The Elevator Group Control System (EGCS) is a critical element in the management of vertical transportation within modern buildings, which are becoming increasingly complex due to urban growth. This work introduces a new paradigm for the management and dispatching of elevator groups, using state-of-the-art communication technologies, artificial intelligence, and cloud computing. The proposed framework enhances the computational capabilities of existing systems by integrating edge computing with cloud services, enabling real-time data processing and advanced dispatch algorithms. The framework also incorporates machine learning and computer vision technologies to optimize dispatching based on user behavior, building dynamics, and energy consumption patterns. Furthermore, it facilitates predictive maintenance and the design of future elevator systems tailored to specific building types and user needs. The paper explores the potential benefits, including improved system performance, increased user satisfaction, and the integration of Smart City principles, contributing to the sustainability and efficiency of vertical transportation in modern urban environments.