## 4 Proposed Model  
The model illustrated in Figure 2 aims to address the limitations identified in the base model to enhance the quality of experience (QoE) for players. The following are the ways these limitations are addressed:  
1. **Player behavior assumptions:** In the simulation of the proposed model, more complex player behaviors were considered. Not only was the variability in player connections and disconnections taken into account, but so too were player movement patterns, such as remaining on a server for a period of time and transferring between servers.
2. **Fog deployment scenarios:** The simulation of the improved model incorporated the geographic locations of players and servers. This approach enhances user experience and optimizes system performance.  
3. **Network latency consideration:** For the simulation of the proposed model, network latency for each user was considered. Factors such as the distance between the server and client, server load, and network conditions were taken into account.
4. **More realistic environment modeling:** The simulation of the proposed model considered the geographic location of players and the location of their avatars in the game world. This approach provides more accurate modeling of the game environment.
5. **Scalability:** The proposed model aims to reduce the average load per server by increasing the number of fog servers. This optimization in load distribution will lead to more efficient load balancing within the cluster, highlighting the system's ability to adapt and manage more demanding loads.
6. **Evaluation of fog implementation strategies:** For the proposed model, factors such as the geographic location of servers and fog nodes, server load, and variability in network conditions were implemented. These factors allow for a more precise evaluation of fog implementation strategies.  
Additionally, the proposed model also implemented latency reduction strategies such as load balancing and server clustering.  
**Load Balancing**  
Load balancing is a fundamental strategy for improving latency and quality of experience in online games. In this model, it is implemented through a combination of techniques that leverage the hybrid cloud gaming architecture, integrating both cloud and fog servers. The load balancing algorithm designed for this model dynamically manages the distribution of functionality between cloud and fog servers. This algorithm adapts according to server capacity and system conditions, ensuring balanced load distribution at all times. This adaptability ensures efficient workload distribution, optimizing system performance and enhancing the end-user experience.  
**Server Clustering**  
The subdivision of the game world into clusters is an essential practice that facilitates equitable distribution of game traffic and processing load. Each cluster is managed by a different server, allowing for efficient allocation of resources and tasks. Additionally, multiple servers per cluster are employed, which enhances redundancy and system responsiveness during peak demand periods. The invocation of fog nodes to assist in processing is another key strategy, allowing for decentralization of part of the workload and positioning resources closer to end-users, reducing latency and improving user experience.  
This combination of strategies, along with the dynamic load balancing algorithm, ensures optimal operation of the online gaming system, providing a smooth and high-quality user experience.