Abstract--Unlike traditional multi-agent coordination frameworks, which assume a fixed number of agents, UAS traffic management (UTM) requires a platform that enables Uncrewed Aerial Systems (UAS) to freely enter or exit constrained low-altitude airspace. Consequently, the number of UAS operating in a given region is time-varying, with vehicles dynamically joining or leaving even in dense, obstacle-laden environments. The primary goal of this paper is to develop a computationally efficient management system that maximizes airspace usability while ensuring safety and efficiency. T o achieve this, we first introduce physics-informed methods to structure fixed skyroads across multiple altitude layers of urban airspace, with the directionality of each skyroad designed to guarantee full reachability. We then present a novel Continuous UTM (C-UTM) framework that optimally allocates skyroads to UAS requests while accounting for the time-varying capacity of the airspace. Collectively, the proposed model addresses the key challenges of low-altitude UTM by providing a scalable, safe, and efficient solution for urban airspace usability.