## 4 Proposed Algorithm (NCRA-DP-ACO)
### Pheromone Management
#### 4.2.7 Algorithm
These profiles serve as \(H_{t}\) in Equation (7) to compute each site's dynamic PUE at every hour. The hourly temperatures for the sites are represented in Figure 4.

#### 5.1.5 Energy Price

Energy prices were obtained from the U.S. Energy Information Administration [42]. The average industrial electricity price for each site is listed in Table 3. We considered datacenters as an industrial sector and used the average price of electricity. On-site solar has zero incremental cost in our model, since capital and maintenance expenses are fixed. #### 5.1.6 Carbon Tax and Carbon Footprint

Datacenter carbon intensities (ton CO\({}_{2}\)/MWh) were sourced from the EPA's eGRID database (eGRID) [43]. Carbon tax rates (USD/ton CO\({}_{2}\)) are from the Carbon Tax Center [44]. Each site's carbon intensity and tax rate appear in Table 3.

#### 5.1.7 PUE Model

For all datacenters, we use the PUE model discussed in Section 3.1. We assume that the efficiencies of the entire datacenter site infrastructure are all the same. The PUE model is shown in Table 3.

#### 5.1.8 Server Power Consumption

As mentioned in Section 3.1, we adopt the approximate linear relation with server utilization against SpecPower results for two HP ProLiant servers (HP ProLiant MI110 G4 and G5), and their respective power models are stated in Table 6.

#### 5.1.9 Workload

This work uses real workload from the Metacentrum cloud provider, a distributed computing environment for providing resources for scientific research, including high-performance computing (HPC) and cloud computing. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Server Model** & **CPU Utilization (\%)** & **0\%** & **10\%** & **20\%** & **30\%** & **40\%** & **50\%** & **60\%** & **70\%** & **80\%** & **90\%** & **100\%** \\ \hline G4 & Power (W) & 86 & 89.4 & 92.6 & 96 & 99.5 & 102 & 106 & 108 & 112 & 114 & 117 \\ \hline G5 & Power (W) & 93.7 & 97 & 101 & 105 & 110 & 116 & 121 & 125 & 129 & 133 & 135 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Power modeling. Figure 4: Hourly outside temperature (°C) over five days at four datacenter sites. This workload is represented in SWF (Standard Workload Format). It represents different types of jobs, including bag-of-tasks jobs, long running computational tasks, and batch jobs, as demonstrated in Table 7.

Most jobs are batch-style, submitted to a queue. A substantial portion are bag-of-tasks jobs--many independent, short-lived tasks ideal for parallel execution--reflecting the characteristics of distributed computing. The workload also contains long-running, computer- or memory-intensive jobs (scientific simulations, data analysis, machine learning). This diversity makes the Metacentrum traces well suited for evaluating VM placement in hybrid cloud/HPC environments. After extensive experiments, the interval for cloudlets submission is set to 600 s (10 min), particularly because the ACO algorithm is performing a search for the best placement at every submission. This allows the ACO algorithm to have sufficient time to process a significant batch of cloudlets, for example, up to 500 cloudlets (VM request), rather than being overwhelmed with frequent and small submissions for shorter intervals (less than 10 cloudlets). ### Result Analysis

The experimental analysis evaluates our proposed ACO-based VMP's efficiency in reducing energy consumption, minimizing carbon emissions, assuring SLA compliance, and reducing operational costs. All experiments were performed in a simulated cloud environment. ACO was compared against well-accepted heuristic methods --BFD and FFD [39] --which are widely adopted baselines in the literature, as well as against Cost and Renewable-Aware with Dynamic PUE (CRADP) [3] and the metaheuristic Unified Ant Colony System (UACS) [45]. CRADP was selected because it explicitly models both renewable energy availability and dynamic PUE in its cost function, penalizing placements with low solar input or high cooling overheads.