The 2D carbon material graphene exhibits strong light-matter interaction over a very wide wavelength range from the far infrared to the ultraviolet . The tunability of the density-of-states and Fermi energy in graphene along with its excellent transport properties provide a path for graphene photonic applications such as quantum optics, photo-voltaics, photo-detectors, and biological sensing . In this paper, we propose exploiting collective electron-light oscillations or plasmons in patterned graphene nano-ribbons (GNRs) for low energy, high-speed on-chip interconnects that can potentially overcome the latency and power constraints of the current copper/low-K on-chip interconnects [3-4]. The contributions of this paper are threefold. First, compact models for evaluating the plasmon-damping rate in GNRs are introduced. The models account for plasmon-damping pathways through phonons (intrinsic and substrate), substrate charged impurities, and edge-states in ribbons. The compact models introduced in this paper are also applicable to other photonic applications of graphene beyond just on-chip interconnects. Secondly, compact models for evaluating the propagation speed and energy consumption of plasmonic waveguides based on their shot-noise limits are introduced. Finally, the fundamental limits and device implications of on-chip plasmonic waveguides are quantified. In particular, propagation speed and energy consumption are compared with copper/low-K on-chip interconnects at advanced technology nodes.