# Verification of a Probabilistic Model and Optimization in Long-Range Networks
## 3 Results
By focusing on short distances, this study isolates and evaluates the fundamental behavior of the proposed probabilistic model, providing a robust foundation for its application in scenarios requiring extended communication ranges, such as smart agriculture or wide-area sensor networks. Future work could validate these findings further by extending the experiments to real-world deployments over longer distances, incorporating additional environmental complexities to confirm scalability. In the experimental setup shown in Figure 3, the ESP32 was mounted on a protoboard to construct the circuit. The circuit was distributed across four separate protoboard to demonstrate the experiment effectively. The ESP32 was programmed to function as a server, enabling seamless communication and configuration of the Reyax RYLR998 modules. A custom real-time interface was developed to dynamically adjust key transmission parameters, including spreading factor, bandwidth, and power levels. This system, illustrated in Figure 4, displays all the parameters measured during the experiment. The interface not only streamlined the configuration process but also facilitated rapid prototyping and testing of various communication scenarios, enhancing the overall experimental efficiency and adaptability. To monitor the performance and reliability of the network in real time, a web-based dashboard was implemented. The dashboard, built using modern web development frameworks, was connected to an SQL database that logged all transmitted and received data. This allowed for continuous tracking of packet success rates, RSSI values, and interference metrics. The use of a database ensured that data could be easily queried and analyzed for trends and anomalies, providing valuable insights into network performance [28]. The first experiment aimed to evaluate the system's behavior in a controlled environment over a 10-min period. The setup included multiple Reyax RYLR998 modules transmitting packets to a central gateway managed by the ESP32. The transmission interval was set to 1000 ms (1 packet per second), and key parameters such as transmission power and spreading factor were adjusted to study their impact on packet loss and network reliability. The experimental data were visualized on the dashboard, providing a  
Figure 4: Interface used to control each ESP32. Figure 3: Experimental deployment. Figure 2: Experimental setup using Reyax RYLR998. clear representation of the system's performance. Table 1 provides a detailed summary of the transmission results obtained over a 10-min experimental period, showcasing the performance of the transmitters in terms of the number of data points transmitted, success probability (SP), and average RSSI. These results offer valuable insights into the behavior of the network under the tested conditions and highlight key aspects of the performance of the model and devices used [29]. Transmitters 1 and 3 exhibited an identical performance, each successfully transmitting 63 data points with a success probability of 87.5% and achieving average RSSI values of \(-43\) dBm and \(-41\) dBm, respectively. These values indicate a relatively high level of reliability, although some packet losses occurred due to interference or other factors such as path loss variability. The consistency in their performance suggests that the experimental setup provided stable conditions, allowing these devices to operate with comparable efficiency. On the other hand, transmitters 4 and 5 demonstrated optimal performance, achieving a 100% success probability by transmitting 72 data points each without any packet losses. Their respective average RSSI values, \(-47\) dBm and \(-46\) dBm, reflect strong and stable signal strengths at the receiver. The superior performance of these transmitters could be attributed to several factors, including their proximity to the gateway, favorable environmental conditions, or reduced interference during their operation.