## 4 Proposed Algorithm (NCRA-DP-ACO)
### Pheromone Management
#### 4.2.7 Algorithm
This aligns directly with our objectives of minimizing energy and carbon emissions under variable environmental conditions. UACS, on the other hand, represents a recent, state-of-the-art ACO variant that extends classical pheromone-update rules with multi-objective weighting and adaptive heuristic factors. To ensure a direct comparison, we re-implemented all algorithms (BFD, FFD, CRADP, UACS, and NCRA-DP-ACO) from scratch in CloudSimPlus. We used identical server configurations, workload traces, and algorithm parameters for UACS and NCRA-DP-ACO. Running all algorithms under the same simulation conditions allows us to directly compare their responses across different workload intensities (500-14,000 VMs). Because NCRA-DP-ACO is nondeterministic, each workload configuration was run 30 times to ensure statistical robustness. The reported performance metrics represent the mean values across these runs. Performance trends are visualized and discussed in detail in subsequent sections. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Cloudlet PEs** & **VM Type** & **Cloudlets Percentage** & **Example Workload** \\ \hline
1 & Type 1 & 40\% & Small web apps, APIs, development environments \\ \hline
2 & Type 2 & 30\% & Medium-sized apps, databases, caching servers \\ \hline
4 & Type 3 & 20\% & Enterprise apps, high-traffic web servers \\ \hline
8 & Type 4 & 8\% & Video encoding, data processing \\ \hline
16+ & Type 5 & 2\% & Machine learning, big data \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Workload characteristics. #### 5.2.1 Energy Consumption

For the sustainability of clouds, energy efficiency is of significant importance. A much lower energy consumption is expected from the proposed ACO placement because of the dynamic VM consolidation strategy, which minimizes the number of servers in an active state. It shows the total energy consumed by each algorithm for different VM workload sizes, as depicted in Figure 5.

Figure 5 shows that the ACO algorithm achieves lower energy consumption compared to the best baseline heuristics. It becomes evident when the number of VMs increases; for example, at 14,000 VMs, ACO saves approximately 18% energy compared to BFD. This is because ACO uses pheromone-guided search, which efficiently consolidates VMs onto fewer active PMs and thus reduces both dynamic and idle power consumption. #### 5.2.2 Carbon Footprint (kg CO\({}_{2}\))

This outcome aligns with the well-established correlation between energy consumption and carbon emissions that less energy use will result in a lower carbon footprint. Figure 6 gives a comparative analysis of carbon emissions using different algorithms for various workloads. Figure 5: Energy consumption comparison across algorithms for varying workloads. Figure 6: Carbon footprint trends for proposed ACO vs. baseline algorithms under differing request numbers. The slight carbon footprint spike for ACO at 500-1000 VM workloads occurs because consolidation is less effective at low scales: ACO may keep more servers active to accommodate renewable usage, resulting in higher idle power. As workloads exceed 1000 VMs, ACO's carbon emission savings surpass 15% relative to BFD and FFD, due to energy-efficient consolidation and renewable-first placement. These results confirm ACO's scalability for green cloud computing. #### 5.2.3 Total Cost

The total cost (energy + carbon tax) is a major financial parameter for cloud service providers. Figure 7 compares the total operational cost outcomes of the different algorithms. The ACO algorithm achieved the least total cost for various workloads, as depicted in Figure 7. This cost advantage is enhanced for larger workloads up to 17% with respect to the standard heuristics. The cost savings are primarily attributed to improved energy efficiency and reduced emissions, establishing the new method as an economically viable solution for green cloud computing.