Visible Light Communication (VLC) has been emerging as a promising technology to address the increasingly high data-rate and time-critical demands that the Internet of Things (IoT) and 5G paradigms impose on the underlying Wireless Sensor Actuator Networking (WSAN) technologies. In this line, the IEEE 802.15.7 standard proposes several physical layers and Medium Access Control (MAC) sub-layer mechanisms that support a variety of VLC applications. Particularly, at the MAC sub-layer, it can support contention-free communications using Guaranteed Timeslots (GTS), introducing support for time-critical applications. However, to effectively guarantee accurate usage of such functionalities, it is vital to derive the worst-case bounds of the network. In this paper, we use network calculus to carry out the worst-case bounds analysis for GTS utilization of IEEE 802.15.7 and complement our model with an in-depth performance analysis. We also propose the inclusion of an additional mechanism to improve the overall scalability and effective bandwidth utilization of the network.