Visible light communications (VLCs) relying on commercially available light-emitting diode (LED) transmitters offer a huge data rate potential in this license-free spectral domain, while simultaneously satisfying energy-efficient conventional illumination demands. In an LED-based VLC system, the achievable data rate may be severely degraded owing to the interference, when the VLC system employs the unity frequency reuse (FR) approach. In order to mitigate the effects of interference, we propose a pair of interference avoidance approaches, namely, FR-based transmission and vectored transmission (VT). Furthermore, the resource allocation (RA) problems of indoor mobile terminals (MTs) are investigated based on different transmission strategies. Inspired by the concept of effective capacity (EC), we formulate our RA optimization problems applying proportional fairness, while satisfying specific statistical delay constraints. Our optimization procedure solves the RA problem of indoor MTs with the aid of a decentralized algorithm. Simulation results are also presented for quantifying the performance of the proposed algorithm. It is shown that both of our interference avoidance approaches are capable of reducing the interference, hence improving the overall performance. Furthermore, it is also observed that our VT transmission is capable of achieving a higher EC than the FR approach, when the statistical delay requirements are loose. By contrast, the FR-based transmission attains the best performance, when we tighten the delay requirements.