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A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem

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  1. Evstigneev, Igor & Taksar, Michael, 2009. "Dynamic interaction models of economic equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 166-182, January.
  2. Han, Ke & Friesz, Terry L. & Yao, Tao, 2013. "A partial differential equation formulation of Vickrey’s bottleneck model, part I: Methodology and theoretical analysis," Transportation Research Part B: Methodological, Elsevier, vol. 49(C), pages 55-74.
  3. Huang, Hai-Jun & Lam, William H. K., 2002. "Modeling and solving the dynamic user equilibrium route and departure time choice problem in network with queues," Transportation Research Part B: Methodological, Elsevier, vol. 36(3), pages 253-273, March.
  4. Jozwiak, Akos & Milkovics, Matyas & Lakner, Zoltan, 2016. "A Network-Science Support System for Food Chain Safety: A Case from Hungarian Cattle Production," International Food and Agribusiness Management Review, International Food and Agribusiness Management Association, vol. 19(A), pages 1-26, June.
  5. M Carey, 2009. "A framework for user equilibrium dynamic traffic assignment," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(3), pages 395-410, March.
  6. Long, Jiancheng & Szeto, W.Y. & Gao, Ziyou & Huang, Hai-Jun & Shi, Qin, 2016. "The nonlinear equation system approach to solving dynamic user optimal simultaneous route and departure time choice problems," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 179-206.
  7. Han, Ke & Gayah, Vikash V. & Piccoli, Benedetto & Friesz, Terry L. & Yao, Tao, 2014. "On the continuum approximation of the on-and-off signal control on dynamic traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 61(C), pages 73-97.
  8. Lam, William H. K. & Yin, Yafeng, 2001. "An activity-based time-dependent traffic assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 35(6), pages 549-574, July.
  9. Qixiu Cheng & Zhiyuan Liu & Feifei Liu & Ruo Jia, 2017. "Urban dynamic congestion pricing: an overview and emerging research needs," International Journal of Urban Sciences, Taylor & Francis Journals, vol. 21(0), pages 3-18, August.
  10. Moore, II, James E. & Kim, Geunyoung & Cho, Seongdil & Hu, Hsi-hwa & Xu, Rong, 1997. "Evaluating System ATMIS Technologies Via Rapid Estimation Of Network Flows: Final Report," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt5c70f3d9, Institute of Transportation Studies, UC Berkeley.
  11. Bartolozzi, F. & de Gaetano, A. & Di Lena, E. & Marino, S. & Nieddu, L. & Patrizi, G., 2000. "Operational research techniques in medical treatment and diagnosis: A review," European Journal of Operational Research, Elsevier, vol. 121(3), pages 435-466, March.
  12. Du, Jie & Wong, S.C. & Shu, Chi-Wang & Zhang, Mengping, 2015. "Reformulating the Hoogendoorn–Bovy predictive dynamic user-optimal model in continuum space with anisotropic condition," Transportation Research Part B: Methodological, Elsevier, vol. 79(C), pages 189-217.
  13. Dial, Robert B., 1999. "Minimal-revenue congestion pricing part I: A fast algorithm for the single-origin case," Transportation Research Part B: Methodological, Elsevier, vol. 33(3), pages 189-202, April.
  14. Nie, Xiaojian & Zhang, H.M., 2005. "Delay-function-based link models: their properties and computational issues," Transportation Research Part B: Methodological, Elsevier, vol. 39(8), pages 729-751, September.
  15. Nie, Yu (Marco), 2010. "Equilibrium analysis of macroscopic traffic oscillations," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 62-72, January.
  16. Zhang, Michael & Shen, Wei & Nie, Yu & Ma, Jingtao, 2008. "Integrated Construction Zone Traffic Management," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt1bd50918, Institute of Transportation Studies, UC Berkeley.
  17. Daoli Zhu & Patrice Marcotte, 2000. "On the Existence of Solutions to the Dynamic User Equilibrium Problem," Transportation Science, INFORMS, vol. 34(4), pages 402-414, November.
  18. 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.
  19. Song, Wenjing & Han, Ke & Wang, Yiou & Friesz, Terry L. & del Castillo, Enrique, 2018. "Statistical metamodeling of dynamic network loading," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 740-756.
  20. Malachy Carey & Y. E. Ge, 2005. "Alternative Conditions for a Well-Behaved Travel Time Model," Transportation Science, INFORMS, vol. 39(3), pages 417-428, August.
  21. Florian, Michael & Mahut, Michael & Tremblay, Nicolas, 2008. "Application of a simulation-based dynamic traffic assignment model," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1381-1392, September.
  22. Takamasa Iryo, 2015. "Investigating Factors for Existence of Multiple Equilibria in Dynamic Traffic Network," Networks and Spatial Economics, Springer, vol. 15(3), pages 599-616, September.
  23. Soulaymane Kachani & Georgia Perakis, 2009. "A Dynamic Travel Time Model for Spillback," Networks and Spatial Economics, Springer, vol. 9(4), pages 595-618, December.
  24. Light, Bar & Weintraub, Gabriel, 2018. "Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics," Research Papers 3731, Stanford University, Graduate School of Business.
  25. Bierlaire, Michel, 2002. "The total demand scale: a new measure of quality for static and dynamic origin-destination trip tables," Transportation Research Part B: Methodological, Elsevier, vol. 36(9), pages 837-850, November.
  26. Karakostas, George & Kim, Taeyon & Viglas, Anastasios & Xia, Hao, 2011. "On the degradation of performance for traffic networks with oblivious users," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 364-371, February.
  27. S. Waller & Athanasios Ziliaskopoulos, 2006. "A Combinatorial user optimal dynamic traffic assignment algorithm," Annals of Operations Research, Springer, vol. 144(1), pages 249-261, April.
  28. Han, Ke & Friesz, Terry L. & Yao, Tao, 2013. "A partial differential equation formulation of Vickrey’s bottleneck model, part II: Numerical analysis and computation," Transportation Research Part B: Methodological, Elsevier, vol. 49(C), pages 75-93.
  29. Rui Ma & Xuegang Ban & Jong-Shi Pang & Henry Liu, 2015. "Submission to the DTA2012 Special Issue: Approximating Time Delays in Solving Continuous-Time Dynamic User Equilibria," Networks and Spatial Economics, Springer, vol. 15(3), pages 443-463, September.
  30. Jiancheng Long & Hai-Jun Huang & Ziyou Gao & W. Y. Szeto, 2013. "An Intersection-Movement-Based Dynamic User Optimal Route Choice Problem," Operations Research, INFORMS, vol. 61(5), pages 1134-1147, October.
  31. Duong Viet Thong & Aviv Gibali & Mathias Staudigl & Phan Tu Vuong, 2021. "Computing Dynamic User Equilibrium on Large-Scale Networks Without Knowing Global Parameters," Networks and Spatial Economics, Springer, vol. 21(3), pages 735-768, September.
  32. Nie, Yu (Marco), 2011. "A cell-based Merchant-Nemhauser model for the system optimum dynamic traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 329-342, February.
  33. Laura Scrimali, 2012. "Infinite Dimensional Duality Theory Applied to Investment Strategies in Environmental Policy," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 258-277, July.
  34. Gentile, Guido & Meschini, Lorenzo & Papola, Natale, 2005. "Macroscopic arc performance models with capacity constraints for within-day dynamic traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 39(4), pages 319-338, May.
  35. Ban, Xuegang (Jeff) & Pang, Jong-Shi & Liu, Henry X. & Ma, Rui, 2012. "Modeling and solving continuous-time instantaneous dynamic user equilibria: A differential complementarity systems approach," Transportation Research Part B: Methodological, Elsevier, vol. 46(3), pages 389-408.
  36. Wie, Byung-Wook & Tobin, Roger L. & Carey, Malachy, 2002. "The existence, uniqueness and computation of an arc-based dynamic network user equilibrium formulation," Transportation Research Part B: Methodological, Elsevier, vol. 36(10), pages 897-918, December.
  37. Jang, Wonjae & Ran, Bin & Choi, Keechoo, 2005. "A discrete time dynamic flow model and a formulation and solution method for dynamic route choice," Transportation Research Part B: Methodological, Elsevier, vol. 39(7), pages 593-620, August.
  38. Friesz, Terry L. & Han, Ke & Bagherzadeh, Amir, 2021. "Convergence of fixed-point algorithms for elastic demand dynamic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 336-352.
  39. Huang, Y.P. & Xiong, J.H. & Sumalee, A. & Zheng, N. & Lam, W.H.K. & He, Z.B. & Zhong, R.X., 2020. "A dynamic user equilibrium model for multi-region macroscopic fundamental diagram systems with time-varying delays," Transportation Research Part B: Methodological, Elsevier, vol. 131(C), pages 1-25.
  40. Dial, Robert B., 2006. "A path-based user-equilibrium traffic assignment algorithm that obviates path storage and enumeration," Transportation Research Part B: Methodological, Elsevier, vol. 40(10), pages 917-936, December.
  41. Chen, Xiaoming & Zhou, Xuesong & List, George F., 2011. "Using time-varying tolls to optimize truck arrivals at ports," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(6), pages 965-982.
  42. Szeto, W. Y. & Lo, Hong K., 2004. "A cell-based simultaneous route and departure time choice model with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 38(7), pages 593-612, August.
  43. Li, Jun & Fujiwara, Okitsugu & Kawakami, Shogo, 2000. "A reactive dynamic user equilibrium model in network with queues," Transportation Research Part B: Methodological, Elsevier, vol. 34(8), pages 605-624, November.
  44. Iryo, Takamasa, 2011. "Multiple equilibria in a dynamic traffic network," Transportation Research Part B: Methodological, Elsevier, vol. 45(6), pages 867-879, July.
  45. Carey, Malachy & Subrahmanian, Eswaran, 2000. "An approach to modelling time-varying flows on congested networks," Transportation Research Part B: Methodological, Elsevier, vol. 34(3), pages 157-183, April.
  46. Chen, Huey-Kuo & Hsueh, Che-Fu, 1998. "A model and an algorithm for the dynamic user-optimal route choice problem," Transportation Research Part B: Methodological, Elsevier, vol. 32(3), pages 219-234, April.
  47. Han, Sangjin, 2007. "A route-based solution algorithm for dynamic user equilibrium assignments," Transportation Research Part B: Methodological, Elsevier, vol. 41(10), pages 1094-1113, December.
  48. Long, Jiancheng & Wang, Chao & Szeto, W.Y., 2018. "Dynamic system optimum simultaneous route and departure time choice problems: Intersection-movement-based formulations and comparisons," Transportation Research Part B: Methodological, Elsevier, vol. 115(C), pages 166-206.
  49. Antonino Maugeri & Laura Scrimali, 2016. "A New Approach to Solve Convex Infinite-Dimensional Bilevel Problems: Application to the Pollution Emission Price Problem," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 370-387, May.
  50. Richard Mounce, 2007. "Convergence to Equilibrium in Dynamic Traffic Networks when Route Cost Is Decay Monotone," Transportation Science, INFORMS, vol. 41(3), pages 409-504, August.
  51. Friesz, Terry L. & Han, Ke, 2019. "The mathematical foundations of dynamic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 309-328.
  52. Wie, Byung-Wook & Tobin, Roger L., 1998. "Dynamic congestion pricing models for general traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 32(5), pages 313-327, June.
  53. Rui Ma & Xuegang (Jeff) Ban & Jong-Shi Pang, 2018. "A Link-Based Differential Complementarity System Formulation for Continuous-Time Dynamic User Equilibria with Queue Spillbacks," Transportation Science, INFORMS, vol. 52(3), pages 564-592, June.
  54. Zhu, Feng & Ukkusuri, Satish V., 2017. "Efficient and fair system states in dynamic transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 272-289.
  55. Chow, Andy H.F., 2009. "Properties of system optimal traffic assignment with departure time choice and its solution method," Transportation Research Part B: Methodological, Elsevier, vol. 43(3), pages 325-344, March.
  56. Ban, Xuegang (Jeff) & Pang, Jong-Shi & Liu, Henry X. & Ma, Rui, 2012. "Continuous-time point-queue models in dynamic network loading," Transportation Research Part B: Methodological, Elsevier, vol. 46(3), pages 360-380.
  57. Robert B. Dial, 1999. "Network-Optimized Road Pricing: Part I: A Parable and a Model," Operations Research, INFORMS, vol. 47(1), pages 54-64, February.
  58. S. Mahmassani, Hani & F. Hyland, Michael, 2016. "Gap-based transit assignment algorithm with vehicle capacity constraints: Simulation-based implementation and large-scale applicationAuthor-Name: Verbas, Ömer," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 1-16.
  59. Tong, C. O. & Wong, S. C., 2000. "A predictive dynamic traffic assignment model in congested capacity-constrained road networks," Transportation Research Part B: Methodological, Elsevier, vol. 34(8), pages 625-644, November.
  60. Han, Ke & Friesz, Terry L. & Szeto, W.Y. & Liu, Hongcheng, 2015. "Elastic demand dynamic network user equilibrium: Formulation, existence and computation," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 183-209.
  61. Nantes, Alfredo & Ngoduy, Dong & Miska, Marc & Chung, Edward, 2015. "Probabilistic travel time progression and its application to automatic vehicle identification data," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 131-145.
  62. Ziyou Gao & Yunchao Qu & Xingang Li & Jiancheng Long & Hai-Jun Huang, 2014. "Simulating the Dynamic Escape Process in Large Public Places," Operations Research, INFORMS, vol. 62(6), pages 1344-1357, December.
  63. Ximing Wang & Panos M. Pardalos, 2017. "A modified active set algorithm for transportation discrete network design bi-level problem," Journal of Global Optimization, Springer, vol. 67(1), pages 325-342, January.
  64. Lu, Gongyuan & Nie, Yu(Marco) & Liu, Xiaobo & Li, Denghui, 2019. "Trajectory-based traffic management inside an autonomous vehicle zone," Transportation Research Part B: Methodological, Elsevier, vol. 120(C), pages 76-98.
  65. Lo, Hong K. & Chen, Anthony, 2000. "Traffic equilibrium problem with route-specific costs: formulation and algorithms," Transportation Research Part B: Methodological, Elsevier, vol. 34(6), pages 493-513, August.
  66. Adlakha, Sachin & Johari, Ramesh & Weintraub, Gabriel Y., 2015. "Equilibria of dynamic games with many players: Existence, approximation, and market structure," Journal of Economic Theory, Elsevier, vol. 156(C), pages 269-316.
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  68. Ke Han & Terry L. Friesz, 2017. "Continuity of the Effective Delay Operator for Networks Based on the Link Delay Model," Networks and Spatial Economics, Springer, vol. 17(4), pages 1095-1110, December.
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