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Continuous kinematic wave models of merging traffic flow

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  • Jin, Wen-Long

Abstract

Merging junctions are important network bottlenecks, and a better understanding of merging traffic dynamics has both theoretical and practical implications. In this paper, we present continuous kinematic wave models of merging traffic flow which are consistent with discrete Cell Transmission Models with various distribution schemes. In particular, we develop a systematic approach to constructing kinematic wave solutions to the Riemann problem of merging traffic flow in supply-demand space. In the new framework, Riemann solutions on a link consist of an interior state and a stationary state, subject to admissible conditions such that there are no positive and negative kinematic waves on the upstream and downstream links, respectively. In addition, various distribution schemes in Cell Transmission Models are considered entropy conditions. In the proposed analytical framework, we prove that the stationary states and boundary fluxes exist and are unique for the Riemann problem for both fair and constant distribution schemes. We also discuss two types of invariant merge models, in which local and discrete boundary fluxes are the same as global and continuous ones. With numerical examples, we demonstrate the validity of the analytical solutions of interior states, stationary states, and corresponding kinematic waves. Discussions and future studies are presented in the conclusion section.

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  • Jin, Wen-Long, 2010. "Continuous kinematic wave models of merging traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1084-1103, September.
    • Handle: RePEc:eee:transb:v:44:y::i:8-9:p:1084-1103
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    Cited by:

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    2. 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.
    3. Tampère, Chris M.J. & Corthout, Ruben & Cattrysse, Dirk & Immers, Lambertus H., 2011. "A generic class of first order node models for dynamic macroscopic simulation of traffic flows," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 289-309, January.
    4. Jin, Wen-Long, 2012. "A kinematic wave theory of multi-commodity network traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 46(8), pages 1000-1022.
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    7. Wen-Long Jin, 2015. "Analysis of Kinematic Waves Arising in Diverging Traffic Flow Models," Transportation Science, INFORMS, vol. 49(1), pages 28-45, February.
    8. Jin, Wen-Long, 2012. "The traffic statics problem in a road network," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1360-1373.
    9. 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.
    10. Jin, Wen-Long, 2015. "On the existence of stationary states in general road networks," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 917-929.
    11. Han, Ke & Piccoli, Benedetto & Friesz, Terry L., 2016. "Continuity of the path delay operator for dynamic network loading with spillback," Transportation Research Part B: Methodological, Elsevier, vol. 92(PB), pages 211-233.
    12. Jin, Wen-Long & Gan, Qi-Jian & Lebacque, Jean-Patrick, 2015. "A kinematic wave theory of capacity drop," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 316-329.
    13. Yan, Qinglong & Sun, Zhe & Gan, Qijian & Jin, Wen-Long, 2018. "Automatic identification of near-stationary traffic states based on the PELT changepoint detection," Transportation Research Part B: Methodological, Elsevier, vol. 108(C), pages 39-54.
    14. 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.
    15. Friesz, Terry L. & Han, Ke & Neto, Pedro A. & Meimand, Amir & Yao, Tao, 2013. "Dynamic user equilibrium based on a hydrodynamic model," Transportation Research Part B: Methodological, Elsevier, vol. 47(C), pages 102-126.
    16. Smith, Mike & Huang, Wei & Viti, Francesco & Tampère, Chris M.J. & Lo, Hong K., 2019. "Quasi-dynamic traffic assignment with spatial queueing, control and blocking back," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 140-166.
    17. Jin, Wen-Long, 2017. "A Riemann solver for a system of hyperbolic conservation laws at a general road junction," Transportation Research Part B: Methodological, Elsevier, vol. 98(C), pages 21-41.

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