Studied for decades, traffic dynamics modeling is one of the most challenging problems in transportation science. It aims at predicting traffic system states, including flow, density, and speed over time in a highway network. Traditional models mainly analyze the impact of congestion on commuters' travel behavior and choices in a single mode --- solo driving. The emerging ridesharing services including heterogeneous travelers and relevant infrastructure such as High Occupancy Toll (HOT) lanes, however, provide more flexibility for travelers at the same time pose more challenges for this classic problem. In this dissertation, we will discuss how to integrate emergent transportation modes, i.e., ridesharing services and infrastructures into traffic dynamic problems to benefit all travelers using either theoretical or data-driven approaches.
From the perspective of the theoretical approach, we treat it as a morning commute problem and develop a general modeling framework for continuous-time bottleneck models with ridesharing services, including travel modes, infrastructure, and business model. Formulated as Linear Complementary Systems, the proposed models can simultaneously capture travelers’ departure time choice, lane choice between HOT lane and General Purpose lane, as well as mode choice between ridesharing and solo driving. We prove that the continuous-time models with ridesharing will exist a solution. To approximate the continuous-time models, discrete-time models are generated using an implicit time discretization scheme, with the theoretical guarantee to converge back to the continuous-time models. Dynamic ridesharing prices, including drivers’ incomes and riders’ payments, are derived to make sure the ridesharing services can make profits as a business model. Together with the dynamic HOT lane toll charges, the HOT lane is induced to be congestion-free. The proposed continuous-time bottleneck models with ridesharing and the proposed dynamic pricing strategies are validated in numerical experiments. Results show that our proposed methodology provides a rare win-win-win outcome between travelers, companies, and the system toward urban sustainability through ridesharing.
The theoretical approach provides a rigorous analysis of the extended version of traffic dynamics and evidence to improve transportation system performance under well-developed pricing strategies. From the perspective of the data-driven approach, we propose a model based on a more realistic scenario where travelers with multiple origins and multiple destinations are involved. To tackle this complex problem, we first present a comprehensive approach that integrates Long Short Term Memory (LSTM) based models to discern speed-toll patterns across various lanes, evaluating the efficiency of tolling strategies. Then, a novel LQR feedback control system is proposed to manage tolling in HOT lanes with multiple gantries, ensuring convergence to optimal states. Utilizing the I-580 express lane dataset, the study uncovers non-linear correlations between SOV traffic flow and toll rates, demonstrating toll control's significant impact on traffic. Key findings highlight the efficacy of the LSTM model in predicting traffic speed, the congestion-reducing impacts of LQR tolling on both General Purpose (GP) and HOT lanes, and the overall benefits of tolling strategies for all travelers, showcasing travel time savings and improved reliability across weekdays.
