Analysis of ride-hailing systems’ stability and dynamics around equilibrium points

Emerging transportation services, particularly ride-hailing, are rapidly reshaping urban mobility and often outpacing our understanding of their operational characteristics. A prominent challenge in these services is the ``wild goose chase" (WGC) phenomenon, an inefficient state resulting from dynamic and stochastic behavior. Despite its prominence, no systematic and rigorous framework currently exists to assess its effects over the stability of the system equilibrium points or predict its duration. Herein, this study proposes such a framework to assess the stability of equilibrium points, and provide accurate predictions on the duration of the WGC phenomenon. The main findings used pivotal operational thresholds (e.g., equilibrium points and the boundary between efficient and inefficient operational conditions) to identify three regions with contrasting efficiency and stability characteristics. A queuing model is developed and compared to a numerical simulation, demonstrating that the efficient equilibrium is not the most typical operating state unless fleet sizes significantly exceed a determined minimum threshold. Moreover, the queuing model quantifies the risks associated with prolonged operation in inefficient states, revealing potential system instability. These results reveal previously overlooked risks for ride-hailing services associated with long and repeated periods of inefficient operation. By enabling quantitative characterization of the WGC phenomenon, this work offers a fundamental tool for guiding future research and informing operational strategies in ride-hailing services.