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A Link Queue Model of Network Traffic Flow

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  • Wen-Long Jin

    (Department of Civil and Environmental Engineering, California Institute for Telecommunications and Information Technology, Institute of Transportation Studies, University of California, Irvine, Irvine, California 92697)

Abstract

Fundamental to many transportation network studies, traffic flow models can be used to describe traffic dynamics determined by drivers’ car-following, lane-changing, merging, and diverging behaviors. In this study, we develop a deterministic queueing model of network traffic flow, in which traffic on each link is considered as a queue. In the link queue model (LQM), the demand and supply of a link queue are defined in the queue size (number of vehicles), and its in- and out-flows are computed from junction flux functions corresponding to macroscopic merging and diverging rules. The new model is a system of ordinary differential equations that is mathematically tractable and computationally efficient and can capture queue spillbacks and interactions among links. We further demonstrate that the LQM is fundamentally different from the cell transmission model (CTM) and link transmission model (LTM) for a road segment, a signalized ring road, and a diverge-merge network, with respect to the shock and rarefaction waves, network fundamental diagram, and stability property. In a sense, the new model is a space-continuous approximation of the kinematic wave model and can be a useful addition to the multiscale modeling framework of network traffic flow. The model has been applied to formulate and solve network traffic control and observation problems.

Suggested Citation

  • Wen-Long Jin, 2021. "A Link Queue Model of Network Traffic Flow," Transportation Science, INFORMS, vol. 55(2), pages 436-455, March.
    • Handle: RePEc:inm:ortrsc:v:55:y:2021:i:2:p:436-455
    DOI: 10.1287/trsc.2020.1012
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    References listed on IDEAS

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    1. Qi-Jian Gan & Wen-Long Jin & Vikash V. Gayah, 2017. "Analysis of Traffic Statics and Dynamics in Signalized Networks: A Poincaré Map Approach," Transportation Science, INFORMS, vol. 51(3), pages 1009-1029, August.
    2. Castillo, J. M. Del & Benítez, F. G., 1995. "On the functional form of the speed-density relationship--II: Empirical investigation," Transportation Research Part B: Methodological, Elsevier, vol. 29(5), pages 391-406, October.
    3. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part III: Multi-destination flows," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 305-313, August.
    4. Arnott, Richard & Buli, Joshua, 2018. "Solving for equilibrium in the basic bathtub model," Transportation Research Part B: Methodological, Elsevier, vol. 109(C), pages 150-175.
    5. Omar Drissi-Kaïtouni & Abdelhamid Hameda-Benchekroun, 1992. "A Dynamic Traffic Assignment Model and a Solution Algorithm," Transportation Science, INFORMS, vol. 26(2), pages 119-128, May.
    6. Kuwahara, Masao & Akamatsu, Takashi, 2001. "Dynamic user optimal assignment with physical queues for a many-to-many OD pattern," Transportation Research Part B: Methodological, Elsevier, vol. 35(5), pages 461-479, June.
    7. Kuwahara, Masao & Akamatsu, Takashi, 1997. "Decomposition of the reactive dynamic assignments with queues for a many-to-many origin-destination pattern," Transportation Research Part B: Methodological, Elsevier, vol. 31(1), pages 1-10, February.
    8. Malachy Carey, 1986. "A Constraint Qualification for a Dynamic Traffic Assignment Model," Transportation Science, INFORMS, vol. 20(1), pages 55-58, February.
    9. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    10. Terry L. Friesz & David Bernstein & Tony E. Smith & Roger L. Tobin & B. W. Wie, 1993. "A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem," Operations Research, INFORMS, vol. 41(1), pages 179-191, February.
    11. Geroliminis, Nikolas & Daganzo, Carlos F., 2008. "Existence of urban-scale macroscopic fundamental diagrams: Some experimental findings," Transportation Research Part B: Methodological, Elsevier, vol. 42(9), pages 759-770, November.
    12. 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.
    13. G. C. D'Ans & D. C. Gazis, 1976. "Optimal Control of Oversaturated Store-and-Forward Transportation Networks," Transportation Science, INFORMS, vol. 10(1), pages 1-19, February.
    14. MERCHANT, Deepak K. & NEMHAUSER, George L., 1978. "A model and an algorithm for the dynamic traffic assignment problems," LIDAM Reprints CORE 346, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    15. Denos C. Gazis & Robert Herman & Richard W. Rothery, 1961. "Nonlinear Follow-the-Leader Models of Traffic Flow," Operations Research, INFORMS, vol. 9(4), pages 545-567, August.
    16. Daganzo, Carlos F., 1995. "The cell transmission model, part II: Network traffic," Transportation Research Part B: Methodological, Elsevier, vol. 29(2), pages 79-93, April.
    17. Jin, Wen-Long, 2013. "Stability and bifurcation in network traffic flow: A Poincaré map approach," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 191-208.
    18. 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.
    19. Terry L. Friesz & Javier Luque & Roger L. Tobin & Byung-Wook Wie, 1989. "Dynamic Network Traffic Assignment Considered as a Continuous Time Optimal Control Problem," Operations Research, INFORMS, vol. 37(6), pages 893-901, December.
    20. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part I: General theory," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 281-287, August.
    21. Jin, Wen-Long, 2020. "Generalized bathtub model of network trip flows," Transportation Research Part B: Methodological, Elsevier, vol. 136(C), pages 138-157.
    22. Jin, Wen-Long, 2010. "A kinematic wave theory of lane-changing traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1001-1021, September.
    23. Carey, Malachy & Ge, Y.E., 2007. "Retaining desirable properties in discretising a travel-time model," Transportation Research Part B: Methodological, Elsevier, vol. 41(5), pages 540-553, June.
    24. David E. Boyce & Hani S. Mahmassani & Anna Nagurney, 2005. "A retrospective on Beckmann, McGuire and Winsten's Studies in the Economics of Transportation," Papers in Regional Science, Wiley Blackwell, vol. 84(1), pages 85-103, March.
    25. 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.
    26. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    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. Roberto Cominetti & José Correa & Omar Larré, 2015. "Dynamic Equilibria in Fluid Queueing Networks," Operations Research, INFORMS, vol. 63(1), pages 21-34, February.
    29. Daganzo, Carlos F., 2007. "Urban gridlock: Macroscopic modeling and mitigation approaches," Transportation Research Part B: Methodological, Elsevier, vol. 41(1), pages 49-62, January.
    30. Daganzo, Carlos F., 2007. "Corrigendum to "Urban gridlock: Macroscopic modeling and mitigation approaches" [Transportation Research Part B 41 (2007) 49-62]," Transportation Research Part B: Methodological, Elsevier, vol. 41(3), pages 379-379, March.
    31. Jin, Wen-Long, 2009. "Asymptotic traffic dynamics arising in diverge-merge networks with two intermediate links," Transportation Research Part B: Methodological, Elsevier, vol. 43(5), pages 575-595, June.
    32. Gipps, P. G., 1986. "A model for the structure of lane-changing decisions," Transportation Research Part B: Methodological, Elsevier, vol. 20(5), pages 403-414, October.
    33. W.L. Jin & L. Chen & Elbridge Gerry Puckett, 2009. "Supply-demand Diagrams and a New Framework for Analyzing the Inhomogeneous Lighthill-Whitham-Richards Model," Springer Books, in: William H. K. Lam & S. C. Wong & Hong K. Lo (ed.), Transportation and Traffic Theory 2009: Golden Jubilee, chapter 0, pages 603-635, Springer.
    34. Deepak K. Merchant & George L. Nemhauser, 1978. "A Model and an Algorithm for the Dynamic Traffic Assignment Problems," Transportation Science, INFORMS, vol. 12(3), pages 183-199, August.
    35. 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.
    36. 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.
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