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On the stability of stationary states in general road networks

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  • Jin, Wen-Long

Abstract

In [Jin, W.-L., 2015. On the existence of stationary states in general road networks. Transportation Research Part B 81, 917–929.], with a discrete map in critical demand levels, it was proved that there exist stationary states for the kinematic wave model of general road networks with constant origin demands, route choice proportions, and destination supplies. In this study we further examine the stability property of stationary states with the same map, and the results will help us to understand the long-term trend of a network traffic system. We first review a network kinematic wave model and properties of stationary states on a link, define the criticality of junctions in stationary states, and discuss information propagation in stationary states on links and junctions. We then present the map and examine information propagation in the map. We apply the map to analytically study the stability of stationary states on ring roads and diverge-merge networks with circular information propagation and compare them with results obtained from the Poincaré map [Jin, W.-L., 2013. Stability and bifurcation in network traffic flow: A Poincaré map approach. Transportation Research Part B 57, 191–208]. We further study the stability property of general stationary states in a grid network. We find that the stability of fixed points of the map is the same as that of stationary states in a network, and the new approach is more general than the Poincaré map approach. We conclude the study with future directions and implications.

Suggested Citation

  • Jin, Wen-Long, 2017. "On the stability of stationary states in general road networks," Transportation Research Part B: Methodological, Elsevier, vol. 98(C), pages 42-61.
    • Handle: RePEc:eee:transb:v:98:y:2017:i:c:p:42-61
    DOI: 10.1016/j.trb.2016.12.010
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    References listed on IDEAS

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    1. Oded Galor, 2007. "Discrete Dynamical Systems," Springer Books, Springer, edition 1, number 978-3-540-36776-5, June.
    2. 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.
    3. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    4. MERCHANT, Deepak K. & NEMHAUSER, George L., 1978. "Optimality conditions for a dynamic traffic assignment model," LIDAM Reprints CORE 345, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Jin, Wen-Long, 2012. "The traffic statics problem in a road network," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1360-1373.
    6. 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.
    7. 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.
    8. Yang, Hai & Yagar, Sam, 1995. "Traffic assignment and signal control in saturated road networks," Transportation Research Part A: Policy and Practice, Elsevier, vol. 29(2), pages 125-139, March.
    9. 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.
    10. 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.
    11. Yan, Hai & Lam, William H. K., 1996. "Optimal road tolls under conditions of queueing and congestion," Transportation Research Part A: Policy and Practice, Elsevier, vol. 30(5), pages 319-332, September.
    12. 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.
    13. Daganzo, Carlos F., 2007. "Urban gridlock: Macroscopic modeling and mitigation approaches," Transportation Research Part B: Methodological, Elsevier, vol. 41(1), pages 49-62, January.
    14. Deepak K. Merchant & George L. Nemhauser, 1978. "Optimality Conditions for a Dynamic Traffic Assignment Model," Transportation Science, INFORMS, vol. 12(3), pages 200-207, August.
    15. 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.
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    1. (Sean) Qian, Zhen & Li, Jia & Li, Xiaopeng & Zhang, Michael & Wang, Haizhong, 2017. "Modeling heterogeneous traffic flow: A pragmatic approach," Transportation Research Part B: Methodological, Elsevier, vol. 99(C), pages 183-204.
    2. 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.

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