Planning ride-pooling services with detour restrictions for spatially heterogeneous demand: A multi-zone queuing network approach

This study presents a multi-zone queuing network model for steady-state ride-pooling operations that serve heterogeneous demand, and then builds upon this model to optimize the design of ride-pooling services. Spatial heterogeneity is addressed by partitioning the study region into a set of relatively homogeneous zones, and a set of criteria are imposed to avoid significant detours among matched passengers. A generalized multi-zone queuing network model is then developed to describe how vehicles' states transition within each zone and across neighboring zones, and how passengers are served by idle or partially occupied vehicles. A large system of equations is constructed based on the queuing network model to analytically evaluate steady-state system performance. Then, we formulate a constrained nonlinear program to optimize the design of ride-pooling services, such as zone-level vehicle deployment, vehicle routing paths, and vehicle rebalancing operations. A customized solution approach is also proposed to decompose and solve the optimization problem. The proposed model and solution approach are applied to a hypothetical case and a real-world Chicago case study, so as to demonstrate their applicability and to draw insights. Agent-based simulations are also used to corroborate results from the proposed analytical model. These numerical examples not only reveal interesting insights on how ride-pooling services serve heterogeneous demand, but also highlight the importance of addressing demand heterogeneity when designing ride-pooling services.