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Asymptotic traffic dynamics arising in diverge-merge networks with two intermediate links

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  • Jin, Wen-Long

Abstract

Basic road network components, such as merging and diverging junctions, contribute much to formation and propagation of traffic congestion. However, in contrast to extensive studies of traffic dynamics on a road link, little is understood for those on a road network. In this study, we provide a comprehensive analysis of asymptotic traffic dynamics arising in diverge-merge networks with two intermediate links with first-order kinematic wave models. In addition, traffic demand at the origin and traffic demand at the destination are constant and maximum, and the proportion of vehicles choosing an intermediate link is constant. First, we examine all possible asymptotic stationary states and the sufficient and necessary conditions for their existence. With an example, we find that non-stationary states can include damped (DPO) and persistent periodic oscillations (PPO), and present an equivalent dynamical system that can be used to distinguish these two types of oscillations. This study can be a springboard for better understanding of traffic dynamics, especially formation and propagation of traffic congestion, on general road networks.

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  • 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.
    • Handle: RePEc:eee:transb:v:43:y:2009:i:5:p:575-595
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    References listed on IDEAS

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    Cited by:

    1. Nie, Yu (Marco), 2010. "Equilibrium analysis of macroscopic traffic oscillations," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 62-72, January.
    2. Jin, Wen-Long & Zhang, H. Michael, 2013. "An instantaneous kinematic wave theory of diverging traffic," Transportation Research Part B: Methodological, Elsevier, vol. 48(C), pages 1-16.
    3. 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.
    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.
    5. Gong, Siyuan & Du, Lili, 2016. "Optimal location of advance warning for mandatory lane change near a two-lane highway off-ramp," Transportation Research Part B: Methodological, Elsevier, vol. 84(C), pages 1-30.
    6. Wen-Long Jin, 2021. "A Link Queue Model of Network Traffic Flow," Transportation Science, INFORMS, vol. 55(2), pages 436-455, March.
    7. 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.
    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. Yanhong Wang & Rui Jiang & Yu (Marco) Nie & Ziyou Gao, 2021. "Impact of Information on Topology-Induced Traffic Oscillations," Transportation Science, INFORMS, vol. 55(2), pages 475-490, March.
    10. 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.
    11. Zhao, Tingting & Nie, Yu (Marco) & Zhang, Yi, 2014. "Extended spectral envelope method for detecting and analyzing traffic oscillations," Transportation Research Part B: Methodological, Elsevier, vol. 61(C), pages 1-16.
    12. 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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