SpringerLink
Log in

A quantitatively controllable mesoscopic reliability model of an interdependent public transit network considering congestion, time-delay interaction and self-organization effects

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper establishes a multi-parameter controlling cascading failures (CFs) model for measuring interdependent public transit network (PTN) reliability under mesoscopic perspective. First, we abstract the weighted PTN and geospatial PTN into a double-layered passenger flow system that considers the influences of the transportation infrastructure and the interaction between the passenger flow transited via the public transit mode and that transited via all other urban traffic modes. Second, for embedding the congestion, time-delay interaction and self-organization effects in the CFs model of an interdependent PTN, we propose the failure load dynamic redistribution (FLDR) considering the congestion effect in each sub-network, define the interaction way (another FLDR form) considering time-delay effect between two sub-networks and establish the CFs judging method considering the self-organization effect in the interdependent PTN. Furthermore, the multi-perspective measurement indicator system (i.e., (i) the global and local perspectives and (ii) the aggregated and discretized perspectives) is defined to provide a full viewing perspective for better understanding and capturing the CFs process. Finally, through a simulation analysis of **an’s PTN, the adaptability of the proposed CFs model is verified, and the significant nonlinearity is found, i.e., there is a threshold value of the station load tolerance parameter \(\lambda _C\), making the cascading survivability of interdependent PTN significantly increase, when the actual station load tolerance parameter is larger than \(\lambda _C\); moreover, increasing the control parameter of the connected edge transit capacity (parameter \(\theta \)) can speed up the process of finding this \(\lambda _C\) of an interdependent PTN. This nonlinearity provides the simulation evidence of the CFs controllability in the interdependent PTN.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Cervero R.: The transit metropolis : a global inquiry. Development. 1998

  2. Wang, Y., **ao, R.: An ant colony based resilience approach to cascading failures in cluster supply network. Phys. A Stat. Mech. Appl. 462, 150–166 (2016)

    Article  MATH  Google Scholar 

  3. Wang, J.: Mitigation of cascading failures on complex networks. Nonlinear Dyn. 70(3), 1959–1967 (2012)

    Article  MathSciNet  Google Scholar 

  4. Yi, C., Bao, Y., Jiang, J., et al.: Modeling cascading failures with the crisis of trust in social networks. Phys. A Stat. Mech. Appl. 436, 256–271 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  5. Wu, J.J., Sun, H.J., Gao, Z.Y.: Cascading failures on weighted urban traffic equilibrium networks. Phys. A Stat. Mech. Appl. 386(1), 407–413 (2007)

    Article  Google Scholar 

  6. Qian, Y., Wang, B., Xue, Y., et al.: A simulation of the cascading failure of a complex network model by considering the characteristics of road traffic conditions. Nonlinear Dyn. 80(1–2), 413–420 (2015)

    Article  Google Scholar 

  7. Soh, H., Lim, S., Zhang, T., et al.: Weighted complex network analysis of travel routes on the Singapore public transportation system. Phys. A Stat. Mech. Appl. 389(24), 5852–5863 (2010)

    Article  Google Scholar 

  8. Cai, Z., Wang, D., Chen, X.: A Novel Trip Coverage Index for Transit Accessibility Assessment Using Mobile Phone Data. J. Adv. Transp. 2017(10), 1–14 (2017)

    Article  Google Scholar 

  9. Chen, J., Liu, Z., Zhu, S., et al.: Design of limited-stop bus service with capacity constraint and stochastic travel time. Transp. Res. Part E 83, 1–15 (2015)

    Article  Google Scholar 

  10. Dou, X., Meng, Q., Guo, X.: Bus schedule coordination for the last train service in an intermodal bus-and-train transport network. Transp. Res. Part C Emerg. Technol. 60(3n04), 360–376 (2015)

    Article  Google Scholar 

  11. Yan, Y., Meng, Q., Wang, S., et al.: Robust optimization model of schedule design for a fixed bus route. Transp. Res. Part C Emerg. Technol. 25(8), 113–121 (2012)

    Article  Google Scholar 

  12. Sergey, V.B., Roni, P., Gerald, P., et al.: Catastrophic cascade of failures in interdependent networks. Nature 464(7291), 1025 (2010)

    Article  Google Scholar 

  13. Pant, R., Barker, K., Grant, F.H., et al.: Interdependent impacts of inoperability at multi-modal transportation container terminals. Transp. Res. Part E 47(5), 722–737 (2011)

    Article  Google Scholar 

  14. Du, W.B., Zhou, X.L., Lordan, O., et al.: Analysis of the Chinese Airline Network as multi-layer networks. Transp. Res. Part E 89, 108–116 (2016)

    Article  Google Scholar 

  15. Veremyev, A., Sorokin, A., Boginski, V., et al.: Minimum vertex cover problem for coupled interdependent networks with cascading failures. Eur. J. Oper. Res. 232(3), 499–511 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  16. Tang, L., **g, K., He, J., et al.: Complex interdependent supply chain networks: cascading failure and robustness. Phys. A Stat. Mech. Appl. 443, 58–69 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  17. Rosato, V., Issacharoff, L., Tiriticco, F., et al.: Modelling interdependent infrastructures using interacting dynamical models. Int. J. Crit. Infrastruct. 4(1/2), 63–79 (2016)

    Article  Google Scholar 

  18. Zhang, L., Lu, J., Fu, B., et al.: A review and prospect for the complexity and resilience of urban public transit network based on complex network theory. Complexity 2018, 2156309 (2018)

    Google Scholar 

  19. Qian, Y.S., Wang, M., Kang, H.X., et al.: Study on the road network connectivity reliability of Valley City based on complex network. Math. Probl. Eng. 8, 924–941 (2012)

    MATH  Google Scholar 

  20. Leng, B., Zhao, X., **ong, Z.: Evaluating the evolution of subway networks: evidence from Bei**g subway network. Epl 105(5), 58004 (2014)

    Article  Google Scholar 

  21. Yang, Y., Huang, A., Guan, W.: Statistic properties and cascading failures in a coupled transit network consisting of bus and subway systems. Int. J. Mod. Phys. B 28(30), 1450212 (2014)

    Article  Google Scholar 

  22. Su, Z., Li, L., Peng, H., et al.: Robustness of interrelated traffic networks to cascading failures. Sci. Rep. 4, 5413 (2014)

    Article  Google Scholar 

  23. Huang, A., Zhang, H.M., Wei, G., et al.: Cascading failures in weighted complex network of public transit system based on coupled map lattices. Math. Probl. Eng. 2015, 940795 (2015)

    Google Scholar 

  24. Zhang, L., Fu, B.B., Li, S.B.: Cascading failures coupled model of interdependent double layered public transit network. Int. J. Mod. Phys. C 27(12), 1650145 (2016)

    Article  MathSciNet  Google Scholar 

  25. Sheffi, Y.: Urban transportation networks: equilibrium analysis with mathematical programming methods, pp. 118–121. Prentice Hall Press, Englewood Cliffs (1985)

    Google Scholar 

  26. Zhang, L., Fu, B.B., Li, Y.X.: Cascading failure of urban weighted public transit network under single station happening emergency. Procedia Eng. 137, 259–266 (2016)

    Article  Google Scholar 

  27. Wang, J., Jiang, C., Qian, J.: Robustness of interdependent networks with different link patterns against cascading failures. Phys. A Stat. Mech. Appl. 393(1), 535–541 (2014)

    Article  Google Scholar 

  28. Fu, B., Zhang, L., Li, S., et al.: Survivability of public transit network based on network structure entropy. Int. J. Mod. Phys. C 26(9), 1550104 (2015)

    Article  Google Scholar 

  29. Kim, T.J.: Advanced Transport and Spatial Systems Models. Springer, New York (1990)

    Book  Google Scholar 

  30. Wang, J., Li, S.: The impact of travelers’ rationality degree heterogeneity in the advanced traveler information system on the network traffic flow evolution. SIMULATION: Trans. Soc. Model. Simul. Int. 93(6), 447–457 (2017)

    Article  Google Scholar 

  31. Zheng, J., Gao, Z., Fu, B.: Load distribution in congested scale-free networks. Int. J. Mod. Phys. C 20(02), 197–207 (2009)

    Article  MATH  Google Scholar 

  32. Wardrop, J.G.: Some theoretical aspects of road traffic research. OR 4(4), 72–73 (1953)

    Google Scholar 

  33. Beckmann, M.J., McGuire, C.B., Winsten, C.B.: Studies in the Economics of Transportation. Yale University Press, Connecticut (1956)

    Google Scholar 

  34. Zhang, L., Lu, J., Man, L., et al.: A cascading failures perspective based mesoscopic reliability model of weighted public transit network considering congestion effect and user equilibrium evacuation. Math. Probl. Eng. 2018, 9292375 (2018)

    Google Scholar 

  35. Frank, M., Wolfe, P.: An algorithm for quadratic programming. Naval Res. Logist. Q. 3(1–2), 95–110 (1956)

    Article  MathSciNet  Google Scholar 

  36. Leblanc, L.J., Morlok, E.K., Pierskalla, W.P.: An efficient approach to solving the road network equilibrium traffic assignment problem. Transp. Res. 9(5), 309–318 (1975)

    Article  Google Scholar 

  37. Zheng, X., Chen, J.P., Shao, J.L., et al.: Analysis on topological properties of Bei**g urban public transit based on complex network theory. Acta Physica Sinica 61(19), 190379–190510 (2012)

    Google Scholar 

  38. Motter, A.E., Lai, Y.C.: Cascade-based attacks on complex networks. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 66(2), 65102 (2002)

    Google Scholar 

  39. Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393, 440–442 (1998)

    Article  MATH  Google Scholar 

  40. Barabási, A., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  41. Zhang, L., Lu, J., Yue, X., et al.: An auxiliary optimization method for complex public transit route network based on link prediction. Mod. Phys. Lett. B 32(5), 1850066 (2018)

    Article  MathSciNet  Google Scholar 

  42. Wang, Z., Kokubo, S., Jusup, M., et al.: Universal scaling for the dilemma strength in evolutionary games. Phys. Life Rev. 14, 1–30 (2015)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 51478110, 71471104, 71871130), the Scientific Study Foundation of Graduate School of Southeast University (No. YBPY1884), the Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX17_0144), and the Science and Technology Program of Jiangsu Province (No. BY2016076-05).

Author information

Authors and Affiliations

  1. Jiangsu Key Laboratory of Urban ITS, Southeast University, Nan**g, 211189, People’s Republic of China

    Lin Zhang, Jian Lu, Yun-xuan Li & Man Long

  2. Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, Southeast University, Nan**g, 211189, People’s Republic of China

    Lin Zhang, Jian Lu, Yun-xuan Li & Man Long

  3. School of Transportation, Southeast University, Nan**g, 211189, People’s Republic of China

    Lin Zhang, Jian Lu, Yun-xuan Li & Man Long

  4. School of Architecture and Urban Planning, Shandong Jianzhu University, **an, 250101, People’s Republic of China

    Bai-bai Fu

  5. Department of Traffic Management Engineering, Shandong Police College, **an, 250014, People’s Republic of China

    Shu-bin Li

Authors
  1. Lin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jian Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bai-bai Fu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shu-bin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yun-xuan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Man Long
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jian Lu.

Ethics declarations

Conflicts of interest

All authors declare that they have no conflicts of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, L., Lu, J., Fu, Bb. et al. A quantitatively controllable mesoscopic reliability model of an interdependent public transit network considering congestion, time-delay interaction and self-organization effects. Nonlinear Dyn 96, 933–958 (2019). https://doi.org/10.1007/s11071-019-04831-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-019-04831-y

Keywords

Search

Navigation