection. Two main results are proved: (i) the existence of a globally optimal solution, minimizing the sum of the costs to all drivers, and (ii) the existence of a Nash equilibrium solution, where no driver can lower his own cost by changing his departure time or the route taken to reach destination.

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