An optimization problem with dynamic route-departure time choice and pricing

Dynamic pricing is a strategy that has not yet been widely applied in the area of dynamic traffic management; this might be due to the fact that a time-varying toll has not yet been widely accepted by the authorities. The increasing congestion is therefore pushing the trend to use whatever strategy in order to alleviate delays. The use of Dynamic Network Loading (DNL) and Dynamic Traffic Assignment (DTA) permits one to estimate travel times during different periods of the day and above all during congestion. This allows one to calculate the dynamic path disutilities faced by travelers when these consist of travel time and dynamic tolls. This study combines two avenues of modeling innovation. Firstly it relaxes the assumption of fixed departure times during the evaluation periods. It does so by including a departure time choice model that uses the time dependent path disutility calculated by a Dynamic Traffic Assignment model which incorporates the DNL. Secondly it integrates this with the problem of finding the dynamic tolls that minimize the total system cost. It does so by solving a bilevel optimization in which tolls are set in an upper level problem (aimed at minimizing the system cost), and the dynamic user-optimal response of the transport system (in terms of route choice and departure-time choice) is calculated in a lower level problem. Software was prepared to solve the upper level of the bilevel problem iteratively, at each step determining the user-optimal response of the lower level. The simplification leads the problem to a single level problem in which the strategy is iteratively adapted to the demand. Consequently, this paper aims at finding consistency of user response with respect to pricing and to show how, in some cases pricing is beneficial for the societal purposes

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