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Steady-state solution of traffic flow on a simple road network

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Abstract

The steady-state traffic flow on a simply circled road network is analytically studied using the Lighthill-Witham-Richards (LWR) model. The network is typically composed of a diverging and a merging junction together with three connected road sections. At the diverging junction, traffic flow is assigned to satisfy the user-equilibrium condition. At the merging junction, queuing or shock structures due to the bottleneck effect is taken into account. We indicate that the solution depends on the total number of vehicles on the road network, and that the bottleneck effect gives rise to not only capacity drop but inefficient utilization of the two road sections upstream the merging junction. To further validate the derived steady-state solution, a first-order Godunov scheme of the LWR model is adopted for simulation of traffic flow in each road section and the demand-supply concept is applied to provide boundary values at the junctions for the scheme. By varying the total number of vehicles from zero to the maximum, the simulation shows that a randomly distributed state of traffic flow is bound to evolve into a steady state, which is completely in agreement with the analytical solution.

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Acknowledgements

This work was supported by the China Postdoctoral Science Foundation (Grant No. 2019M661362), the Opening Research Fund of National Engineering Laboratory for Surface Transportation Weather Impacts Prevention (Grant No. NEL-2019-02).

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200072, China

    Yu-pei Lyu & Peng Zhang

  2. Department of Aeronautics and Astronautics, Fudan University, Shanghai, 200433, China

    Ming-min Guo & Zhi-yang Lin

  3. National Engineering Laboratory For Surface Transportation Weather Impacts Prevention, Broadvision Engineering Consultants Co., Ltd, Kunming, 650200, China

    Rui Fang

  4. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, China

    Ya-li Duan

Authors
  1. Yu-pei Lyu
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  2. Ming-min Guo
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  3. Peng Zhang
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  4. Rui Fang
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  5. Zhi-yang Lin
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Corresponding author

Correspondence to Ming-min Guo.

Additional information

Projects supported by the National Natural Science Foundation of China (Grant Nos. 11972121, 11672348), the National Key Research Development Program of China (Grant No. 2018YFB1600900).

Biography

Yu-pei Lyu (1978-), Female, Ph. D., E-mail: peipei@zjhu.edu.cn

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Lyu, Yp., Guo, Mm., Zhang, P. et al. Steady-state solution of traffic flow on a simple road network. J Hydrodyn 33, 950–957 (2021). https://doi.org/10.1007/s42241-021-0084-y

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  • DOI: https://doi.org/10.1007/s42241-021-0084-y

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