The presentation starts with some epistemological remarks regarding traffic flow modeling, its usefulness, and the role of optimality, while emphasizing the need for practical progress in road traffic operations. A space/time-discretized macroscopic traffic flow model is presented next, along with selected validation and application results and discussion of encountered difficulties. The model is extended to enable consideration of route guidance and dynamic traffic assignment. An Extended Kalman Filter is derived on the basis of the same model, and selected application results are presented. A nonlinear constrained optimal control problem formulation and efficient numerical solution tool for integrated freeway traffic control are presented next, and diverse application examples are provided. Problems, difficulties, and solution avenues for traffic signal control algorithms applicable to urban road networks are outlined. The value of simple feedback algorithms for traffic control and the related uncertainty is highlighted, along with corresponding application examples.
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