# Performance Analysis of P2P Networks with Light Communication Links: The Static Managed Case
## 1 Introduction
LiFi 2.0 works through the 802.11 bb standard and concentrates energy to achieve high rates of transmission. However, LiFi systems require a relatively high alignment accuracy among nodes, effectively reducing the mobility of nodes. Since nodes are considered to have null mobility capabilities, otherwise the use of LiFi would not be possible or effective, nodes cannot arrive or leave the system as it occurs in conventional P2P networks. Hence, the population in the system is considered to be finite and closed. This is a major challenge, and required important modifications to the traditional models developed in previous P2P studies. Building on this, we consider managed networks where the download procedure is initiated and controlled by the system administrator. There are many systems with these characteristics, such as in education, where the teacher shares files with the rest of the class; museums, where people get close to a particular display (where they remain static during a certain period) and information is downloaded to the visitor's devices; in cultural and sporting events, where people are seated with no mobility, and the stadium or concert hall distributes information regarding the event or in future applications where augmented reality and virtual reality capabilities are downloaded to the attending audience. Note that in different scenarios, where high degrees of mobility are allowed, it would not be possible to provide a fair performance comparison between LiFi and WiFi systems, since the link quality is greatly degraded if the node alignment is lost in light-based transmissions. In such cases, it is clear that RF-based transmissions should be adopted. Based on this, for applications where nodes are without mobility, it is not clear or straightforward to choose among these technologies, i.e., choose between RF or light, as a communication technology. In this work, we provide a mathematical analysis, based on continuous-time Markov chains (CTMCs), of P2P networks using either RF or light transmissions to study and understand the limitations and advantages of each technology. To the best of our knowledge, this is the first work that considers and models a P2P network with LiFi capabilities. As such, we aim to supply clear guidelines for the implementation of these systems by providing quantitative performance results in terms of the average file download time for the different number of nodes and network architectures. Specifically, we model both WiFi and LiFi wireless technologies in their most recent versions (_WiFi 7_ and _LiFi 2.0_), contemplating these technologies in _static_ node scenarios (considering _line-of-sight (LOS)_ and _non-line-of-sight (NLOS)_ propagation modes for LiFi environments) for centralized and decentralized networks. The main contributions of the article are listed below:  
* We develop a mathematical analysis of P2P-managed systems with no mobility capabilities that allow for the introduction of light-based transmissions. * We provide a detailed performance comparison between LiFi 2.0 and WiFi 7 networks. * Several scenarios are proposed in order to evaluate average download time and node variation in networks (P2P-WiFi, P2P-LiFi, centralized WiFi (C-WiFi) and centralized-LiFi (C-LiFi) networks). * A P2P-LiFi concept is introduced based on the operation and characteristics of LOS and NLOS scenarios. * We provide performance metrics in terms of the average download time for different file sizes across different network population sizes. * In addition to a numerical solution for the continuous-time Markov chain (CTMC), discrete event simulations (DES) of each scenario are provided to validate the analytical model. In the following, the organization of the paper is detailed: In Section 2, we present a short brief about some articles related to P2P, LiFi, and WiFi networks in a general way, since Sections 3 and 4 address these issues by detailing the features and models of P2P networks and the operating modes in which LiFi and WiFi networks will be used.