By Anna Nagurney
In this chapter, we provide the foundations of the rigorous formulation, analysis, and solution of transportation network problems. We discuss user-optimization, which corresponds to decentralized decision-making, and system-optimization, which corresponds to centralized decision-making where the central controller can route the traffic in an optimal manner. We describe a spectrum of increasingly sophisticated models and also relate transportation networks to other network application domains in which flows (and associated decision-making) are essential, such as the Internet, supply chains, electric power distribution and generation networks, as well as financial networks. Finally, we demonstrate how the importance of transportation network components, that is, nodes and links can be identified (and ranked) through a recently proposed transportation network efficiency measure and accompanying component importance definition. Examples are included throughout the chapter for illustrative purposes.
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