63
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Steady-state solution to the LWR model on a single origin-destination parallel road network

ORCID Icon, , , , , & show all
Article: 2341012 | Received 06 Dec 2022, Accepted 05 Apr 2024, Published online: 19 Apr 2024

References

  • Bell, M. G. H. 1995. “Stochastic User Equilibrium Assignment in Networks with Queues.” Transportation Research Part B: Methodological 29 (2): 125–137. https://doi.org/10.1016/0191-2615(94)00030-4.
  • Bliemer, M. C. J., and M. P. H. Raadsen. 2020. “Static Traffic Assignment with Residual Queues and Spillback.” Transportation Research Part B: Methodological 132:303–319. https://doi.org/10.1016/j.trb.2019.02.010.
  • Bliemer, M. C. J., M. P. H. Raadsen, E. S. Smits, B. Zhou, and M. G. H. Bell. 2014. “Quasi-dynamic Traffic Assignment with Residual Point Queues Incorporating a First Order Node Model.” Transportation Research Part B: Methodological 68:363–384. https://doi.org/10.1016/j.trb.2014.07.001.
  • Bureau of Public Roads. 1964. “Traffic Assignment Manual for Application with a Large.” High Speed Computer, US Department of Commerce.
  • Cheng, Q., Z. Liu, and W. Y. Szeto. 2019. “A Cell-based Dynamic Congestion Pricing Scheme Considering Travel Distance and Time Delay.” Transportmetrica B: Transport Dynamics 7 (1): 1286–1304.
  • Coclite, G. M., M. Garavello, and B. Piccoli. 2005. “Traffic Flow on a Road Network.” SIAM Journal on Mathematical Analysis 36 (6): 1862–1886. https://doi.org/10.1137/S0036141004402683.
  • Daganzo, C. F. 1995. “The Cell Transmission Model, Part II: Network Traffic.” Transportation Research Part B: Methodological 29 (2): 79–93. https://doi.org/10.1016/0191-2615(94)00022-R.
  • Friesz, T. L., K. Han, P. A. Neto, A. Meimand, and T. Yao. 2013. “Dynamic User Equilibrium Based on a Hydrodynamic Model.” Transportation Research Part B: Methodological 47:102–126. https://doi.org/10.1016/j.trb.2012.10.001.
  • Garavello, M., R. Natalini, B. Piccoli, and A. Terracina. 2007. “Conservation Laws with Discontinuous Flux.” Networks and Heterogeneous Media 2 (1): 159–179. https://doi.org/10.3934/nhm.2007.2.159.
  • Graf, L., and T. Harks. 2023. "Side-constrained Dynamic Traffic Equilibria." In Proceedings of the 24th ACM Conference on Economics and Computation, 814–814. New York: Association for Computing Machinery.
  • Hoang, N. H., H. L. Vu, M. Panda, and H. K. Lo. 2019. “A Linear Framework for Dynamic User Equilibrium Traffic Assignment in a Single Origin-destination Capacitated Network.” Transportation Research Part B: Methodological 126:329–352. https://doi.org/10.1016/j.trb.2017.11.013.
  • Jin, W. L. 2012. “A Kinematic Wave Theory of Multi-commodity Network Traffic Flow.” Transportation Research Part B: Methodological 46 (8): 1000–1022. https://doi.org/10.1016/j.trb.2012.02.009.
  • Jin, W. L. 2015. “On the Existence of Stationary States in General Road Networks.” Transportation Research Part B: Methodological 81:917–929. https://doi.org/10.1016/j.trb.2015.05.010.
  • Jin, W. L. 2017. “On the Stability of Stationary States in General Road Networks.” Transportation Research Part B: Methodological 98:42–61. https://doi.org/10.1016/j.trb.2016.12.010.
  • Lam, W. H. K., and Y. Zhang. 2000. “Capacity-constrained Traffic Assignment in Networks with Residual Queues.” Journal of Transportation Engineering Part A: Systems 126 (2): 121–128. https://doi.org/10.1061/(ASCE)0733-947X(2000)126:2(121).
  • Larsson, T., and M. Patriksson. 1995. “An Augmented Lagrangean Dual Algorithm for Link Capacity Side Constrained Traffic Assignment Problems.” Transportation Research Part B: Methodological 29 (6): 433–455. https://doi.org/10.1016/0191-2615(95)00016-7.
  • Lebacque, J. P.. 1995. “The Godunov Scheme and What it Means for First Order Traffic Flow Models.”In Proceedings of the 13th International Symposium on Transportation and Traffic Theory, 647–677. New York: Pergamon Press.
  • Li, H. Y., Z. Y. Lin, P. Zhang, and Y. L. Duan. 2020. “Modeling and Simulation of Dynamic Traffic Assignment Based on Conserved Higher-order Model.” Chinese Journal of Computational Physics 37:162–174.
  • Lighthill, M. J., and G. B. Whitham. 1955. “On Kinematic Waves: II. A Theory of Traffic Flow on Long Crowded Roads.” Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 229 (1178): 317–345.
  • Lin, Z. Y., S. C. Wong, X. N. Zhang, and P. Zhang. 2022. “Higher-order Traffic Flow Model Extended to Road Networks.” Journal of Transportation Engineering, Part A: Systems 149 (4): 04023006.
  • Lin, Z. Y., P. Zhang, L. Y. Dong, S. C. Wong, and K. Choi. 2015. “Traffic Flow on a Road Network Using a Conserved Higher-order Model.” AIP Conference Proceedings 1648 (1): 530006. https://doi.org/10.1063/1.4912739.
  • Lo, H. K., and W. Y. Szeto. 2002. “A Cell-based Variational Inequality Formulation of the Dynamic User Optimal Assignment Problem.” Transportation Research Part B: Methodological 36 (5): 421–443. https://doi.org/10.1016/S0191-2615(01)00011-X.
  • Lyu, Y. P., M. M. Guo, P. Zhang, R. Fang, Z. Y. Lin, and Y. L. Duan. 2021. “Steady-state Solution of Traffic Flow on a Simple Road Network.” Journal of Hydrodynamics 33 (5): 950–957. https://doi.org/10.1007/s42241-021-0084-y.
  • Meng, Q., W. H. K. Lam, and L. Yang. 2008. “General Stochastic User Equilibrium Traffic Assignment Problem with Link Capacity Constraints.” Journal of Advanced Transportation 42 (4): 429–465. https://doi.org/10.1002/atr.v42:4.
  • Payne, H. J., and W. A. Thompson. 1975. “Traffic Assignment on Transportation Networks with Capacity Constraints and Queueing.” Paper presented at the 47th National ORSA/TIMS 1975 North American Meeting. Chicago, IL, April 30-May 2, 1975.
  • Richards, R. I. 1956. “Shockwaves on the Highway.” Operations Research 4 (1): 42–51. https://doi.org/10.1287/opre.4.1.42.
  • Smith, M. J.. 1987. “Traffic Control and Traffic Assignment in A Signal-controlled Network with Queueing.” In Proceedings of the 12th International Symposium on Transportation and Traffic Theory, 61–77. Cambridge, MA: Elsevier.
  • Smith, M. J., W. Huang, and F. Viti. 2013. “Equilibrium in Capacitated Network Models with Queueing Delays, Queue-storage, Blocking Back and Control.” Procedia Social and Behavioral Sciences80:860–879. https://doi.org/10.1016/j.sbspro.2013.05.047.
  • Toro, E. F. 1999. Riemann Solvers and Numerical Methods for Fluid Dynamics. Berlin Heidelberg: Springer–Verlay.
  • Whitham, G. B. 1974. Linear and Nonlinear Waves. New York: John Wiley and Sons.
  • Wong, G. C. K., and S. C. Wong. 2002. “A Multi-class Traffic Flow Model–an Extension of LWR Model with Heterogeneous Drivers.” Transportation Research Part A: Policy and Practice 36 (9): 827–841.
  • Yang, H., and S. Yagar. 2008. “Traffic Assignment and Traffic Control in General Freeway-arterial Corridor Systems.” Transportation Research Part B: Methodological 28 (6): 463–486. https://doi.org/10.1016/0191-2615(94)90015-9.
  • Zhang, P., Y. P. Lyu, M. M. Guo, Z. Y. Lin, R. Fang, X. Y. Li, and X. N. Zhang. 2021. “Steady-state Solutions of Traffic Flow in a Simple Circled Road Network.” Applied Mathematics and Mechanics 42 (2): 123–132. https://doi.org/10.1007/s10483-021-2705-7.
  • Zhang, Z., B. Wolshon, and V. V. Dixit. 2015. “Integration of a Cell Transmission Model and Macroscopic Fundamental Diagram: Network Aggregation for Dynamic Traffic Models.” Transportation Research Part C: Emerging Technologies 55:298–309. https://doi.org/10.1016/j.trc.2015.03.040.
  • Zhong, R. X., A. Sumalee, T. L. Friesz, and W. H. Lam. 2011. “Dynamic User Equilibrium with Side Constraints for a Traffic Network: Theoretical Development and Numerical Solution Algorithm.” Transportation Research Part B: Methodological 45 (7): 1035–1061. https://doi.org/10.1016/j.trb.2011.05.004.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.