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On the variational theory of traffic flow: wellposedness, duality and applications
The many facets of internet topology and traffic
1.  Operations Research Department, Naval Postgraduate School, Monterey, CA 93943, United States 
2.  Department of EECS, University of Michigan, Ann Arbor, MI 481092122, United States 
3.  School of Mathematical Sciences, University of Adelaide, Adelaide 5005, Australia 
4.  Network Architectures and Services, Delft University of Technology, Delft, Netherlands 
5.  AT&T LabsResearch, Florham Park, NJ 07932, United States 
[1] 
Ángela JiménezCasas, Aníbal RodríguezBernal. Linear model of traffic flow in an isolated network. Conference Publications, 2015, 2015 (special) : 670677. doi: 10.3934/proc.2015.0670 
[2] 
Tibye Saumtally, JeanPatrick Lebacque, Habib HajSalem. A dynamical twodimensional traffic model in an anisotropic network. Networks & Heterogeneous Media, 2013, 8 (3) : 663684. doi: 10.3934/nhm.2013.8.663 
[3] 
H. Thomas Banks, Shuhua Hu, Zackary R. Kenz, Carola Kruse, Simon Shaw, John Whiteman, Mark P. Brewin, Stephen E. Greenwald, Malcolm J. Birch. Model validation for a noninvasive arterial stenosis detection problem. Mathematical Biosciences & Engineering, 2014, 11 (3) : 427448. doi: 10.3934/mbe.2014.11.427 
[4] 
Zsolt Saffer, Miklós Telek. Analysis of globally gated Markovian limited cyclic polling model and its application to uplink traffic in the IEEE 802.16 network. Journal of Industrial & Management Optimization, 2011, 7 (3) : 677697. doi: 10.3934/jimo.2011.7.677 
[5] 
E. Audusse. A multilayer SaintVenant model: Derivation and numerical validation. Discrete & Continuous Dynamical Systems  B, 2005, 5 (2) : 189214. doi: 10.3934/dcdsb.2005.5.189 
[6] 
Thomas Wanner. Computerassisted equilibrium validation for the diblock copolymer model. Discrete & Continuous Dynamical Systems  A, 2017, 37 (2) : 10751107. doi: 10.3934/dcds.2017045 
[7] 
Shu Zhang, Jian Xu. Timevarying delayed feedback control for an internet congestion control model. Discrete & Continuous Dynamical Systems  B, 2011, 16 (2) : 653668. doi: 10.3934/dcdsb.2011.16.653 
[8] 
Shu Zhang, Yuan Yuan. The Filippov equilibrium and sliding motion in an internet congestion control model. Discrete & Continuous Dynamical Systems  B, 2017, 22 (3) : 11891206. doi: 10.3934/dcdsb.2017058 
[9] 
David J. Aldous. A stochastic complex network model. Electronic Research Announcements, 2003, 9: 152161. 
[10] 
Yongming Liu, Lei Yao. Global solution and decay rate for a reduced gravity two and a half layer model. Discrete & Continuous Dynamical Systems  B, 2019, 24 (6) : 26132638. doi: 10.3934/dcdsb.2018267 
[11] 
Mauro Garavello. The LWR traffic model at a junction with multibuffers. Discrete & Continuous Dynamical Systems  S, 2014, 7 (3) : 463482. doi: 10.3934/dcdss.2014.7.463 
[12] 
Jiangtao Mo, Liqun Qi, Zengxin Wei. A network simplex algorithm for simple manufacturing network model. Journal of Industrial & Management Optimization, 2005, 1 (2) : 251273. doi: 10.3934/jimo.2005.1.251 
[13] 
Martina Bukač, Sunčica Čanić. Longitudinal displacement in viscoelastic arteries: A novel fluidstructure interaction computational model, and experimental validation. Mathematical Biosciences & Engineering, 2013, 10 (2) : 295318. doi: 10.3934/mbe.2013.10.295 
[14] 
Oliver Kolb, Simone Göttlich, Paola Goatin. Capacity drop and traffic control for a second order traffic model. Networks & Heterogeneous Media, 2017, 12 (4) : 663681. doi: 10.3934/nhm.2017027 
[15] 
Shuping Li, Zhen Jin. Impacts of cluster on network topology structure and epidemic spreading. Discrete & Continuous Dynamical Systems  B, 2017, 22 (10) : 37493770. doi: 10.3934/dcdsb.2017187 
[16] 
Gabriella Bretti, Roberto Natalini, Benedetto Piccoli. Numerical approximations of a traffic flow model on networks. Networks & Heterogeneous Media, 2006, 1 (1) : 5784. doi: 10.3934/nhm.2006.1.57 
[17] 
Gabriella Bretti, Roberto Natalini, Benedetto Piccoli. Fast algorithms for the approximation of a traffic flow model on networks. Discrete & Continuous Dynamical Systems  B, 2006, 6 (3) : 427448. doi: 10.3934/dcdsb.2006.6.427 
[18] 
Fabio Della Rossa, Carlo D’Angelo, Alfio Quarteroni. A distributed model of traffic flows on extended regions. Networks & Heterogeneous Media, 2010, 5 (3) : 525544. doi: 10.3934/nhm.2010.5.525 
[19] 
Florent Berthelin, Damien Broizat. A model for the evolution of traffic jams in multilane. Kinetic & Related Models, 2012, 5 (4) : 697728. doi: 10.3934/krm.2012.5.697 
[20] 
Wen Shen, Karim ShikhKhalil. Traveling waves for a microscopic model of traffic flow. Discrete & Continuous Dynamical Systems  A, 2018, 38 (5) : 25712589. doi: 10.3934/dcds.2018108 
2018 Impact Factor: 0.871
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