## 1 Introduction  
Software-defined networking (SDN), a rapidly growing networking management paradigm, has been investigated and enhanced, including efforts to enhance consistency and standardization in various aspects [1; 2; 3; 4; 5]. The distributed SDN controllers are interconnected in several ways, such as hierarchical or flat. Flat architecture can be Physically Distributed Logically Centralized or Fully Distributed [6; 7]. Focusing on a Physically Distributed Logically Centralized (PDLC) SDN control plane framework, each controller is responsible for its domain by addressing the failure in its domain data plan and traffic flow congestion. These changes must be communicated across all controllers in different domains within the cluster to attain a globally consistent view in a timely manner. However, achieving such a time rigorous level of consistency while preserving good performance is a complicated task [4]. A key concern is balancing performance and consistency without altering SDN protocols [8]. Several challenges with the PDLC control of SDNs demand particular consideration, including scalability, reliability, consistency and synchronization overhead, interoperability, East-West interface implementations, and security, as depicted in Figure 1[9; 10]. Reliability and scalability, often viewed as primary concerns in centralized SDN control architecture, are equally crucial in developing a PDLC SDN architecture. Furthermore, examining consistency issues while making trade-offs for an SDN controller platform is crucial. Consistency requires a synchronization process, which can present a harmful overhead for the system [9; 11; 12]. We will focus on the consistency and synchronization overhead challenge. Designing applications that run on the SDN approach on top of the distributed environment is a crucial task because of the complexity of synchronizing controllers and the network state, which will affect the performance of the applications and network efficiency [13; 14]. The consistency management is handled with an inter-controller synchronization process, as per the deployed application's consistency level preferences (strong or eventual) [15]. The frequency of distributed control plane-wide state updates and the eventual resolution of state conflicts are governed by consistency levels. In loose consistency levels, synchronization overhead decreases, but the possibility of state conflicts arising increases. Contradictorily, strict consistency levels result in more frequent synchronization, resulting in more overhead in the control plane [4; 13; 16; 17; 18; 19]. The resulting overhead will increase latency and affect the scalability of the system. We refer to latency (sometimes called responsiveness) as the time the system takes to reply to flow requests. Trade-offs between various consistency models and responsiveness features are present with PDLC topology [3; 5; 6; 9; 16; 20]. As observed from the literature, the PDLC SDN architecture inter-controller synchronization process can be applied in static or adaptive approaches. Static Inter-Controller Synchronization ApproachA static synchronization technique provides fixed, predetermined intervals (for instance, every 3-4 s), which can affect the application's performance by utilizing outdated data or irritating the network with unnecessary synchronization messages [18]. Adaptive Inter-Controller Synchronization ApproachThe adaptive synchronization approach involves adjusting the consistency levels according to the correctness thresholds. This cost-aware approach determines the balance between two major performance metrics: the synchronization overhead and the system accuracy of the distributed control plan [19]. Additionally, it can leverage the performance of the applications that can tolerate some inconsistency. It is important to strike a balance with adaptive synchronization to avoid excessive overhead or delays in propagating critical updates.