A network efficiency measure with application to critical infrastructure networks
 Anna Nagurney,
 Qiang Qiang
 … show all 2 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
In this paper, we demonstrate how a new network performance/efficiency measure, which captures demands, flows, costs, and behavior on networks, can be used to assess the importance of network components and their rankings. We provide new results regarding the measure, which we refer to as the Nagurney–Qiang measure, or, simply, the N–Q measure, and a previously proposed one, which did not explicitly consider demands and flows. We apply both measures to such critical infrastructure networks as transportation networks and the Internet and further explore the new measure through an application to an electric power generation and distribution network in the form of a supply chain. The Nagurney and Qiang network performance/efficiency measure that captures flows and behavior can identify which network components, that is, nodes and links, have the greatest impact in terms of their removal and, hence, are important from both vulnerability as well as security standpoints.
 Beckmann M.J., McGuire C.B., Winsten C.B. (1956). Studies in the Economics of Transportation. Yale University Press, New Haven, Connecticut
 Bertsekas D.P., Gafni E.M. (1982). Projection methods for variational inequalities with application to the traffic assignment problem. Math. Program. Study 17: 139–159
 Braess D. (1968). Uber ein paradoxon aus der verkehrsplaning. Unternehmenforschung 12: 258–268 CrossRef
 Braess D., Nagurney A., Wakolbinger T. (2005). On a paradox of traffic planning, Translation of the 1968 Article by Braess. Trans. Sci. 39: 446–450 CrossRef
 Dafermos S.C. (1980). Traffic equilibrium and variational inequalities. Trans. Sci. 14: 42–54 CrossRef
 Dafermos S.C., Sparrow F.T. (1969). The traffic assignment problem for a general network. J. Res. Nat. Bur. Stand. 73: 91–118
 Jenelius E., Petersen T., Mattsson L.G. (2006). Road network vulnerability: identifying important links and exposed regions. Trans. Res. A 40: 537–560
 Latora V., Marchiori M.: Efficient behavior of smallworld networks. Phys. Rev. Lett. 87 (Article No. 198701) (2001)
 Latora V., Marchiori M. (2003). Economic smallworld behavior in weighted networks. Eur. Phys. J. B 32: 249–263 CrossRef
 Latora V., Marchiori M. (2004). How the science of complex networks can help developing strategies against terrorism. Chaos, Soliton Frac. 20: 69–75 CrossRef
 Liu Z., Nagurney A.: Financial networks with intermediation and transportation network equilibria: a supernetwork equivalence and reinterpretation of the equilibrium conditions with computations. Comput. Manage. Sci. 4, 243–281 (2007) CrossRef
 MurrayTuite P.M., Mahmassani H.S. (2004). Methodology for determining vulnerable links in a transportation network. Trans. Res. Record 1882: 88–96 CrossRef
 Nagurney A. (1999). Network Economics: A Variational Inequality Approach, Second and Revised Edition. Kluwer Academic Publishers, Dordrecht, The Netherlands
 Nagurney A. (2006). Supply Chain Networks Economics: Dynamics of Prices, Flows and Profits. Edward Elgar Publishing, Cheltenham, England
 Nagurney, A., Qiang, Q.: A Network Efficiency Measure for Congested Networks. Europhys. Lett. (2007) (in press),
 Nagurney A., Zhang D. (1996). Projected Dynamical Systems and Variational Inequalities with Applications. Kluwer Academic Publishers, Boston, Massachusetts
 Nagurney, A., Liu, Z., Cojocaru, M.G., Daniele, P.: Dynamic electric power supply chains and transportation networks: an evolutionary variational inequality formulation. Trans. Res. Europhys. Lett. (2007) (in press) 43, 624–646 (2007)
 Nagurney, A., Parkes, D., Daniele, P.: The Internet, evolutionary variational inequalities, and the timedependent Braess Paradox. Comput.Manage. Sci. see also: http://www.supernet.som.umass.edu (2006) (in press)
 Newman M. (2003). The structure and function of complex networks. SIAM Rev. 45: 167–256 CrossRef
 Patriksson M. (1994). The Traffic Assignment Problem—Models and Methods. VSP, BV, Utrecht, The Netherlands
 Roughgarden T. (2005). Selfish Routing and the Price of Anarchy. MIT Press, Cambridge, Massachusetts
 Smith M. (1979). Existence, uniqueness and stability of traffic equilibria. Trans. Res. B 13: 259–304 CrossRef
 Wardrop J.G.: Some theoretical aspects of road traffic research. In Proceedings of the Institute of Civil Engineers, Part II, pp. 325–378 (1952)
 Watts D.J., Strogatz S.H. (1998). Collective dynamics of “smallworld” networks. Nature 393: 440–442 CrossRef
 Wu K., Nagurney A., Liu Z., Stranlund J.K. (2006). Modeling generator power plant portfolios and pollution taxes in electric power supply chain networks: a transportation network equilibrium transformation. Trans. Res. D 11: 171–190 CrossRef
 Title
 A network efficiency measure with application to critical infrastructure networks
 Journal

Journal of Global Optimization
Volume 40, Issue 13 , pp 261275
 Cover Date
 20080301
 DOI
 10.1007/s1089800791981
 Print ISSN
 09255001
 Online ISSN
 15732916
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Network efficiency measure
 Network component importance ranking
 Braess Paradox
 Transportation networks
 Internet
 Electric power supply chain networks
 Infrastructure networks
 Network vulnerability
 Critical infrastructure protection
 Industry Sectors
 Authors

 Anna Nagurney ^{(1)}
 Qiang Qiang ^{(1)}
 Author Affiliations

 1. Isenberg School of Management, University of Massachusetts, Amherst, MA, 01003, USA