The Virtual Center for Supernetworks

Navigating the Network Economy
World Map
Anna Nagurney

(an abridged version of this article appears in OR/MS Today, June 2000)

Networks permeate our daily lives, underpinning our societies and economies and providing the infrastructure for business, science and technology, social systems, and education. Examples of networks which supply the basic foundation for economic and social activity are: transportation, communication, and energy networks.

Transportation networks give us the means to cross physical distance in order to conduct our business and to see clients, as well as to visit colleagues, friends, and family members, and to explore new vistas and expand our horizons. They provide us with access to both food as well as consumer products and come in a myriad of forms: road, air, rail, or waterway. According to the U.S. Department of Transportation, the significance of transportation in dollar value alone as spent by US consumers, businesses, and governments was $950 billion in 1998.

Communication networks, in turn, allow us to communicate within our communities and across regions and national boundaries. They, through such innovations as the Internet, have transformed the manner in which we live, work, and conduct business today. Communication networks allow the transmission of voice, data/information, and/or video and can involve telephones, computers, as well as satellites, and microwaves. The trade publication Purchasing reports that corporate buyers alone spent $517.6 billion on telecommunications goods and services in 1999.

Energy networks, in addition, are essential to the very existence of the Network Economy and help to fuel not only transportation networks but in many settings also communication networks. They provide electricity to run the computers and to light our businesses, oil and gas to heat our homes and to power vehicles, and water for our very survival. In 1995, according to the U. S. Department of Commerce, the energy expenditures in the United States were $515.8 billion.

The topic of networks and the management thereof dates to ancient times with such classical examples including the publicly provided Roman road network and the time of day chariot policy, whereby chariots were banned from the ancient city of Rome at particular times of day.

The formal study of networks, consisting of nodes, links, and flows involves: how to model such applications (as well as numerous other ones) as mathematical entities, how to study the models qualitatively, and how to design algorithms to solve the resulting models effectively. The study of networks is necessarily interdisciplinary in nature due to their breadth of appearance and is based on scientific techniques from applied mathematics, computer science, and engineering with applications as varied as finance and even biology. The field of operations research/management science, in particular, has fostered both the development and application of network models and tools which are widely used by businesses, industries, as well as governments today.

Basic examples of network problems are: the shortest path problem, in which one seeks to determine the most efficient path from an origin node to a destination node; the maximum flow problem, in which one wishes to determine the maximum flow that one can send from an origin node to a destination node, given that there are capacities on the links that cannot be exceeded, and the minimum cost flow problem, where there are both costs and capacities associated with the links and one must satisfy the demands at the destination nodes, given supplies at the origin nodes, at minimal total cost associated with shipping the flows, and subject to not exceeding the arc capacities. Applications of the shortest path problem are found in transportation and telecommunications, whereas the maximum flow problem arises in machine scheduling and network reliability settings, with applications of the minimum cost flow problem ranging from warehousing and distribution to vehicle fleet planning and scheduling.

Networks also appear in surprising and fascinating ways for problems, which initially may not appear to involve networks at all, such as a variety of financial problems and in knowledge production and dissemination. Hence, the study of networks is not limited to only physical networks where nodes coincide with locations in space but also to abstract networks. The ability to harness the power of a network formalism provides a competitive advantage since:

Reality of Today's Networks

Indeed, the reality of many of today's networks further emphasizes the importance of the application of methodologies from operations research/management science. The characteristics of today's networks include: large-scale  nature and complexity of network topology, congestion, alternative behavior of users of the network, which may lead to paradoxical phenomena, and the interactions among networks themselves such as in transportation versus telecommunications networks. Moreover, policies surrounding networks today may have a major impact not only economically but also socially.

Large-Scale Nature and Complexity

Many of today's networks are characterized by both a large-scale nature and complexity of the underlying network topology. For example, in Chicago's Regional Transportation Network, there are 12,982 nodes, 39,018 links, and 2,297,945 origin/destination (O/D) pairs, whereas in the Southern California Association of Governments model there are 3,217 origins and/or destinations, 25,428 nodes, and 99,240 links, plus 6 distinct classes of users.

In terms of the size of existing telecommunications networks, AT&T's domestic network has 100,000 origin/destination pairs, whereas in their detail graph applications in which nodes are phone numbers and edges are calls, there are 300 million nodes and 4 billion edges.


Congestion is playing an increasing role in not only transportation networks but also in telecommunication networks. For example, in the case of transportation networks in the United States alone, congestion results in $100 billion in lost productivity, whereas the figure in Europe is estimated to be $150 billion. The number of cars is expected to increase by 50% by 2010 and to double by 2030.

In terms of the Internet, with 275 million present users, the Federal Communications Commission reports that the volume of traffic is doubling every 100 days, which is remarkable given that telephone traffic has typically increased only by about 5 percent a year. As individuals increasingly access the Internet through wireless communication such as through handheld computers and cellular phones, experts fear that the heavy use of airwaves will create additional bottlenecks and congestion that could impede the further development of the technology. Operations research/management science can assist not only in the modeling of congestion itself but also in the design of appropriate policies for congestion management.

System-Optimization versus User-Optimization

In many of today's networks, not only is congestion a characteristic feature leading to nonlinearities, but the behavior of the users of the networks themselves may be that of noncooperation. For example, in the case of urban transportation networks, travelers select their routes of travel from an origin to a destination so as to minimize their own travel cost or travel time, which although optimal from an individual's perspective (user-optimization) may not be optimal from a societal one (system-optimization) where one has control over the flows on the network  and, in contrast, seeks to minimize the total cost in the network and, hence, the total loss of productivity. Consequently, in making any kind of policy decisions in such networks one must take into consideration the users of the particular network. Indeed, this point is vividly illustrated through a famous example known as the Braess paradox, in which it is assumed that the underlying behavioral principle is that of user-optimization. In the Braess network, the addition of a new road with no change in the travel demand results in all travelers in the network incurring a higher travel cost and, hence, being worse off.

The increase in travel cost on the paths is due, in part, to the fact that in this network two links are shared by distinct paths and these links incur an increase in flow and associated cost. Hence, Braess's paradox is related to the underlying topology of the networks. One may show, however, that the addition of a path connecting an O/D pair that shares no links with the original O/D pair will never result in Braess's paradox for that O/D pair.

Interestingly, as reported in the New York Times, this phenomenon has been observed in practice both in the case of New York City when in 1990, 42nd Street was closed for Earth Day and the traffic flow actually improved. Just to show that it is not a purely New York or US phenomena concerning drivers and their behavior an analogous situation was observed in Stuttgart where a new road was added to the downtown but the traffic flow worsened and following complaints, the new road was torn down.

This phenomenon is also relevant to telecommunications networks and, in particular, to the Internet which is another example of a noncooperative network and, therefore, network tools from operations research/management science have wide application in this setting as well especially in terms of congestion management and network design.

Network Interactions

Clearly, one of the principal facets of the Network Economy is the interaction among networks themselves. For example, the increasing use of e-commerce especially in business to business transactions is changing not only the utilization and structure of the underlying logistical networks but is revolutionizing how business itself is transacted and the structure of firms and industries. Cellular phones are being using as vehicles move dynamically over transportation networks resulting in dynamic evolutions of the topologies themselves. The interactions among transportation networks, telecommunication networks, as well as financial networks is creating supernetworks whose study can greatly benefit from the disciplines of operations research/management science. We now turn to how networks are being used in novel ways both in financial systems as well as the policy arena of transportation/environment interactions and in knowledge production.

Financial Systems

Financial networks date to Quesnay, who in his Tableau Economique, published in the mid 1700s, conceptualized the circular flow of funds in an economy as a network. Two centuries later, Copeland is his book A Study of Moneyflows in the United States, raised the question,Does money flow like water or like electricity?. In fact, the classical portfolio optimization problem of the Nobel prize winner Harry Markowitz is actually a nonlinear network flow problem.

Recently, networks have been used by myself, along with June Dong and Stavros Siokos, presently of Salomon Smith Barney, to visualize sectors and their investment decisions in an economy, single country as well as international, both in equilibrium and in disequilibrium where one needs to determine the sectors' optimal holdings of the assets, liabilities, as well as the instrument prices (and exchange rates). Such tools have also been applied in the case of hedging. Such formulations allow each sector to have its own distinct utility function as well as constraints and the algorithms take advantage of the identified network structure of the problem. This application setting is an example in which the network topologies themselves evolve over time, with the network structure of the financial economy in equilibrium being distinct from it in disequilibrium.

Transportation and the Environment

The demand for transportation on the one hand with a growing realization of the associated negative externalities due, for example, to pollution since 15% of the world's emissions of carbon dioxide are due to motor vehicles, 50% of the emissions of nitrogen oxide, and 90% of the carbon monoxide, are raising questions of sustainability of the transportation infrastructure. In this setting, there may occur emission paradoxes and, hence, one must incorporate both the network topology and the relevant cost and demand structure as well as the behavior of the users into any policy aimed at pollution abatement. Recently, there has been much progress in the development of appropriate policy tools in the form of emission pricing and even tradable pollution permits in this setting.

Knowledge Networks

Knowledge is unarguably the most important factor in today's economy and its production involves both the creation of new knowledge and the understanding from old knowledge. In order to comprehend the regional division of production, knowledge, and capital, as well as their evolution, it is necessary to introduce network dimensions to the analysis of interactions between firms, individuals, and organizations.

Knowledge networks is a concept invented and utilized by Swedish economists in an atmosphere of growing international competition, which has led Sweden to focus on high technology industries which are knowledge intensive. In today's Network Economy the existence of highly skilled workers is essential for: innovation, research and development, and for increasing the competitive position of regions and nations. Indeed, differences in creativity, labor skills, and innovation diffusion can explain quite convincingly why some economies have prospered while others have declined.

Knowledge networks are conceptualized on both transportation and telecommunication networks, with transportation distance playing an important role in impeding the movement of individuals for purposes of information and knowledge exchange with distance, in terms of knowledge exchange on telecommunications networks, playing a less critical role. Such a formalism can capture not only the dispersion of knowledge workers, under various degrees of competition, but also the requirements for information systems.

For a general background on networks and network systems, see:

Ahuja, R. K., Magnanti, T. L., and Orlin, J. B. (1993), Network Flows: Theory, Algorithms, and Applications, Prentice Hall, Upper Saddle River, New Jersey.

Nagurney, A. (1999),  Network Economics: A Variational Inequality Approach, second and revised edition, Kluwer Academic Publishers, Dordrecht, The Netherlands.

For references to transportation networks used in the preparation of this essay, see:

Bar-Gera, H. (1999), "Origin-Based Algorithms for Transportation Network Modeling," National Institute of Statistical Sciences, Technical Report # 103, PO Box 14006, Research Triangle Park, North Carolina 27709.

Bass, T. (1992), "Road to Ruin," Discover, May, 56-61.

Beckmann, M. J., McGuire, C. B., and Winsten, C, B. (1956), Studies in the Economics of Transportation, Yale University Press, New Haven, Connecticut.

Braess, D. (1968), "Uber ein Paradoxon der Verkehrsplanung," Unternehmenforschung12, 258-268.

Dafermos, S., and Nagurney, A. (1984), "On Some Traffic Equilibrium Theory Paradoxes," Transportation Research18B, 101-110.

Dafermos, S. C., and Sparrow, F. T. (1969), "The Traffic Assignment Problem for a General Network," Journal of Research of the National Bureau of Standards 73B, 91-118.

Kolata, G. (1990), "What if They Closed 42d Street and Nobody Noticed?" The New York Times, December 25, 1990.

Nagurney, A. (2000), Sustainable Transportation Networks, Edward Elgar Publishers, Cheltenham, England.

Wu, J. H., Florian, M., and He, S. G. (2000), "EMME/2 Implementation of the SCAG-II Model: Data Structure, System Analysis and Computation," submitted to the Southern California Association of Governments, INRO Solutions Internal Report, Montreal, Quebec, Canada.

References to telecommunications used in the preparation of this essay:

Abello, J., Pardalos, P. M., and Resende, M. G. C. (1999), "On Maximum Clique Problems in Very Large Graphs," in External Memory Algorithms, J. Abello and J. Vitter, editors, AMS-DIMACS Series on Discrete Mathematics and Theoretical Computer Science 50.

Cohen, J. E., and Kelly, F. P. (1990), "A Paradox of Congestion in a Queuing Network," Journal of Applied Proability 27, 730-734.

Korilis, Y., Lazar, A. A., and Orda, A. (1999), "Avoiding the Braess Paradox in Non-Cooperative Networks," Journal of Applied Probability 36, 211-222.

Labaton, S. (2000), "F.C.C. to Promote a Trading System to Sell AirWaves," The New York Times, March 13, 2000.

References to networks in finance and additional background are:

Copeland (1952), A Study of Moneyflows in the United States, National Bureau of Economic Research, New York.

Markowitz, H. M. (1952), "Portfolio Selection," The Journal of Finance 7, 77-91.

Mulvey, J. M. (1987), "Nonlinear Networks in Finance," in Advances in Mathematical Programming and Financial Planning 1, 253-271.

Nagurney, A., and Siokos (1997), Financial Networks: Statics and Dynamics, Springer-Verlag, Heidelberg, Germany,

Nagurney, A., and Siokos, S. (1998), "Dynamics of International Financial Networks: Modeling, Stability Analysis, and Computation," in Networks and Knowledge in a Dynamic Economy, M. J. Beckmann, B. Johansson, F. Snickars, and R. Thord, editors, Springer-Verlag, Heidelberg, Germany, pp. 119-150.

Quesnay, F. (1758), Tableau Economique, reproduced in facsimile with an introduction by H. Higgs by the British Economic Society, 1895.

References to the environment and networks used in this essay preparation are:

Banister, D., and Button, K. J. (1993), "Environmental Policy and Transport: An Overview," in Transport, Environment, and Sustainable Development,  D. Banister and K. J. Button, editors, E. & F. N., London, England.

Dhanda, K. K., Nagurney, A., and Ramanujam, P. (1999), Environmental Networks: A Framework for Economic Decision-Making and Policy Analysis, Edward Elgar Publishers, Cheltenham, England.

Nagurney, A. (2000), Sustainable Transportation Networks, Edward Elgar Publishers, Cheltenham, England.

References to knowledge networks:

Beckmann, M. J. (1995), "Economic Models of Knowledge Networks," in Networks in Action, D. Batten, J. Casti, and R. Thord, editors, pp, 150-174, Springer-Verlag, Berlin, Germany.

Nagurney, A. (1999), Network Economics: A Variational Inequality Approach, second and revised edition, Kluwer Academic Publishers, Dordrecht, The Netherlands.

The data used in this essay was culled from a variety of sources including:

Labaton, S. (2000), "F.C.C. to Promote a Trading System to Sell AirWaves," The New York Times, March 13, 2000.

Purchasing (2000), "Corporate Buyers Spent $517.6 Billion on Telecommunication," 128, 110.

Resende, M. G. C. (2000), personal communication.

US Department of Commerce (2000), Statistical Abstract of the United States, Bureau of the Census, Washington, DC.

US Department of Transportation (1999), Guide to Transportation, Bureau of Transportation Statistics, BTS99-06, Washington, DC.

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