Investigating transport network vulnerability by capacity weighted spectral analysis

Transport networks operating at or near capacity are vulnerable to disruptions, so flow bottlenecks are potent sources of vulnerability. This paper presents an efficient method for finding transport network cuts, which may constitute such bottlenecks. Methods for assessing network vulnerability found in the literature require origin-destination demands and path assignment. However, in transport network planning and design, demand information is often missing, out of date, partial or inaccurate. Capacity weighted spectral partitioning is proposed to identify potential flow bottlenecks in the network, without reference to demand information or path assignments. This method identifies the network cut with least capacity, taking into account the relative sizes of the sub-networks either side of the cut. Spectral analysis has the added advantage of tractability, even for large networks, as shown by numerical examples for a five-node illustrative example, the Sioux Falls road network and the Gifu Prefecture road network.

[1]  Daniel A. Spielman,et al.  Spectral Graph Theory , 2012 .

[2]  Matthew Andrews,et al.  Spectral analysis of communication networks using Dirichlet eigenvalues , 2011, WWW.

[3]  Chung-Kuan Cheng,et al.  Linear decomposition algorithm for VLSI design applications , 1995, Proceedings of IEEE International Conference on Computer Aided Design (ICCAD).

[4]  Jason Cong,et al.  A Parallel Bottom-up Clustering Algorithm with Applications to Circuit Partitioning in VLSI Design , 1993, 30th ACM/IEEE Design Automation Conference.

[5]  Michael A. P. Taylor,et al.  Remoteness and accessibility in the vulnerability analysis of regional road networks , 2012 .

[6]  Michael G.H. Bell,et al.  A game theory approach to measuring the performance reliability of transport networks , 2000 .

[7]  Aura Reggiani,et al.  Resilience and Vulnerability of Spatial Economic Networks , 2015 .

[8]  Ulrike von Luxburg,et al.  A tutorial on spectral clustering , 2007, Stat. Comput..

[9]  Elise Miller-Hooks,et al.  Measuring the performance of transportation infrastructure systems in disasters: a comprehensive review , 2015 .

[10]  Bruce Hendrickson,et al.  An Improved Spectral Graph Partitioning Algorithm for Mapping Parallel Computations , 1995, SIAM J. Sci. Comput..

[11]  Tom Petersen,et al.  Importance and Exposure in Road Network Vulnerability Analysis , 2006 .

[12]  T. B Boffey.  Graph theory in operations research , 1982 .

[13]  Glen M. D'Este,et al.  Application of Accessibility Based Methods for Vulnerability Analysis of Strategic Road Networks , 2006 .

[14]  Eric Rondeau,et al.  Reducing energy consumption of network infrastructure using spectral approach , 2016, ArXiv.

[15]  Shashi Shekhar,et al.  Multilevel hypergraph partitioning: applications in VLSI domain , 1999, IEEE Trans. Very Large Scale Integr. Syst..

[16]  Jitendra Malik,et al.  Normalized Cuts and Image Segmentation , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Anthony Chen,et al.  ANALYSIS OF TRANSPORTATION NETWORK CAPACITY RELATED TO DIFFERENT SYSTEM CAPACITY CONCEPTS , 2005 .

[18]  Anna Nagurney,et al.  Fragile Networks: Identifying Vulnerabilities and Synergies in an Uncertain World , 2009 .

[19]  Yi-Chang Chiu,et al.  Urban traffic signal control network automatic partitioning using laplacian eigenvectors , 2009, 2009 12th International IEEE Conference on Intelligent Transportation Systems.

[20]  Shing Chung Josh Wong,et al.  Reserve capacity of a signal-controlled road network , 1997 .

[21]  Hai Yang,et al.  Modeling the capacity and level of service of urban transportation networks , 2000 .

[22]  Anthony Chen,et al.  Network-based Accessibility Measures for Vulnerability Analysis of Degradable Transportation Networks , 2007 .

[23]  Gary L. Miller,et al.  Graph Partitioning by Spectral Rounding: Applications in Image Segmentation and Clustering , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).

[24]  Feng Lu,et al.  Robustness of city road networks at different granularities , 2014 .

[25]  Jianbo Shi,et al.  A Random Walks View of Spectral Segmentation , 2001, AISTATS.

[26]  H. W. Ho,et al.  Large-scale road network vulnerability analysis: a sensitivity analysis based approach , 2011 .

[27]  Horst D. Simon,et al.  Fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems , 1994, Concurr. Pract. Exp..

[28]  Fumitaka Kurauchi,et al.  Network Evaluation Based on Connectivity Vulnerability , 2009 .

[29]  Aura Reggiani,et al.  Guest editorial: Resilience of Networks , 2015 .

[30]  M G H Bell,et al.  Attacker–defender models and road network vulnerability , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[31]  Horst D. Simon,et al.  Partitioning of unstructured problems for parallel processing , 1991 .

[32]  Alexandre M. Bayen,et al.  A Weighted-Graph Approach for Dynamic Airspace Configuration , 2007 .

[33]  Bi Yu Chen,et al.  Vulnerability analysis for large-scale and congested road networks with demand uncertainty , 2012 .

[34]  Alan T. Murray,et al.  Critical infrastructure : reliability and vulnerability , 2007 .

[35]  Wai Yuen Szeto,et al.  Quantitative Approaches to Resilience in Transport Networks , 2015 .

[36]  Erik Jenelius,et al.  Vulnerability and resilience of transport systems : A discussion of recent research , 2015 .

[37]  H. J. Van Zuylen,et al.  Link-level vulnerability indicators for real-world networks , 2010 .

[38]  Roy D. Williams,et al.  Performance of dynamic load balancing algorithms for unstructured mesh calculations , 1991, Concurr. Pract. Exp..

[39]  Albert P.C. Chan,et al.  Recent advances in modeling the vulnerability of transportation networks , 2015 .

[40]  Frank M. Johannes.  Partitioning of VLSI circuits and systems , 1996, DAC '96.

[41]  Katja Berdica,et al.  AN INTRODUCTION TO ROAD VULNERABILITY: WHAT HAS BEEN DONE, IS DONE AND SHOULD BE DONE , 2002 .

[42]  Kirsi Virrantaus,et al.  Identifying Critical Locations in a Spatial Network with Graph Theory , 2008, Trans. GIS.