# Stable Throughput Analysis of Heterogeneous Hybrid FSO/RF Networks with Cognitive Radio Capability
###### Abstract
Our work further explores buffer management in hybrid FSO/RF systems, identifying the optimal buffer size required to ensure effective data transmission under dynamic, bursty arrival rates. The inclusion of cognitive capability in FSO/RF systems has also been investigated in several studies [24; 25; 26]. These studies primarily focus on transmitted packet delays as a performance metric across different network and operational settings: utilizing multiple FSO channels [24], offloading packets based on the buffer states of FSO and RF channels [25], and aggregating RF channels for macro and small cells [26]. The previous research has indicated that the packet delay becomes infinite when the arrival rate exceeds a certain threshold. In this study, we aim to analyze the stability region of combined FSO and RF traffic, which ensures the packet delays remain finite in various cognitive FSO/RF system settings. To the best of our knowledge, no prior study has specifically analyzed the stability region of cognitive FSO/RF systems. This study proposes a heterogeneous hybrid FSO/RF system structured around cognitive and economic frameworks. In the cognitive system, FSO and RF channels operate as a heterogeneous network with distinct RF resources shared dynamically to provide additional transmission opportunities. The economic system (placing the proposed system in currently practical environments), in contrast, restricts RF resources exclusively to RF links, allowing hybrid FSO/RF systems to access RF resources only when the FSO link is degraded. By employing both a stay-and-switch (SAS) method and a simultaneous multipacket transmission (SMT) strategy, this study investigates the stability region as a performance metric. The stability region is defined by the range of data arrival rates that maintain finite queue lengths across hybrid FSO/RF and RF links, offering a valuable indicator of network performance under bursty data traffic and probabilistic interference conditions. This analysis provides insights into network stability, highlighting the significance of stability regions as a measure of performance. By applying the static domain concept in [27], this work explores throughput within interaction queues, advancing our understanding of how hybrid FSO/RF systems can be optimized for robust, high-performance wireless communication. The key contributions of this study are summarized as follows:  
* This study presents a cognitive hybrid FSO/RF system model and its operational scenarios consisting of cooperative and economic mode operations. In addition, a reference mode of operation is also defined to evaluate the performance of the proposed usages. * For each operational scenario, this study conducts thorough stability analyses for two transmission strategies (i.e., SAS and SMT transmissions), and obtains the respective stable throughput. Furthermore, a hybrid SAS and SMT transmission is investigated for the cooperative mode and the stable throughput is also obtained. * This study illustrates and compares the performance of the proposed methods through numerical evaluations. The data used in the simulation are sources from various relevant studies in the literature. The advantages of the proposed system are assessed against the reference system. The numerical results indicate that the cooperative system utilizing SMT generally outperforms the reference system, achieving an increase in stable throughput of up to 52%. However, this advantage diminishes when the SAS strategy is employed. The low-cost economic model demonstrates performance levels comparable to the reference model, particularly under conditions of low incoming traffic and when SAS is applied in clear or hazy environments. The remainder of this paper is organized as follows: Section 2 presents the system models considered in this study, which define the heterogeneous hybrid network operations, including the cooperative, economic, and reference systems.