## 4 Proposed Solution  
There have been various approaches proposed to address the challenges faced by IoT networks. One popular approach involves leveraging SDN to address the issue of heterogeneity. However, there are still several open research gaps in SDN-IoT networks. In this study, we propose an extension to an existing method that aims to alleviate heterogeneity while maintaining QoS in SDN-IoT networks. We identified a research gap in the method proposed by [13], which demonstrated the effectiveness of their framework in addressing heterogeneity and maintaining QoS, as well as improving security. However, their approach had certain limitations. To address this, we introduce the concept of the controller bandwidth in the network and evaluate the performance of the improved approach. We believe that our proposed approach will help fill the identified research gap and provide valuable insights into the effectiveness of this approach in addressing the challenges faced by SDN-IoT networks. In the previous section, we discussed the impact of the service rate of controllers on the SDN-IoT network's QoS and security mechanism. To alleviate heterogeneity while maintaining QoS, controllers with different service rates are grouped together. In our experimentation, we considered two algorithms: the random algorithm (RA) [50] and the first come first serve (FCFS) algorithm. The RA algorithm selects a controller randomly  
Figure 4: The high-level architecture of SDN-IoT to alleviate heterogeneity. to serve the incoming flow, while the FCFS algorithm prioritizes the first request in the queue [51]. There is a central controller and to achieve the closed-form expression of many metrics of interest, the M/M/1 queuing discipline is selected. It also aligns with the previous research conducted in this domain. The M/M/1 queue represents a basic system with a single controller, where the queue length corresponds to the number of incoming IoT flows following a Poisson distribution. IoT flows are considered two events in our model that occur in different time periods. Incoming IoT flows follow the Poisson distribution, and the service rate of each SDN controller follows an exponential distribution. These are the basics of queuing theory, and M/M/1 is the most suitable choice. To analyze the system's performance, we treated the entire IoT network as an M/M/1 queuing discipline [52]. The arrival rate of packets is denoted by \(\lambda\), while the control flow rate of each individual controller is denoted by \(\lambda\). In our heterogeneous network, m controllers are divided into n homogeneous groups, resulting in a service rate of m.\(\mu\) for the whole system and n.\(\mu\) for each individual controller. The degree of heterogeneity is determined by the service rate of the controllers, and we define the system as heterogeneous when h > 2; otherwise, it is homogeneous. Previous research work related to SDN-IoT networks provided us with important variables and equations for this heterogeneous system. Overall, our proposed solution aims to fill the research gaps in the SDN-IoT network's heterogeneity issues, while maintaining the QoS and increasing the security performance and mechanism:  
\[h=\left[\frac{\mu_{max}}{\mu_{min}}\right] \tag{1}\]  
The service rate is the average time of the packet or flow spent in the queue in waiting and time spent in utilizing resources of the controller. The average time flow, waiting time, and service rate of the controller are used to represent the complete network service rate. These general formulas are given below, and the changes in these formulas are also presented below with respect to the RA algorithm and the first come first serve algorithm (FCFS). Table 2 represent a description of variables that are used in formulas.