## 1 Introduction

Table 1: Summary of SF allocation schemes and contributions. The comparison between abovementioned SF allocation schemes was performed over the three following features:  
1. Performance: indication of the overall system throughput. 2. Ease of implementation (complexity): indication of the amount of processing resource required at the gateway to decode a transmitted packet from a node. 3. Application: indication of ability to handle dynamic scale of the network such as scenario mitigation, number of nodes, and inclusion and exclusion of nodes. Results are shown in Table 2.  
While these mentioned SF allocation schemes often enhance network throughput, they typically require increased energy consumption. To achieve a balance between throughput and energy consumption, several strategies can be considered. Dynamic SF allocation schemes, which can adjust SFs based on current network conditions, are generally preferable to static schemes. Additionally, implementing power-saving modes and adaptive transmission power can help conserve energy. Furthermore, clustering nodes and allocating SFs within each cluster based on individual node requirements can improve overall energy efficiency. However, when making trade-offs, the specific needs of the application must be carefully considered. Our research applied the proposed GD algorithm to the LoRaWAN simulations conducted using the LoRaSIM simulator, a widely known Python-based LoRaWAN simulator developed by [PERSON] and [PERSON] from University of Lancaster in UK. To assess the impact of node distribution on network performance, a comparative analysis was undertaken. This analysis compared results obtained from the uniform random node distribution scenario to those obtained from the fixed node distribution assumed based on the locations of dairy farms around the Photharam district, Ratchaburi province, Thailand [23]. This particular site was selected because it plans to implement Internet of Things (IoT) sensors to collect behavior data from dairy cows. The novelty of our algorithm lies in its ability to work effectively with biased node distributions and still achieve high DER values by finely tuning the weight factor. This adaptability ensures the algorithm's efficacy across various scenarios, which provides valuable insights for improving network performance under diverse conditions. The paper is divided into subsections as follows. Section 2 provides a brief overview of LoRaWAN. Section 3 delves into the comparison of fixed and random node simulation, while Sections 4 and 5 expound on the geometric distribution mathematical model and the proposed algorithm, respectively. Section 6 covers the details of the experimental simulation, and the discussion and analysis of results are presented in Section 7. The \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**SF Allocation Scheme** & **Type** & **Performance** & \
\begin{tabular}{c} **Ease of** \\ **Implementation** \\ **(Complexity)** \\ \end{tabular} & **Application** & **References** \\ \hline ADR & Dynamic & High & High & Yes & [11, 25] \\ \hline SNR-based SFs & Dynamic & High & High & Yes & [13, 14, 25] \\ \hline RSSI-based SFs & Dynamic & Moderate & Moderate & Yes & [15, 16] \\ \hline Time-on-Air-based SFs & Dynamic & High & Moderate & Yes & [15, 16] \\ \hline Distance-based SFs & Static & Moderate & Moderate & No & [12, 25] \\ \hline Machine learning-based SFs & Dynamic & High & High & Yes & [17, 18, 25] \\ \hline Descriptive Statistics-based SFs & Dynamic &
\begin{tabular}{c} QCVM—Moderate \\ SD–High \\ \end{tabular} & Moderate & Yes & [19, 20] \\ \hline The proposed GD algorithm & Dynamic & High & Moderate & Yes & This paper \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of SF allocation schemes with various features. research concludes with a summarizing section outlining the key findings and implications of the study.