Skip to main content
SpringerLink
Log in

Assessing network vulnerability of heavy rail systems with the impact of partial node failures

  • Published:
Transportation Aims and scope Submit manuscript

Abstract

Much of the literature in recent years has examined the vulnerability of transportation networks. To identify appropriate and operational measures of nodal centrality using connectivity in the case of heavy rail systems, this paper presents a set of comprehensive measures in the form of a Degree of Nodal Connection (DNC) index. The DNC index facilitates a reevaluation of nodal criticality among distinct types of transfer stations in heavy rail networks that present a number of multiple lines between stations. Specifically, a new classification of transfer stations—mandatory transfer, non-mandatory transfer, and end transfer—and a new measure for linkages—link degree and total link degree—introduces the characteristics of heavy rail networks when we accurately expose the vulnerability of a node. The concept of partial node failure is also introduced and compare the results of complete node failure scenarios. Four local and global indicators of network vulnerability are derived from the DNC index to assess the vulnerability of major heavy rail networks in the United States. Results indicate that the proposed DNC indexes can inform decision makers or network planners as they explore and compare the resilience of multi-hubs and multi-line networks in a comprehensive but accurate manner regardless of their network sizes.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

(Source: https://www.bart.gov/stations)

Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  • Albert, R., Jeong, H., Barabasi, A.L.: Error and attack tolerance of complex networks. Nature 406, 378–382 (2000)

    Article  Google Scholar 

  • Angeloudis, P., Fisk, D.: Large subway systems as complex networks. Physica A 367, 553–558 (2006)

    Article  Google Scholar 

  • Arulselvan, A., Commander, C. W., Elefteriadou, L., Pardalos, P. M.: Detecting critical nodes in sparse graphs. Comput. Oper. Res. 36(7), 2193–2200 (2009)

    Article  Google Scholar 

  • Cats, O., Jenelius, E.: Beyond a complete failure: the impact of partial capacity degradation on public transport network vulnerability. Transp. B Transp. Dyn. (2016). https://doi.org/10.1080/21680566.2016.1267596

    Article  Google Scholar 

  • Chiou, S.W.: Vulnerability analysis of a signal-controlled road network for equilibrium flow. In: Márquez, F.P.G., Lev, B. (eds.) Advanced Business Analytics, pp. 109–142. Springer, Cham (2015)

    Chapter  Google Scholar 

  • D’Este, G.M., Taylor, M.A.P.: Network vulnerability: an approach to reliability analysis at the level of national strategic transport networks. In: Iida, Y., Bell, M.G.H. (eds.) The Network Reliability of Transport, pp. 23–44. Pergamon, New York (2003)

    Google Scholar 

  • D’lima, M., Medda, F.: A new measure of resilience: an application to the London underground. Transp. Res. Part A 81, 35–46 (2015)

    Google Scholar 

  • Demsar, U., Spatenkova, O., Virrantaus, K.: Identifying critical locations in a spatial network with graph theory. Trans. GIS 12, 61–82 (2008)

    Article  Google Scholar 

  • Derrible, S., Kennedy, C.: Characterizing metro networks: state, form, and structure. Transportation 37(2), 275–297 (2010a)

    Article  Google Scholar 

  • Derrible, S., Kennedy, C.: The complexity and robustness of metro networks. Physica A 389(17), 3678–3691 (2010b)

    Article  Google Scholar 

  • El-Rashidy, R.A., Grant-Muller, S.M.: An assessment method for highway network vulnerability. J. Transp. Geogr. 34, 34–43 (2014)

    Article  Google Scholar 

  • Grubesic, T.H., O’Kelly, M.E., Murray, A.T.: A geographic perspective on commercial Internet survivability. Telemat. Inform. 20(1), 51–69 (2003)

    Article  Google Scholar 

  • Holmgren, A.J.: A framework for vulnerability assessment of electric power systems. In: Murray, A.T., Grubesic, T.H. (eds.) Critical Infrastructure, pp. 31–55. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  • Kim, H.: Geographical analysis on network reliability of public transportation systems: a case study of subway network system in Seoul. J. Korean Geogr. Soc. 44(2), 187–205 (2009)

    Google Scholar 

  • Kim, H.: p-Hub protection models for survivable hub network design. J. Geogr. Syst. 14(4), 437–461 (2012)

    Article  Google Scholar 

  • Kim, H., Kim, C., Chun, Y.: Network reliability and resilience of rapid transit systems. Prof. Geogr. 68(1), 53–65 (2016)

    Article  Google Scholar 

  • Kim, H., Ryerson, M.S.: The q-Ad hoc hub location problem. Netw. Spat. Econ. 17(3), 1015–1041 (2017)

    Article  Google Scholar 

  • Kim, H., Song, Y.: Examining accessibility and reliability in the evolution of subway systems. J. Public Transp. 18(3), 89–106 (2015)

    Article  Google Scholar 

  • Kurauchi, F., Sumalee, A., Seto, Y.: Network evaluation based on connectivity vulnerability. In: Lam, W.H.K., Wong, S.C., Lo, H.K. (eds.) Transportation and Traffic Theory, pp. 637–676. Routledge, New York (2009)

    Google Scholar 

  • Li, Y., Kim, H.: Assessing survivability of the Beijing subway system. Int. J. Geospat. Environ. Res. 1(1), 1–22 (2014)

    Google Scholar 

  • Matisziw, T.C., Murray, A.T., Grubesic, T.H.: Exploring the vulnerability of network infrastructure to interdiction. Ann. Reg. Sci. 43(2), 307–321 (2009)

    Article  Google Scholar 

  • Murray, A.T.: An overview of network vulnerability modeling approaches. GeoJournal 78(2), 209–221 (2013)

    Article  Google Scholar 

  • Murray, A.T., Grubesic, T.: Reliability and Vulnerability in Critical Infrastructure: A Quantitative Geographic Perspective. Springer, Heidelberg (2007)

    Book  Google Scholar 

  • Murray, A.T., Matisziw, T.C., Grubesic, T.H.: Critical network infrastructure analysis: interdiction and system flow. J. Geogr. Syst. 9, 103–117 (2007)

    Article  Google Scholar 

  • Myung, Y.S., Kim, H.J.: A cutting plane algorithm for computing k-edge survivability of a network. Eur. J. Oper. Res. 156, 579–589 (2004)

    Article  Google Scholar 

  • Nakanishi, Y.J.: Securing America’s mass transit systems. J. Transp. Secur. 2(1), 9–11 (2009)

    Article  Google Scholar 

  • O’Kelly, M.E., Kim, H.: Survivability of commercial backbones with peering: a case study of Korean networks critical infrastructure. In: Murray, A.T., Grubesic, T.H. (eds.) Reliability and Vulnerability, pp. 107–128. Springer, Berlin (2007)

    Google Scholar 

  • O’Kelly, M.E.: Network hub structure and resilience. Netw. Spat. Econ. 15(2), 235–251 (2014)

    Article  Google Scholar 

  • Rashidi, E.: Optimization models and algorithms for vulnerability analysis and mitigation planning of pyro-terrorism. ProQuest Dissertations Publishing, Mississippi State University (2016)

  • Rodrigue, J.P., Comtois, C., Slack, B.: The Geography of Transport Systems, 4th edn. Routledge, New York (2017)

    Google Scholar 

  • Rodríguez-Núñez, E., García-Palomares, J.C.: Measuring the vulnerability of public transport networks. J. Transp. Geogr. 35, 50–63 (2014)

    Article  Google Scholar 

  • Schoon, M.: A short historical overview of the concepts of resilience, vulnerability, and adaptation. Workshop in Political Theory and Policy Analysis, Indiana University Working Paper W05-4 (2005)

  • Sun, D., Guan, S.: Measuring vulnerability of urban metro network from line operation perspective. Transp. Res. Part A 94, 348–359 (2016)

    Google Scholar 

  • Sun, D., Zhao, Y., Lu, Q.C.: Vulnerability analysis of urban rail transit networks: a case study of Shanghai, China. Sustainability 7(6), 6919–6936 (2015)

    Article  Google Scholar 

  • The BART (San Francisco, CA) network https://www.bart.gov/stations. Accessed April 2016

  • The CTA (Chicago, IL) network http://www.transitchicago.com/assets/1/maps/ctatrainmap.png. Accessed July 2017

  • The GCRTA (Cleveland, OH) network http://www.riderta.com/sites/default/files/pdf/maps/System_Map_Rapid_Connect.pdf. Accessed Apr 2016

  • The LACMTA (Los Angeles, CA) network https://media.metro.net/documents/8f0fe43e-da3b-4a10-bd8e-4cfd54e30eb3.pdf. Accessed Sept 2016

  • The Local fr (2017). https://www.thelocal.fr/20170717/the-transport-works-set-to-disrupt-your-summer-in-parisand-elsewhere-in-france. Accessed Oct 2017

  • The MARTA (Atlanta, GA) network http://www.itsmarta.com/train-stations-and-schedules.aspx. Accessed Apr 2016

  • The MBTA (Boston, MA) network http://www.mbta.com/schedules_and_maps/subway/. Accessed Apr 2016

  • The MDT (Miami, FL) network http://www.miamidade.gov/transit/metrorail-stations.asp and https://www.miami-dade.gov/transit/metromover-stations.asp. Accessed Apr 2016

  • The NYCT (New York, NY) network http://web.mta.info/maps/submap.html. Accessed Apr 2016

  • The PATH (New York, NY) network http://www.panynj.gov/path/maps.html. Accessed Apr 2016

  • The SEPTA (Philadelphia, PA) network http://septa.org/maps/system/. Accessed Apr 2016

  • The WMATA (Washington, DC) network https://wmata.com/schedules/maps/upload/system_map_color.pdf. Accessed May 2017

  • Wan, N., Zhan, F., Cai, Z.: A spatially weighted degree model for network vulnerability analysis. Geo-spat. Inf. Sci. 14(4), 274–281 (2011)

    Article  Google Scholar 

  • Wang, J., Li, Y., Liu, J., He, K., Wang, P.: Vulnerability analysis and passenger source prediction in urban rail transit networks. PLoS ONE 8(11), e80178 (2013)

    Article  Google Scholar 

  • Wood, R.K.: Deterministic network interdiction. Math. Comput. Model. 17, 1–18 (1993)

    Article  Google Scholar 

  • Yates, J., Sanjeevi, S.: Assessing the impact of vulnerability modeling in the protection of critical infrastructure. J. Geogr. Syst. 4(4), 415–435 (2012)

    Article  Google Scholar 

  • Zhang, X., Miller-Hooks, E., Denny, K.: Assessing the role of network topology in transportation network resilience. J. Transp. Geogr. 46, 35–46 (2015)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Geography, The University of Tennessee, Knoxville, TN, USA

    Qian Ye & Hyun Kim

Authors
  1. Qian Ye
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hyun Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Qian Ye: Literature Search and Review, Data Analysis and Index Modeling, Manuscript writing. Hyun Kim: Design Analytical Framework, Data Analysis, and Manuscript writing and Editing.

Corresponding author

Correspondence to Hyun Kim.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ye, Q., Kim, H. Assessing network vulnerability of heavy rail systems with the impact of partial node failures. Transportation 46, 1591–1614 (2019). https://doi.org/10.1007/s11116-018-9859-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11116-018-9859-6

Keywords

Search

Navigation