A network efficiency measure with application to critical infrastructure networks

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.

[1]  C. B. Mcguire,et al.  Studies in the Economics of Transportation , 1958 .

[2]  V Latora,et al.  Efficient behavior of small-world networks. , 2001, Physical review letters.

[3]  Dietrich Braess,et al.  Über ein Paradoxon aus der Verkehrsplanung , 1968, Unternehmensforschung.

[4]  N. F. Stewart,et al.  ON THE CALIBRATION OF THE COMBINED DISTRIBUTION-ASSIGNMENT MODEL , 1979 .

[5]  Martin Suter,et al.  Small World , 2002 .

[6]  A. Nagurney.  Network Economics: A Variational Inequality Approach , 1992 .

[7]  T. Koopmans,et al.  Studies in the Economics of Transportation. , 1956 .

[8]  Massimo Marchiori,et al.  How the science of complex networks can help developing strategies against terrorism , 2004 .

[9]  D. Bertsekas,et al.  Projection methods for variational inequalities with application to the traffic assignment problem , 1982 .

[10]  Tom Petersen,et al.  Road network vulnerability: identifying important links and exposed regions , 2006 .

[11]  Qiang Qiang,et al.  A network efficiency measure for congested networks , 2007 .

[12]  Anna Nagurney,et al.  On a Paradox of Traffic Planning , 2005, Transp. Sci..

[13]  Anna Nagurney,et al.  Dynamic electric power supply chains and transportation networks: An evolutionary variational inequality formulation , 2007 .

[14]  Massimo Marchiori,et al.  Economic small-world behavior in weighted networks , 2003 .

[15]  Mike Smith,et al.  The existence, uniqueness and stability of traffic equilibria , 1979 .

[16]  Tim Roughgarden,et al.  Selfish routing and the price of anarchy , 2005 .

[17]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[18]  A. Nagurney,et al.  Projected Dynamical Systems and Variational Inequalities with Applications , 1995 .

[19]  Stella C. Dafermos,et al.  Traffic assignment problem for a general network , 1969 .

[20]  J. G. Wardrop,et al.  Some Theoretical Aspects of Road Traffic Research , 1952 .

[21]  Anna Nagurney,et al.  The Internet, evolutionary variational inequalities, and the time-dependent Braess paradox , 2007, Comput. Manag. Sci..

[22]  Anna Nagurney,et al.  Supply Chain Network Economics , 2006 .

[23]  Anna Nagurney,et al.  Financial Networks with Intermediation and Transportation Network Equilibria: A Supernetwork Equivalence and Reinterpretation of the Equilibrium Conditions with Computations , 2007, Comput. Manag. Sci..

[24]  J. Wardrop.  ROAD PAPER. SOME THEORETICAL ASPECTS OF ROAD TRAFFIC RESEARCH. , 1952 .

[25]  Stella Dafermos,et al.  Traffic Equilibrium and Variational Inequalities , 1980 .

[26]  Pamela Murray-Tuite,et al.  Methodology for Determining Vulnerable Links in a Transportation Network , 2004 .

[27]  Anna Nagurney,et al.  Modeling Generator Power Plant Portfolios and Pollution Taxes in Electric Power Supply Chain Networks: A Transportation Network Equilibrium Transformation , 2006 .

[28]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.