A Macroscopic Modelling Framework for the Dynamic Pricing of Pool Ride-Splitting Vehicles in Bus Lanes

The impact of ride-hailing vehicles on congestion raises multiple concerns, particularly in areas where the network space is constrained and the route infrastructure is unevenly distributed among multi-modal users. Mainly, idle ride-hailing vehicles pose multiple challenges because they move across the network and contribute to production without delivering any trips. One possible solution to halt the negative effects of ride-hailing on traffic in a network is trip-sharing. To incentivize users to share their rides, we provide in this work a macroscopic dynamic framework for multi-modal networks with on-demand ride-hailing services where pool passengers are allowed on bus lanes. We then develop a pricing policy for solo and pool trips to reduce overall multi-modal network delays. Using a PI and a Model Predictive Control (MPC) framework, we regulate the price difference between the two ride-hailing alternatives with the objective to minimize the Passenger Hours Travelled (PHT) for bus users but also for the users of other concurrent transportation modes. The results show that the ideal set point for the PI controller is heavily dependent on the level of demand. The MPC framework, despite being more complex from an implementation point of view, manages to return lower total network delays.