An equivalent continuous time optimal control problem is formulated for dynamic user-optimized traffic assignment with elastic travel demand. Using the pontryagin minimum principle, optimality conditions are derived and economic interpretations that correspond to a dynamic generalization of wardrop's first principle are provided. The existence and optimality of singular controls are examined. Under steady-state assumptions, the model is shown to be a proper dynamic extension of beckmann's equivalent optimization problem for static user-optimized traffic assignment with elastic demand. Finally, limitations and extensions of the present model are discussed. This paper appears in transportation research record no. 1328, Travel demand forecasting: new methodologies and travel behavior research 1991
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