In the modern landscape of wireless communications, multi-hop, high-bandwidth, indoor Terahertz (THz) wireless communications are gaining significant attention. These systems couple Reconfigurable Intelligent Surface (RIS) and relay devices within the emerging 6G network framework, offering promising solutions for creating cell-less, indoor, and on-demand mesh networks. RIS devices are especially attractive, constructed by an array of reflecting elements that can phase shifts, such that the reflecting signals can be focused, steered, and the power of the signal enhanced towards the destination. This paper presents an in-depth, analytical examination of how path allocation impacts interference within such networks. We develop the first model which analyzes interference based on the geometric parameters of beams (conic, cylindrical) as they interact with RIS, User Equipment (UE), and relay devices. We introduce a transmission scheduling heuristic designed to mitigate interference, alongside an efficient optimization method to maximize throughput. Our performance results elucidate the interference's effect on communication path quality and highlight effective path selection strategies with throughput maximization.
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