Ride-hailing services have transformed urban transportation through convenience yet introduced new complexities around efficiency and traffic management. This study investigates the dual-queuing problem in ride-hailing from the driver perspective using a multi-agent simulation approach. The focus is dissecting the dynamics between driver search times and passenger wait times, which critically influence operational efficiency especially during peak demand. Exploring these interactions aims to uncover insights that could improve service efficiency and customer satisfaction. Addressing such ride-hailing challenges is vital not just for individual providers but also for advancing sustainable mobility across rapidly growing metropolitan regions. Enhanced efficiency connects to broader urban development narratives around livability, accessibility, and responsible mobility ecosystems.