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On-demand trip sharing is an efficient solution to mitigate the negativeimpact e-hailing has on congestion. It motivates platform operators to reducetheir fleet size, and serves the same demand level with a lower effectivedistance traveled. Users nevertheless prefer to travel solo and for shorterdistances despite the fare discount they receive. By offering them the choiceto pool and travel in high occupancy dedicated bus lanes, we provide them witha larger incentive to share their rides, yet this creates additional busdelays. In this work, we develop dynamic feedback-based control schemes thatadjust the price gap between solo and pool trips to improve multi-modal delays.First, we develop a modal- and space-dependent aggregate model for privatevehicles, ride-pooling, and buses, and we use this model to test differentcontrol strategies. To minimize the error between the target and actual speedsin the bus network, we design a PI controller and show that by adjusting pooltrip fares, we can, with little input data, minimize this error. We also putforward a Model Predictive Control (MPC) framework to minimize the totalPassenger Hours Traveled (PHT) and Waiting Times (WT) for the differenttravelers. Moreover, we show how the MPC framework can be utilized to impose aminimum speed in dedicated bus lanes to ensure that the buses operate onschedule. The results mark the possibility of improving the overall networkconditions by incentivizing or discouraging pooling in the vehicle or busnetwork.

A Dynamic Macroscopic Framework for Pricing of Ride-hailing Services with an Optional Bus Lane Access for Pool Vehicles