Visible Light Communication (VLC) offers distinctive advantages over conventional radio frequency; wide unlicensed spectrum, resistance to electrometric interference and low susceptibility to security risks, are few to name. Excitingly, VLC becomes a cornerstone in several communication systems such as light fidelity, optical camera communication and the Internet of Radio Light. Most of these networks adopt the Carrier Sensing Multiple Access-Collision Avoidance (CSMA-CA) of IEEE 802.15.7, the official standard for the VLC, as a Medium Access Control (MAC) protocol. Motivated by the crucial roles of MAC in shaping the performance of the VLC and the wide variety of operational conditions demanded by the enormous applications, this paper proposes a Modular Statistical Analytical Model (MSAM). The fundamental approach of MSAM is to segregate the interacting stochastic processes imposed by the CSMA-CA protocol into a set of its elementary subprocesses. The MSAM then synthesises these processes in such a way that quantifies their mutual dependency without making a strict assumption on their characteristics; thus, different operational conditions can be assessed without a need to reconstruct the model. Besides, MSAM employs the radiometry and photometry of VLC to derive mathematical expressions describing the hidden and exposed nodes from which the Imperfect Carrier Sensing (ICS) conditions are defined. The MSAM exploits statistical and queuing theorems to model a VLC as a network of G/G/1 queues from which several probability distributions, characterising the operations of VLC from different perspectives, are derived. Inter-departure, queuing, service time and successful service time are the main distributions in conjunction with throughput, total delay, probability of exposed and hidden node collisions, which are the main outputs of MSAM. Validation for the integrity of the MSAM under different scenarios is carried out by conducting a head-to-head comparison between its results and simulation outcomes.
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