American Institute of Mathematical Sciences

Advanced
December  2007, 2(4): 569-595. doi: 10.3934/nhm.2007.2.569

Comparison of the performance of four Eulerian network flow models for strategic air traffic management

Dengfeng Sun 1, , Issam S. Strub 2, and  Alexandre M. Bayen 3,

1. 

604 Davis Hall, University of California, Berkeley, CA 94720-1710, United States
2. 

Systems Engineering, Civil and Environmental Engineering, 604 Davis Hall, University of California, Berkeley, CA 94720-1710, United States
3. 

Department of Civil and Environmental Engineering, 711 Davis Hall, University of California, Berkeley, CA 94720-1710, United States

Received  June 2007 Revised  September 2007 Published  September 2007

Four Eulerian network models are implemented to model high altitude air traffic flow. Three of the models use the framework of discrete time dynamical systems, while the fourth consists of a network of partial differential equations. The construction of these models is done using one year of air traffic data. The four models are applied to high altitude traffic for six Air Route Traffic Control Centers in the National Airspace System and surrounding airspace. Simulations are carried out for a full day of data for each of the models, to assess their predictive capabilities. The models’ predictions are compared to the recorded flight data. Several error metrics are used to characterize the relative accuracy of the models. The efficiency of the respective models is also compared in terms of computational time and memory requirements for the scenarios of interest. Control strategies are designed and implemented on similar benchmark scenarios for two of the models. They use techniques such as adjoint-based optimization, as well as mixed integer linear programming. A discussion of the four models’ structural differences explains why one model may outperform another.
Keywords: Network flow model; air traffic flow management.
Mathematics Subject Classification: Primary: 90B10, 90B20; Secondary: 90C11, 76B7.
Citation: Dengfeng Sun, Issam S. Strub, Alexandre M. Bayen. Comparison of the performance of four Eulerian network flow models for strategic air traffic management. Networks and Heterogeneous Media, 2007, 2 (4) : 569-595. doi: 10.3934/nhm.2007.2.569
[1]

Ángela Jiménez-Casas, Aníbal Rodríguez-Bernal. Linear model of traffic flow in an isolated network. Conference Publications, 2015, 2015 (special) : 670-677. doi: 10.3934/proc.2015.0670
[2]

A. Marigo, Benedetto Piccoli. Cooperative controls for air traffic management. Communications on Pure and Applied Analysis, 2003, 2 (3) : 355-369. doi: 10.3934/cpaa.2003.2.355
[3]

Lino J. Alvarez-Vázquez, Néstor García-Chan, Aurea Martínez, Miguel E. Vázquez-Méndez. Optimal control of urban air pollution related to traffic flow in road networks. Mathematical Control and Related Fields, 2018, 8 (1) : 177-193. doi: 10.3934/mcrf.2018008
[4]

Alberto Bressan, Khai T. Nguyen. Conservation law models for traffic flow on a network of roads. Networks and Heterogeneous Media, 2015, 10 (2) : 255-293. doi: 10.3934/nhm.2015.10.255
[5]

Gabriella Bretti, Roberto Natalini, Benedetto Piccoli. Numerical approximations of a traffic flow model on networks. Networks and Heterogeneous Media, 2006, 1 (1) : 57-84. doi: 10.3934/nhm.2006.1.57
[6]

Gabriella Bretti, Roberto Natalini, Benedetto Piccoli. Fast algorithms for the approximation of a traffic flow model on networks. Discrete and Continuous Dynamical Systems - B, 2006, 6 (3) : 427-448. doi: 10.3934/dcdsb.2006.6.427
[7]

Wen Shen, Karim Shikh-Khalil. Traveling waves for a microscopic model of traffic flow. Discrete and Continuous Dynamical Systems, 2018, 38 (5) : 2571-2589. doi: 10.3934/dcds.2018108
[8]

Michael Herty, J.-P. Lebacque, S. Moutari. A novel model for intersections of vehicular traffic flow. Networks and Heterogeneous Media, 2009, 4 (4) : 813-826. doi: 10.3934/nhm.2009.4.813
[9]

Veronika Schleper. A hybrid model for traffic flow and crowd dynamics with random individual properties. Mathematical Biosciences & Engineering, 2015, 12 (2) : 393-413. doi: 10.3934/mbe.2015.12.393
[10]

Emiliano Cristiani, Fabio S. Priuli. A destination-preserving model for simulating Wardrop equilibria in traffic flow on networks. Networks and Heterogeneous Media, 2015, 10 (4) : 857-876. doi: 10.3934/nhm.2015.10.857
[11]

Tong Li. Well-posedness theory of an inhomogeneous traffic flow model. Discrete and Continuous Dynamical Systems - B, 2002, 2 (3) : 401-414. doi: 10.3934/dcdsb.2002.2.401
[12]

Caterina Balzotti, Simone Göttlich. A two-dimensional multi-class traffic flow model. Networks and Heterogeneous Media, 2021, 16 (1) : 69-90. doi: 10.3934/nhm.2020034
[13]

Florent Berthelin, Paola Goatin. Regularity results for the solutions of a non-local model of traffic flow. Discrete and Continuous Dynamical Systems, 2019, 39 (6) : 3197-3213. doi: 10.3934/dcds.2019132
[14]

Nicolas Forcadel, Wilfredo Salazar, Mamdouh Zaydan. Homogenization of second order discrete model with local perturbation and application to traffic flow. Discrete and Continuous Dynamical Systems, 2017, 37 (3) : 1437-1487. doi: 10.3934/dcds.2017060
[15]

Stefano Villa, Paola Goatin, Christophe Chalons. Moving bottlenecks for the Aw-Rascle-Zhang traffic flow model. Discrete and Continuous Dynamical Systems - B, 2017, 22 (10) : 3921-3952. doi: 10.3934/dcdsb.2017202
[16]

Dong Li, Tong Li. Shock formation in a traffic flow model with Arrhenius look-ahead dynamics. Networks and Heterogeneous Media, 2011, 6 (4) : 681-694. doi: 10.3934/nhm.2011.6.681
[17]

Michael Herty, Adrian Fazekas, Giuseppe Visconti. A two-dimensional data-driven model for traffic flow on highways. Networks and Heterogeneous Media, 2018, 13 (2) : 217-240. doi: 10.3934/nhm.2018010
[18]

Marte Godvik, Harald Hanche-Olsen. Car-following and the macroscopic Aw-Rascle traffic flow model. Discrete and Continuous Dynamical Systems - B, 2010, 13 (2) : 279-303. doi: 10.3934/dcdsb.2010.13.279
[19]

Mohamed Benyahia, Massimiliano D. Rosini. A macroscopic traffic model with phase transitions and local point constraints on the flow. Networks and Heterogeneous Media, 2017, 12 (2) : 297-317. doi: 10.3934/nhm.2017013
[20]

Felisia Angela Chiarello, Harold Deivi Contreras, Luis Miguel Villada. Nonlocal reaction traffic flow model with on-off ramps. Networks and Heterogeneous Media, 2022, 17 (2) : 203-226. doi: 10.3934/nhm.2022003

2020 Impact Factor: 1.213

Tools

Metrics

  • PDF downloads (158)
  • HTML views (0)
  • Cited by (26)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy