Dynamic optimal congestion pricing in multi-region urban networks by application of a Multi-Layer-Neural network

Traffic management by applying congestion pricing is a measure for mitigating congestion in protected city corridors. As a promising tool, pricing improves the level of service in a network and reduces travel delays. However, real-world implementations are restricted to static pricing, i.e., the price is fixed and not responsive to the prevailing regional traffic conditions. Dynamic pricing overcomes these limitations but also affects the users route choices. This work uses dynamic pricing's influence and predicts pricing functions to aim for a system optimal traffic distribution. The framework models a large-scale network where every region is considered homogeneous, allowing for the Macroscopic Fundamental Diagram (MFD) application. We compute Dynamic System Optimum (DSO) and a Quasi Dynamic User Equilibrium (QDUE) of the macroscopic model by formulating a linear optimization problem and utilizing the Dijkstra algorithm and a Multinomial Logit model (MNL), respectively. The equilibria allow us to find an optimal pricing methodology by training Multi-Layer-Neural (MLN) network models. We test our framework on a case study in Zurich, Switzerland, and showcase that (a) our neural network model learns the complex user behavior and (b) allows predicting optimal pricing functions. Results show a significant performance improvement when operating a transportation network in the DSO and highlight how dynamic pricing influences the user's route choice behavior towards the system optimal equilibrium.