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A discrete time model is presented for dynamic traffice assignment with a single destination. Congestion is treated explicitly in the flow equations. The model is a nonlinear and nonconvex mathematical programming problem. A piecewise linear version of the model, with additional assumptions on the objective function, can be solved for a global optimum using a one-pass simplex algorithm—branch-and-bound is not required. The piecewise linear program has a staircase structure and can be solved by decomposition techniques or compactification methods for sparse matrices.
Merchant et al. (Tue,) studied this question.