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Congestion has been a longstanding problem in urban transportation systems. It is the root of system deterioration in mobility, safety and sustainability, manifested as travel delay and travel uncertainty, crashes, air pollution, etc. A strong science into the understanding, modeling, computation and control of congestion dynamics in complex, uncertain and intelligent traffic systems is thus at the core of incorporating emerging technologies and devising sound and effective traffic management strategies.This dissertation aims at addressing the shortcomings of classical macroscopic traffic flow models in dealing with the boundary measurements and control. Due to construction, the traditional hydrodynamics based traffic modeling approaches are usually incapable or extremely tedious in incorporating trajectory-level details in either modeling or control. This constitutes the main hurdle for integrating sound physics with empirical observations in traffic systems estimation and control, especially when mobile or other non-regular sensing techniques are involved.In this dissertation, I develop a novel variational theory based traffic flow modeling framework and provide detailed discussions on its implications for traffic systems estimation, computation and control problems. The new modeling approach explores and consolidates the linkage between hyperbolic conservation equations associated with the kinematic wave theory and Hamilton-Jacobi equations associated with the optimal control theory. In a broader context, this linkage represents the translation between PDE (partial differential equation) and ODE (ordinary differential equation) problems. Though mathematically equivalent, the latter perspective allows us to tackle the moving observations more easily because of relaxed assumptions on boundary geometry. In addition, the analytical and numerical difficulties associated with solving traffic flow models are suppressed, thanks to the variational principle pertaining to the latter formulation. Major results presented in this dissertation include the following. First, I derive the variational formulations for multi-class and non-equilibrium traffic flow models respectively, through exploiting the isomorphic relation between a conservation law problem with its auxiliary optimal control problem. In the derivations, the relation of kinematic wave and solution to the optimal control problem are analyzed in detail. Based on the new formulations, simplified solution schemes are proposed. These solution schemes are flexible with the setting of computational grids and boundary conditions. Analysis of their error bounds are given. Then I look into the calibration of Hamiltonian, i.e. fundamental diagram, in multi-lane freeway setting. An automated adaptive calibrator is constructed using the mixed integer programming (MIP) technique and tested using I-80 freeway data. At last, I presented a decentralized urban signalized traffic network control scheme, motivated by the queuing properties implied in the variational principle.