Robustness analysis of a multimodal comprehensive transportation network from the perspectives of infrastructure and operation: A case study

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Abstract

The development of a multimodal comprehensive transportation network (CTN) is crucial for enhancing connectivity and resilience in a regional transportation system. While China has established an extensive transportation infrastructure, the robustness of multimodal transportation systems remains insufficiently explored. Existing research primarily examines transportation networks from a single aspect, focusing either on infrastructure attributes or operational characteristics, while largely neglecting their interactions and disparities. To address this gap, this study analyzed the robustness of CTN from two perspectives, including a comprehensive transportation infrastructure network (CINet) and comprehensive transportation operation network (CONet). Based on complex network theory, optimized modeling methods of the networks were proposed. Utilizing multi-source data, statistical characteristics and robustness were comparatively explored in CINet, CONet, and their single-mode networks including highway, railway, navigation, and airway/airline (HINet, RINet, NINet, AINet, HONet, RONet, NONet, AONet) networks of Jiangsu Province. The results reveal that: 1) In Jiangsu, all the networks are not scale-free. All infrastructure networks (INets), except for AINet, do not exhibit small-world properties, while all the operation networks (ONets) are small-world. 2) All the networks are more robust to random attack than other strategies. CINet demonstrates the highest robustness among INets, whereas surprisingly, RONet is the most robust among ONets. Generally, INets exhibit superior robustness compared to ONets. 3) As the number of optimized hubs increases, the network robustness is much stronger, especially under calculated attacks. The improvements of 𝐼𝑅𝐶 and 𝐼𝑅𝑅 reach 4.55% and 114.56% in CINet, while reaching 4.10% and 99.24% in CONet, respectively, indicating a significant effect of optimized hub designs in network robustness enhancement. 4) When optimizing the same hubs, network robustness enhancement is more pronounced in CONet than in CINet. These findings highlight the importance of optimized hubs to multimodal comprehensive transportation systems, and provide guidance for network planning and management.

Keywords

comprehensive transportation infrastructure network / comprehensive transportation operation network / network modeling method / network robustness analysis

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References

[1] L. F. Xiong, Analysis of Cascading Failure Propagation Mechanism in Comprehensive Transportation Infrastructure Network , Ph.D thesis, Southwest Jiaotong University, 2019.

[2] J. Y. Guo, Approach to Passenger Flow Regulation of Urban Mass Transit Network , Ph.D. thesis, Beijing Jiaotong University, 2016.

[3] V. Nicolosi, M. Augeri, M. D'Apuzzo, A. Evangelisti, D. Santilli, A probabilistic approach to the evaluation of seismic resilience in road asset management, Int. J. Dis. Risk Sci., 13 (2022), 114-124. https://doi.org/10.1007/s13753-022-00395-5

[4] O. Fröidh, Perspectives for a future high-speed train in the Swedish domestic travel market. J. Transp. Geogr., 4 (2008), 16: 268-277. https://doi.org/10.1016/j.jtrangeo.2007.09.005

[5] P. Sen, S. Dasgupta, A. Chatterjee, P. A. Sreeram, G. Mukherjee, S. S. Manna, Small-world properties of the Indian railway network. Phys. Rev. E, 67 (2003). http://dx.doi.org/10.1103/PhysRevE.67.036106

[6] C. von Ferber, T. Holovatch, Y. Holovatch, V. Palchykov, Network harness: Metropolis public transport, Phys. A, 380 (2007), 585-591. https://doi.org/10.1016/J.PHYSA.2007.02.101

[7] Z. X. Wu, H. K. W. Lam, Network equilibrium model for congested multi-mode transport network with elastic demand, J. Adv. Transp., 37 (2003), 295-318. https://doi.org/10.1002/atr.5670370304

[8] C. Cao, Y. Su, Transportation infrastructure and regional resource allocation, Cities, 155 (2024), 105433. https://doi.org/10.1016/j.cities.2024.105433

[9] R. Liu, Measurement of Economic Growth Effect of High-speed Transportation Network in Urban Agglomerations-Taking the Pearl River Delta as an example , Ph.D thesis, Yunnan University of Finance and Economics, 2021.

[10] N. Zhang, A. Alipour, Multi-scale robustness model for highway networks under flood events, Transp. Res. D-Tr. E., 83 (2020), 102281. https://doi.org/10.1016/j.trd.2020.102281

[11] W. H. Zhu, S. D. Wang, S. L. Liu, X. Y. Gao, P. C. Zhang, L. X. Zhang, Reliability and robustness assessment of highway networks under multi-hazard scenarios: a case study in Xinjiang, China, China, Sustainability, 15 (2023), 5379. https://doi.org/10.3390/su15065379

[12] G. Vani, H. Maoh, Characterizing the nature of a multi-regional trucking network using the network robustness index: An application to Ontario, Canada, Appl. Spat. Anal. Policy, 16 (2023), 383-407. https://doi.org/10.1007/s12061-022-09484-w

[13] M. Ouyang, C. Liu, M. Xu, Value of resilience-based solutions on critical infrastructure protection: Comparing with robustness-based solutions, Reliab. Eng. Syst. Saf., 190 (2019), 106506. https://doi.org/10.1016/j.ress.2019.106506

[14] Y. H. Yang, Y. X. Liu, M. X. Zhou, F. X. Li, C. Sun, Robustness assessment of urban rail transit based on complex network theory: A case study of the Beijing Subway, Saf. Sci., 79 (2015), 149-162. https://doi.org/10.1016/j.ssci.2015.06.006

[15] F. Ma, W. J. Shi, K. F. Yuen, Q. P. Sun, X. B. Xu, Y. J. Wang, et al., Exploring the robustness of public transportation for sustainable cities: A double-layered network perspective, J. Clean. Prod., 265 (2020), 121747. https://doi.org/10.1016/j.jclepro.2020.121747

[16] S. Wandelt, Y. F. Xu, X. Q. Sun, Measuring node importance in air transportation systems: On the quality of complex network estimations, Reliab. Eng. Syst. Saf., 240 (2023), 109596. https://doi.org/10.1016/j.ress.2023.109596

[17] V. Latora, M. Marchiori, Is Boston subway a small-world network?, Phys. A, 314 (2002), 109-113. https://doi.org/10.1016/S0378-4371(02)01089-0

[18] J. Sienkiewicz, J. A. Hołyst, Statistical analysis of 22 public transport networks in Poland, Phys. Rev. E, 72 (2005), 046127. https://doi.org/10.1103/PhysRevE.72.046127

[19] G. Domenico, M. Ernesto, Compared analysis of metro networks supported by graph theory, Networks Spat. Econ., 5 (2005), 395-414. https://doi.org/10.1007/s11067-005-6210-5

[20] Y. Wang, O. Zhao, L. M. Zhang, Modeling urban rail transit system resilience under natural disasters: A two-layer network framework based on link flow, Reliab. Eng. Syst. Saf., 241 (2024). https://doi.org/10.1016/j.ress.2023.109619

[21] M. T. Trobajo, M. V. Carriegos, Spanish airport network structure: Topological characterization, Comput. Math. Methods, 2022 (2022), 4952613. https://doi.org/10.1155/2022/4952613

[22] M. Zanin, S. Wandelt, An overview of network structures and node importance in the global aviation system from the year 2011 to 2022, J. Air. Transp. Res. Soc., 1 (2023), 63-80. https://doi.org/10.59521/5E2DDEC9FAD4593B

[23] K. Sugishita, K. Arisawa, S. Hanaoka, Delay propagation patterns in Japan’s domestic air transport network, Transp. Res. Interdiscip. Perspect., 27 (2024), 101235. https://doi.org/10.1016/j.trip.2024.101235

[24] N. Anna, D. June, Supernetworks: Decision-Making for the Information Age , England: Edward Publishing, Incorporated, 2002.

[25] S. C. Dafermos, The traffic assignment problem for multiclass-user transportation networks, Transp. Sci., 6 (1972), 73-87. https://doi.org/10.1287/trsc.6.1.73

[26] M. Beuthe, B. Jourquin, J. F. Geerts, C. K. à Ndjang'Ha, Freight transportation demand elasticities: a geographic multimodal transportation network analysis, Transp. Res. Part E: Logist. Transp. Rev., 37 (2001), 253-266. https://doi.org/10.1016/S1366-5545(00)00022-3

[27] P. Xu . Intercity multi-modal traffic assignment model and algorithm for urban agglomeration considering the whole travel process, in IOP Conference Series: Earth and Environmental Science , 189 (2018), 6. https://doi.org/10.1088/1755-1315/189/6/062016

[28] H. Y. Ding, Research on Urban Multi-Modal Public Transit Network Fast Construction Method and Assignment Model , Ph.D thesis, Southeast University, 2018.

[29] Y. Luo, D. L. Qian, Construction of subway and bus transport networks and analysis of the network topology characteristics, J. Transp. Syst. Eng. Inf. Technol., 15 (2015), 39-44. https://doi.org/10.16097/j.cnki.1009-6744.2015.05.006

[30] X. H. Li, J. Y. Guo, C. Gao, Network-based transportation system analysis: A case study in a mountain city, Chaos, Solitons Fractals, 107 (2018), 256-265. https://doi.org/10.1016/j.chaos.2018.01.010

[31] X. Feng, S. W. He, G. Y. Li, J. S. Chi, Transfer network of high-speed rail and aviation: Structure and critical components, Phys. A, 581 (2021), 126197. https://doi.org/10.1016/j.physa.2021.126197

[32] X. Q. Huang, J. X. Gao, S. V. Buldyrev, S. Havlin, H. E. Stanley, Robustness of interdependent networks under targeted attack, Phys. Rev. E, 83 (2011), 065101. https://doi.org/10.1103/PhysRevE.83.065101

[33] B. Berche, C. V. Ferber, T. Holovatch, Y. Holovatch, Resilience of public transport networks against attacks, Eur. Phys. J. B, 71 (2009), 125-137. https://doi.org/10.1140/epjb/e2009-00291-3

[34] Y. S. Chen, X. Y. Wang, X. W. Song, J. L. Jia, Y. Y. Chen, W. L. Shang, Resilience assessment of multimodal urban transport networks, J. Circuits Syst. Comput., 31 (2022), 18. https://doi.org/10.1142/S0218126622503108

[35] L. Ge, S. Voß, L. Xie, Robustness and disturbances in public transport, Publ. Transp., 14 (2022), 191-261. https://doi.org/10.1007/s12469-022-00301-8

[36] X. L. Hu, J. Huang, F. Shi, A robustness assessment with passenger flow data of high-speed rail network in China, Chaos, Solitons Fractals, 165 (2022), 112792. https://doi.org/10.1016/j.chaos.2022.112792

[37] R. S. Yang, W. Sun, M. L. Le, H. Y. Zhang, The Chinese aviation network: An empirical temporal analysis on its structural properties and robustness, Appl. Sci., 13 (2023), 11627. https://doi.org/10.3390/app132111627

[38] X. Qu, H. Lin, Y. Liu, Envisioning the future of transportation: Inspiration of ChatGPT and large models, Commun. Transp. Res., 3 (2023), 100103. https://doi.org/10.1016/j.commtr.2023.100103

[39] Y. Fei, P. Shi, Y. Liu, L. Wang, Critical roles of control engineering in the development of intelligent and connected vehicles, J. Int. Connected Veh., 7 (2024), 79-85. https://doi.org/10.26599/JICV.2023.9210040

[40] S. Y. Kuang, Y. Liu, X. Wang, X. H. Wu, Y. T. Wei, Harnessing multimodal large language models for traffic knowledge graph generation and decision-making, Commun. Transp. Res., 4 (2024), 100146. https://doi.org/10.1016/j.commtr.2024.100146

[41] Y. Liu, F. Y. Wu, Z. Y. Liu, K. Wang, F. Y. Wang, X. B. Qu, Can language models be used for real-world urban-delivery route optimization, The Innovation, 4 (2023), 6. https://doi.org/10.1016/j.xinn.2023.100520

[42] Z. C. Chen, C. J. Zheng, T. T. Tao, Y. Y. Wang, Reliability analysis of urban road traffic network under targeted attack strategies considering traffic congestion diffusion, Reliab. Eng. Syst. Saf., 248 (2024), 110171. https://doi.org/10.1016/j.ress.2024.110171

[43] Z. L. Ma, D. W. Hu, S. I. J. Chien, J. Liu, Y. Liu, K. Wu, Robustness of urban rail transit networks considering cascade failure under attacks: A case study of Nanjing, China, ASCE-ASME J. Risk U. A, 11 (2025), 04024093. https://doi.org/10.1061/AJRUA6.RUENG-1324

[44] T. Li, L. L. Rong, K. S. Yan, Vulnerability analysis and critical area identification of public transport system: A case of high-speed rail and air transport coupling system in China, Transp. Res. Part A Policy Pract., 127 (2019), 55-70. https://doi.org/10.1016/j.tra.2019.07.008

[45] Y. Chen, J. E. Wang, F. J. Jin, Robustness of China’s air transport network from 1975 to 2017, Phys. A, 539 (2020), 122876. https://doi.org/10.1016/j.physa.2019.122876

[46] S. Wandelt, X. Shi, X. Q. Sun, Estimation and improvement of transportation network robustness by exploiting communities, Reliab. Eng. Syst. Saf., 206 (2021), 107307. https://doi.org/10.1016/j.ress.2020.107307

[47] Z. Xin, F. Niu, Structure and robustness of China’s railway transport network, Transp. Lett., 15 (2023), 375-385. https://doi.org/10.1080/19427867.2022.2053280

[48] V. H. Tran, S. A. Cheong, N. D. Bui, Complex network analysis of the robustness of the hanoi, vietnam bus network, J. Syst. Sci. Complex, 32 (2019), 1251-1263. https://doi.org/10.1007/s11424-019-7431-x

[49] Y. T. Zheng, J. L. Xiao, X. D. Hua, W. Wang, H. Chen, A comparative analysis of the robustness of multimodal comprehensive transportation network considering mode transfer: A case study, Electron. Res. Arch., 31 (2023), 5362-5395. https://doi.org/10.3934/era.2023272

[50] T. Li, L. L. Rong, A comprehensive method for the robustness assessment of high-speed rail network with operation data: A case in China, Transp. Res. Part A Policy Pract., 132 (2020), 666-681. https://doi.org/10.1016/j.tra.2019.12.019

[51] Y. Zhou, J. Wang, G. Q. Huang, Efficiency and robustness of weighted air transport networks, Transp. Res. Part E: Logist. Transp. Rev., 122 (2019), 14-26. https://doi.org/10.1016/j.tre.2018.11.008

[52] J. C. Jiang, L. X. Wu, J. Q. Yu, M. J. S. Wang, K. Hui, Z.X. Zhang, et al., Robustness of bilayer railway-aviation transportation network considering discrete cross-layer traffic flow assignment, Transp. Res. D-Tr. E, 127 (2024), 104071. https://doi.org/10.1016/j.trd.2024.104071

[53] J. H. Zhang, Y. Zhou, S. L. Wang, Q. J. Min, Critical station identification and robustness analysis of urban rail transit networks based on comprehensive vote-rank algorithm, Chaos, Solitons Fractals, 178 (2024), 114379. https://doi.org/10.1016/j.chaos.2023.114379

[54] Y. F. Zhang, S. T. Ng, Robustness of urban railway networks against the cascading failures induced by the fluctuation of passenger flow, Reliab. Eng. Syst. Saf., 219 (2022), 108227. https://doi.org/10.1016/j.ress.2021.108227

[55] Z. Z. Liu, H. Chen, E. Z. Liu, W. Y. Hu, Exploring the resilience assessment framework of urban road network for sustainable cities, Phys. A, 586 (2022), 126465. https://doi.org/10.1016/j.physa.2021.126465