# Fuzzy-Based Multi-Modal Query-Forwarding in Mini-Datacenters
## 6 Results and Discussion
### Query Forwarding Behavior Within Mini-Datacenter
#### 6.1.1 Buffer Occupancy Nearing Saturation  
The experimental setup is comprised of gateways with buffer occupancies ranging from 75 to 95% while they started receiving queries. The buffer occupancy of a gateway \(g_{i}\) is varied with the query arrival rate greater than the service rate, as shown in Equation (16). The buffer occupancy variation over the query forwarding is demonstrated in Figure 7.  
\[\frac{\partial B_{g_{i}}(t)}{\partial t}=\begin{cases}1&\text{if $g_{i}$ is included in redundant transmission}\\ -1/3&\text{for all $g_{i}\in G$}\end{cases} \tag{16}\]  
The proportion of fitted gateways against the redundant gateways is plotted in Figure 8. The redundancy is influenced by the fitness factor and gamma factor, representing the current buffer occupancy and query backlog at the command center. Here, the fitted gateways with fitness values greater than 0.3 were selected to maximize the participation of available gateways.  
The gateway availability, buffer overloading, gamma factor, and redundancy selection all contribute to the query forwarding reliability is as illustrated in Figure 9. A sensitivity analysis was conducted to select the value for the parameter \(\alpha\) (used in the gamma factor), where the values of \(\alpha\) were varied from 0.01 to 0.1 to find out how the proportion of the query backlog influenced the selection of redundant gateways. Initially, the gamma factor was low (0.21) due to a high query backlog at the command center. As the query backlog decreased, the gamma factor increased to 0.73, which in turn increased the proportion of redundant gateways.  
Figure 7: Buffer occupancies of gateways during query forwarding.  
The fitness value is selected as greater than 0.3, and the gateways with buffer occupancies of 70% or more were considered overloaded. The reliability is defined as the probability of successfully forwarding a query through the gateways, and it increases as the number of  
Figure 8: Variation of redundant gateways against fitted gateways during query forwarding.  
Figure 9: Query forwarding within the mini-datacenter.  
gateways increases. While the query forwarding mechanism is designed to consider buffer occupancy and network load for fair distribution, occasional imbalances were observed. Specifically, in scenarios with fewer gateway nodes (around 10), the inherent randomness in gateway selection sometimes caused a repeated selection of the same gateway, leading to localized buffer overload. Although constraints were introduced to prevent immediate reselection, limited gateway availability under these conditions still resulted in repeated assignments and uneven load distribution.  
In this study, we assumed a probability (P) of 0.8 for successful direct transmission using a single gateway, according to [48]. The reliability ranges from 0.8 (for direct query forwarding) to a maximum of 0.9999 (with more than 50% redundancy). Based on the experimental results, it is observed that for a full gateway availability (10/10), with 50% redundancy (5/10), a 45% query backlog, and 50% buffer overloading, the reliability is close to its maximum value of 0.9968.