Optimal toll design problem in dynamic traffic networks with joint route and departure time choice

Road pricing is one of the market-based traffic control measures that can influence travel behavior to alleviate congestion on roads. This paper addresses the effects of uniform (constant, fixed) and time-varying (step) tolls on the travel behavior of users on the road network. The problem of determining optimal prices in a dynamic traffic network is considered by applying second-best tolling scenarios imposing tolls only to a subset of links on the network and considering elastic demand. The optimal toll design problem is formulated as a bilevel optimization problem with the road authority (on the upper level) setting the tolls and the travelers (on the lower level) who respond by changing their travel decisions (route and departure time choice). To formulate the optimal toll design problem, the so-called mathematical program with equilibrium constraints (MPEC) formulation was used, considering the dynamic nature of traffic flows on the one hand and dynamic pricing on the other. Until now, the MPEC formulation has been applied in static cases only. The model structure comprises three interrelated levels: (a) dynamic network loading, (b) route choice and departure time choice, and (c) road pricing level. For solving the optimal toll design problem in dynamic networks, a simple search algorithm is used to determine the optimal toll pattern leading to optimization of the objective function of the road authority subject to dynamic traffic assignment constraints. Nevertheless, uniform and time-varying pricing is analyzed, and a small hypothetical network is considered.