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The role of occupancy on traffic flow in a multiple-loop network

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  • Verma, Muskan
  • Singla, Tanvi
  • Gupta, Arvind Kumar
  • Sharma, Sapna

Abstract

A dynamic model for traffic flow is proposed to analyze the impact of occupancy in a multiple-loop network with a single intersection. The graph representation of multiple-loop lines is obtained utilizing the cell-transmission model, and consequently, the density equations are derived. The macroscopic fundamental diagrams are investigated for different cases of occupancy and the fraction of vehicles. For the double-loop lines, equilibrium densities, traffic currents, and travel time are obtained theoretically and validated via simulation. It is observed that the equilibrium densities increase linearly against the mean density for an equal fraction of vehicles while the traffic currents remain symmetric, unlike the case of an unequal fraction of vehicles. The travel time varies inversely with respect to the occupancy of the loop line. Additionally, when the fraction of vehicles and occupancy at both nodes are different, a critical value of mean density is obtained below (above), in which the travel time at one node is less (more) than the other. To analyze the traffic flow on multiple-loop lines, stability analysis is conducted using the tools from cooperative theory and repelling boundaries. As a result, the vehicular densities converge to a unique equilibrium point irrespective of the initial densities in the multiple-loop network. The theoretical results agree well with the simulation results.

Suggested Citation

  • Verma, Muskan & Singla, Tanvi & Gupta, Arvind Kumar & Sharma, Sapna, 2024. "The role of occupancy on traffic flow in a multiple-loop network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 638(C).
    • Handle: RePEc:eee:phsmap:v:638:y:2024:i:c:s0378437124001250
    DOI: 10.1016/j.physa.2024.129617
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    1. Jiang, Rui & Wu, Qing-Song & Zhu, Zuo-Jin, 2002. "A new continuum model for traffic flow and numerical tests," Transportation Research Part B: Methodological, Elsevier, vol. 36(5), pages 405-419, June.
    2. Zeng, Jiao-Yan & Ou, Hui & Tang, Tie-Qiao, 2019. "Feedback strategy with delay in a two-route traffic network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    3. Wang, Tao & Zang, Rudong & Xu, Keyu & Zhang, Jing, 2019. "Analysis of predictive effect on lattice hydrodynamic traffic flow model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    4. Liao, Peng & Tang, Tie-Qiao & Wang, Tao & Zhang, Jian, 2019. "A car-following model accounting for the driving habits," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 108-118.
    5. Nagatani, Takashi, 2020. "Traffic flow stabilized by matching speed on network with a bottleneck," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    6. Naoki Yoshioka & Kenji Terada & Takashi Shimada & Nobuyasu Ito, 2019. "Macroscopic fundamental diagram in simple street networks," Journal of Computational Social Science, Springer, vol. 2(1), pages 85-95, January.
    7. Nagatani, Takashi, 1998. "Modified KdV equation for jamming transition in the continuum models of traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 599-607.
    8. 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.
    9. Gupta, Arvind Kumar & Redhu, Poonam, 2013. "Analyses of driver’s anticipation effect in sensing relative flux in a new lattice model for two-lane traffic system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5622-5632.
    10. 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.
    11. Verma, Muskan & Sharma, Sapna, 2022. "Chaotic jam and phase transitions in a lattice model with density dependent passing," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    12. Nagatani, Takashi, 1999. "TDGL and MKdV equations for jamming transition in the lattice models of traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 264(3), pages 581-592.
    13. Verma, Muskan & Sharma, Sapna, 2023. "Modeling heterogeneity in an open percolation backbone fractal traffic network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 619(C).
    14. Gupta, A.K. & Katiyar, V.K., 2006. "Phase transition of traffic states with on-ramp," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 674-682.
    15. Nagatani, Takashi, 2022. "Chain reaction of traffic breakdowns in coupled-cycle networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    16. Zhu Su & Weibing Deng & Longfeng Zhao & Jihui Han & Wei Li & Xu Cai, 2016. "The effects of overtaking strategy in the Nagel-Schreckenberg model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(9), pages 1-8, September.
    17. Verma, Muskan & Sharma, Sapna, 2023. "The role of occupancy and transition rate on traffic flow in a percolation-backbone fractal," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    18. Peng, G.H. & Cai, X.H. & Cao, B.F. & Liu, C.Q., 2012. "A new lattice model of traffic flow with the consideration of the traffic interruption probability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 656-663.
    19. Daganzo, Carlos F., 1995. "Requiem for second-order fluid approximations of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 29(4), pages 277-286, August.
    20. Daganzo, Carlos F., 1994. "The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory," Transportation Research Part B: Methodological, Elsevier, vol. 28(4), pages 269-287, August.
    21. Nagatani, Takashi, 2023. "Macroscopic traffic flow in multiple-loop networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    22. Arvind Kumar Gupta, 2013. "A Section Approach To A Traffic Flow Model On Networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 24(05), pages 1-23.
    23. Nagatani, Takashi, 2020. "Traffic flow on percolation-backbone fractal," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    24. Nagatani, Takashi, 2022. "Dynamic transition induced by route choice in two-route traffic network with onramp," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    25. Peng, Guang-han & Cheng, Rong-jun, 2013. "A new car-following model with the consideration of anticipation optimal velocity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3563-3569.
    26. Nagatani, Takashi, 2021. "Traffic flow on star graph: Nonlinear diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
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    Cited by:

    1. Muskan Verma & Arvind Kumar Gupta & Sapna Sharma, 2024. "Traffic flow dynamics and oscillation control in conserved fractal networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(10), pages 1-12, October.

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