Traffic congestion and low vehicle occupancy rates pose significant challenges in urban areas, highlighting the need for efficient, shared transportation systems. Hence, in this work, we introduce an Edge-Enabled Vehicle-as-a-Service scheme, named E-VaaS, designed to improve traffic flow, reduce travel times, and enhance user satisfaction in intelligent transportation networks. By combining the Gale-Shapley stable matching algorithm with edge computing, the proposed E-VaaS system effectively schedules and matches riders to vehicles based on metrics that include travel time, distance, and cost. With the help of edge computing, E-VaaS enables low-latency processing, ensuring that ride-matching decisions are made swiftly and improving system responsiveness and user experience. Experimental results validate the effectiveness of the model, showing improved vehicle occupancy, reduced travel times and costs, and a balanced distribution of shared vehicles across the transportation network. This research advances the development of stable, scalable, and efficient ride-sharing solutions for urban environments.