One of Professor Nagurney’s colleagues, Assistant Professor Georgia Perakis who teaches Management Science at MIT’s Sloan School, explained Nagurney’s work using the very concrete example of getting to the office: “Think of when you want to get to work and get there as fast as you can. You want to do that, and so do many other drivers that are on the streets. Anna’s work tries to analyze these systems with all their complexity.” It is in her reevaluation of the concept of network, that Prof. Nagurney has made a great leap for her field.

We all have understood networks as the connections between two or more places, or in Management Science vocabulary, “nodes.” In human terms, we ‘network’ to find jobs, or contracts, or an apartment. Networks are also systems, such as the telecommunications network, or the Internet. Through her mathematical descriptions, Professor Nagurney brought a more realistic concept of network as a dynamic system with many, many variables. Her networks are spatial. Her systems acknowledge competition instead of assuming cooperation.

Back to the transportation example: there are many drivers trying to reach their destination and they are often, especially in urban areas, in competition in the process. There is no communication in a cooperative way, even though drivers have been known to make their opinions known to other drivers using choice hand signals and other verbal forms of communication. As this kind of competition accelerates, however, it increases the variables that need to be included in the equations that make up the mathematical model. The best models are very close descriptions of reality, explains Professor Perakis. Nagurney’s work, incorporating dynamic and spatial variables in her networks, makes her models better represent reality.

Once Nagurney has developed a model that accurately reflects a problem, such as moving people from point A to point B using a particular method of transportation, she then solves the problem with an algorithm, a step-by-step problem-solving procedure, especially an established, recursive computational procedure for solving a problem in a finite number of steps. So, Professor Nagurney starts with the outcome, arriving at work in one piece, and works backwards, using an algorithm to find a solution.. Here is one of her algorithms derived from her traffic modeling work. It represents how to solve the problem of getting to work in the most efficient way. Remember, nodes are intersections at the nether ends of the network. And when Nagurney is referring to cost, she is using the old adage ‘time is money.’

“Consider an origin/destination pair of nodes; compute the longest used travel path and the shortest travel path; redistribute the flow from the longest to the shortest so that their costs are equalized; continue doing this procedure until the traffic network equilibrium conditions hold for that origin/destination pair and proceed to the next, and so on, until the traffic network equilibrium conditions are satisfied for the entire network, that is, only the minimal cost travel paths are used for each origin/destination pairs and no others.

This algorithm also has a reasonable behavioral underpinning, in that travelers change their paths so as to improve their travel cost or time and will continue to do so until they can’t do any better.’’ So, once the algorithm is applied for each possible route with all the variables that have been plugged into the model, a driver will know which is the most efficient way to get to work. This kind of modeling has practical application potential for in-car systems that communicate with satellites.

Professor Nagurney has extended her models to capture other kinds of networks, including financial networks, where her models can be used by large companies trying to optimize their investments. Using Prof. Nagurney’s models, large firms can make decisions on how to build their portfolios.

Professor Nagurney’s vita is already 29 pages long, and it needs updating regularly. It does not list her newest book on environmental networks, nor does it note the Eisenhower Faculty fellowship from the Federal Highway Administration, an appointment to Girls, Inc., and who knows what else.

Anna Nagurney has written over 50 different algorithms to solve her models. She would like to write a theory of networks that encompasses all of economics and business; in fact, she would like to write a theoretical framework comprising the world as a massive network that could be solved by one algorithm. “That sounds big-headed, doesn’t it?” she asked. No more “big-headed” than writing the Great American Novel.