Abstract
This chapter presents some mathematical models of transportation systems, which have been used in conjunction with application of modern control and optimization techniques to these systems. The term “transportation” carries a variety of possibilities and concepts. There is the air and ground transportation, and private and public transportation of both kinds. The chapter focuses on the ground–automobile transportation problems. The approaches to traffic flow modeling are: first, the macroscopic or continuum model, which describes the flow of highway traffic in a manner that is analogos to fluid flow. The population of vehicles on the highway is treated as a continuous flow and its dynamics are described by partial differential equations. The second method is the microscopic or car-following model, which observes each vehicle individually and takes into account the average response of the driver who follows the string of vehicles ahead of him. The chapter presents a survey of various types of transportation problems, where modern control and optimization practices have been applied.
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