In this dissertation a new algorithm is introduced for the within-day dynamic user equilibrium problem. The within-day dynamic user equilibrium model is then extended to a new day-to-day dynamic user equilibrium model with demand growth. The day-to-day dynamic user equilibrium model combines the within-day time scale for which route and departure time choices fluctuate in continuous time with the day-to-day time scale for which demand evolves in discrete time steps. This problem belongs to the class of problems refered to as differential variational inequalities. For the differential variational inequality formulation, this dissertation presents and establishes convergence of an algorithm that solves day-to-day subproblems using a time-stepping approach and within-day subproblems using a continuous time fixed point scheme. A simplified dynamic network loading scheme is introduced which relies upon an approximation of the equations for the point-queue model of delay. Numerical tests are conducted on a range of network sizes to illustrate that the algorithm and dynamic network loading procedure, separately and in tandem, are scalable and efficient.
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