Abstract
A discrete time model is presented for dynamic traffic assignment. Congestion is treated explicitly in the flow equations. The model is a nonlinear and non-convex 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. The nonlinear model, with the same additional assumptions on the objective function, has the property that all local optima are global.
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Merchant, D.K., Nemhauser, G.L. (1976). A Model and an Algorithm for the Dynamic Traffic Assignment Problem. In: Florian, M.A. (eds) Traffic Equilibrium Methods. Lecture Notes in Economics and Mathematical Systems, vol 118. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48123-9_14
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DOI: https://doi.org/10.1007/978-3-642-48123-9_14
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