An Algorithm for Extremals Calculation in Optimal Control Problems with Applications to the Dynamic Traffic Assignment Problem

In this paper an algorithm to calculate extremals for the dynamic traffic assignment problem (DTAP) using a deterministic optimal control problem formulation is shown. This algorithm is based on a general method to integrate extremals for optimal control problems with inequality constraints in control variables. The DTAP is formulated and discretized and the consideration of using the method for extremals integration is made, showing how its steps would result for the DTAP, specially its inner loop, that becomes a network flow problem very similar to the stationary traffic assignment with separable costs objective function. Also, for the algorithm, it is remarked the need of techniques to update solutions in traffic assignment problems when, on the same network and the same cost functions, the demand varies slightly from one problem to the next. Finally aspects of the algorithm still under study are outlined. These aspects must be specialized for the DTAP in order to make possible the writing of competitive code specially suited to the treatment of medium-large urban networks