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An Efficiency Measure for Dynamic Networks Modeled as Evolutionary Variational Inequalities with Application to the Internet and Vulnerability Analysis

28 Pages Posted: 28 Jan 2008  

Anna Nagurney

University of Massachusetts Amherst - Isenberg School of Management - Department of Operations and Information Management

Qiang Qiang

Pennsylvania State University - Great Valley School of Graduate Professional Studies

Abstract

In this paper, we propose an efficiency/performance measure for dynamic networks, which have been modeled as evolutionary variational inequalities. Such applications include the Internet. The measure, which captures demands, flows, and costs/latencies over time, allows for the identification of the importance of the nodes and links and their rankings. We provide both continuous time and discrete time versions of the efficiency measure. We illustrate the efficiency measure for the time-dependent (demand-varying) Braess paradox and demonstrate how it can be used to assess the most vulnerable nodes and links in terms of the greatest impact of their removal on the efficiency/performance of the dynamic network over time.

Keywords: network efficiency, performance measurement, dynamic networks, Internet, Braess paradox, vulnerability analysis, critical network components, evolutionary variational inequalities

JEL Classification: C61, C63, C73, H56, P47

Suggested Citation

Nagurney, Anna and Qiang, Qiang, An Efficiency Measure for Dynamic Networks Modeled as Evolutionary Variational Inequalities with Application to the Internet and Vulnerability Analysis. Netnomics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1088004

Anna Nagurney (Contact Author)

University of Massachusetts Amherst - Isenberg School of Management - Department of Operations and Information Management ( email )

Amherst, MA 01003-4910
United States

Qiang Qiang

Pennsylvania State University - Great Valley School of Graduate Professional Studies ( email )

30 E. Swedesford Rd
Malvern, PA 19355
United States

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