Lagrangian Road Pricing

We consider the problem of trajectory-based road pricing with the objective of reducing congestion on a road network. It is well-known that traffic conditions resulting from typical non-cooperative behavior of selfish drivers do not minimize total travel time spent on the road network. In the context of real-time GPS data collection from all vehicles, drivers can be charged differently based on their origin and destination, and according to the path they take from that origin to that destination. In this work, we propose a new formulation of the set of multi-commodity prices based on a price potential, and describe an efficient algorithm to construct such multi-commodity prices. We provide an analysis of the subset of valid prices satisfying several specific user-driven constraints. The numerical performances of the method proposed are assessed on a benchmark network, and the social benefits resulting from the commodity-based potential pricing scheme introduced in this article are discussed.