  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.
