Wise Goose Chase: A Predictive Path Planning Algorithm for Dynamic Rebalancing in Ride-Hailing Systems

TL;DR

This work tackles inefficiencies in ride-hailing rebalancing by moving from static destination recommendations to anticipatory, edge-level path planning. It introduces Wise Goose Chase (WGC), a framework that models spatio-temporal supply and demand with Retarded Functional Differential Equations and computes driver-specific cruising paths to minimize expected time to allocation, while accounting for en-route matching and driver competition. Key contributions include a full RFDE-based dynamics formulation for edges and nodes, a forward-Euler numerical approximation, and a beam-search acceleration to enable real-time path planning. Monte Carlo simulations on synthetic urban grids demonstrate that WGC consistently outperforms Random Walk, Greedy, and Hotspot baselines across fleet sizes and demand patterns, highlighting the practical value of predictive, event-driven rebalancing in dynamic mobility systems. The work suggests promising directions for multi-agent coordination and fairness-aware guidance in shared mobility platforms.

Abstract

Traditional rebalancing methods in ride-hailing systems direct idle drivers to fixed destinations, overlooking the fact that ride allocations frequently occur while cruising. This destination-centric view fails to exploit the path-dependent nature of modern platforms, where real-time matching depends on the entire trajectory rather than a static endpoint. We propose the Wise Goose Chase (WGC) algorithm, an event-triggered, driver-specific path planning framework that anticipates future matching opportunities by forecasting spatio-temporal supply and demand dynamics. WGC uses a system of Retarded Functional Differential Equations (RFDEs) to model the evolution of idle driver density and passenger queues at the road-segment level, incorporating both en-route matching and competition among drivers. Upon request, WGC computes personalized cruising paths that minimize each driver's expected time to allocation. Monte Carlo simulations on synthetic urban networks show that WGC consistently outperforms baseline strategies, highlighting the advantage of predictive, context-aware rebalancing in dynamic mobility systems.

Figures (3)

• Figure 1: This figure provides an overview of the WGC system dynamics. The top part presents the set of coupled differential equations describing the evolution of unmatched passengers at the edge level, idle drivers cruising on edges, and idle drivers located at nodes. The bottom part illustrates an example of the predicted state trajectories, showing the evolution from the initial distribution of drivers and passengers to the forecasted supply-demand patterns over time.
• Figure 2: Convergence behavior of the WGC system dynamics over time.
• Figure 3: Comparison of expected allocation time ($T_{alloc}$) under different routing strategies across fleet sizes ($N$).