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A variational formulation of kinematic waves: Solution methods

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  1. Bliemer, Michiel C.J. & Raadsen, Mark P.H., 2019. "Continuous-time general link transmission model with simplified fanning, Part I: Theory and link model formulation," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 442-470.
  2. Laval, Jorge A. & Leclercq, Ludovic, 2013. "The Hamilton–Jacobi partial differential equation and the three representations of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 52(C), pages 17-30.
  3. Zheng, Fangfang & Jabari, Saif Eddin & Liu, Henry X. & Lin, DianChao, 2018. "Traffic state estimation using stochastic Lagrangian dynamics," Transportation Research Part B: Methodological, Elsevier, vol. 115(C), pages 143-165.
  4. Daganzo, Carlos F. & Lehe, Lewis J., 2016. "Traffic flow on signalized streets," Transportation Research Part B: Methodological, Elsevier, vol. 90(C), pages 56-69.
  5. Laval, Jorge A. & Castrillón, Felipe, 2015. "Stochastic approximations for the macroscopic fundamental diagram of urban networks," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 904-916.
  6. Mazaré, Pierre-Emmanuel & Dehwah, Ahmad H. & Claudel, Christian G. & Bayen, Alexandre M., 2011. "Analytical and grid-free solutions to the Lighthill–Whitham–Richards traffic flow model," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1727-1748.
  7. Jin, Wen-Long & Gan, Qi-Jian & Gayah, Vikash V., 2013. "A kinematic wave approach to traffic statics and dynamics in a double-ring network," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 114-131.
  8. Chow, Andy H.F. & Li, Shuai & Zhong, Renxin, 2017. "Multi-objective optimal control formulations for bus service reliability with traffic signals," Transportation Research Part B: Methodological, Elsevier, vol. 103(C), pages 248-268.
  9. Li, Jia & Zhang, H.M., 2013. "Modeling space–time inhomogeneities with the kinematic wave theory," Transportation Research Part B: Methodological, Elsevier, vol. 54(C), pages 113-125.
  10. Wada, Kentaro & Usui, Kento & Takigawa, Tsubasa & Kuwahara, Masao, 2018. "An optimization modeling of coordinated traffic signal control based on the variational theory and its stochastic extension," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 907-925.
  11. Costeseque, Guillaume & Lebacque, Jean-Patrick, 2014. "A variational formulation for higher order macroscopic traffic flow models: Numerical investigation," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 112-133.
  12. Hao, Peng & Ban, Xuegang, 2015. "Long queue estimation for signalized intersections using mobile data," Transportation Research Part B: Methodological, Elsevier, vol. 82(C), pages 54-73.
  13. Lebacque, Jean-Patrick & Khoshyaran, Megan M., 2013. "A variational formulation for higher order macroscopic traffic flow models of the GSOM family," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 245-265.
  14. Ke Han & Gabriel Eve & Terry L. Friesz, 2019. "Computing Dynamic User Equilibria on Large-Scale Networks with Software Implementation," Networks and Spatial Economics, Springer, vol. 19(3), pages 869-902, September.
  15. Jin, Wen-Long, 2018. "Unifiable multi-commodity kinematic wave model," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 639-659.
  16. Himpe, Willem & Corthout, Ruben & Tampère, M.J. Chris, 2016. "An efficient iterative link transmission model," Transportation Research Part B: Methodological, Elsevier, vol. 92(PB), pages 170-190.
  17. Mohebifard, Rasool & Hajbabaie, Ali, 2019. "Optimal network-level traffic signal control: A benders decomposition-based solution algorithm," Transportation Research Part B: Methodological, Elsevier, vol. 121(C), pages 252-274.
  18. Tilg, Gabriel & Ambühl, Lukas & Batista, Sergio & Menendez, Monica & Busch, Fritz, 2021. "On the application of variational theory to urban networks," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 435-456.
  19. Laval, Jorge A. & Costeseque, Guillaume & Chilukuri, Bargavarama, 2016. "The impact of source terms in the variational representation of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 204-216.
  20. Corthout, Ruben & Flötteröd, Gunnar & Viti, Francesco & Tampère, Chris M.J., 2012. "Non-unique flows in macroscopic first-order intersection models," Transportation Research Part B: Methodological, Elsevier, vol. 46(3), pages 343-359.
  21. Jin, Wen-Long, 2016. "On the equivalence between continuum and car-following models of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 543-559.
  22. Leclercq, Ludovic & Geroliminis, Nikolas, 2013. "Estimating MFDs in simple networks with route choice," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 468-484.
  23. van der Gun, Jeroen P.T. & Pel, Adam J. & van Arem, Bart, 2017. "Extending the Link Transmission Model with non-triangular fundamental diagrams and capacity drops," Transportation Research Part B: Methodological, Elsevier, vol. 98(C), pages 154-178.
  24. Raadsen, Mark P.H. & Bliemer, Michiel C.J. & Bell, Michael G.H., 2016. "An efficient and exact event-based algorithm for solving simplified first order dynamic network loading problems in continuous time," Transportation Research Part B: Methodological, Elsevier, vol. 92(PB), pages 191-210.
  25. Lu, Yadong & Wong, S.C. & Zhang, Mengping & Shu, Chi-Wang & Chen, Wenqin, 2008. "Explicit construction of entropy solutions for the Lighthill-Whitham-Richards traffic flow model with a piecewise quadratic flow-density relationship," Transportation Research Part B: Methodological, Elsevier, vol. 42(4), pages 355-372, May.
  26. Jin, Wen-Long, 2015. "Continuous formulations and analytical properties of the link transmission model," Transportation Research Part B: Methodological, Elsevier, vol. 74(C), pages 88-103.
  27. Daganzo, Carlos F. & Geroliminis, Nikolas, 2008. "An analytical approximation for the macroscopic fundamental diagram of urban traffic," Transportation Research Part B: Methodological, Elsevier, vol. 42(9), pages 771-781, November.
  28. Daganzo, Carlos F & Geroliminis, Nikolas, 2008. "An analytical approximation for the macropscopic fundamental diagram of urban traffic," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt4cb8h3jm, Institute of Transportation Studies, UC Berkeley.
  29. Blumberg, Michal & Bar-Gera, Hillel, 2009. "Consistent node arrival order in dynamic network loading models," Transportation Research Part B: Methodological, Elsevier, vol. 43(3), pages 285-300, March.
  30. Hans, Etienne & Chiabaut, Nicolas & Leclercq, Ludovic, 2015. "Applying variational theory to travel time estimation on urban arterials," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 169-181.
  31. Li, Jia & Zhang, H.M., 2013. "The variational formulation of a non-equilibrium traffic flow model: Theory and implications," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 314-325.
  32. Simoni, Michele D. & Claudel, Christian G., 2017. "A fast simulation algorithm for multiple moving bottlenecks and applications in urban freight traffic management," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 238-255.
  33. Ma, Tao & Zhou, Zhou & Abdulhai, Baher, 2015. "Nonlinear multivariate time–space threshold vector error correction model for short term traffic state prediction," Transportation Research Part B: Methodological, Elsevier, vol. 76(C), pages 27-47.
  34. Jin, Wen-Long, 2017. "Kinematic wave models of lane-drop bottlenecks," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 507-522.
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