Experimental Overview
This section explores the assessment of the proposed method through a set of experiments. Initially, we outline the experimental setup and detail the dataset characteristics used in these evaluations. Following this, we clarify the metrics used to gauge the effectiveness of our approach. Finally, we provide and interpret the results from these experiments, along with insights into the significant findings.
Experimental Configuration
The performance assessments and comparisons with established scheduling algorithms were performed utilizing MATLAB R2018b. The experiments were conducted on a DELL PC equipped with an Intel Core i5-2430 2.40 GHz CPU and 4 GB of RAM, running on Windows 10 Professional 64-bit. The experimental framework featured a fog-cloud environment that included two data centers, four host machines, and 25 virtual machines (VMs) with varied specifications. The parameters for the experiment have been detailed in Tables 2-3. This configuration facilitated extensive evaluations of scheduling algorithms under different conditions, accounting for various client numbers, resource capacities, and VM setups within the fog-cloud ecosystem.
Task Size Selection
Task sizes of 1000, 2000, 3000, 4000, and 5000 were selected to thoroughly evaluate the scalability and resilience of the proposed TS-GWO algorithm in managing different workloads within fog-cloud settings. These sizes reflect a range of task loads, from moderate to high, which are typical in real-world scenarios involving Internet of Things (IoT) applications. By testing this spectrum, we can effectively gauge the algorithm’s performance under varying levels of computational demand, demonstrating its adaptability and efficiency. Furthermore, these task sizes correspond with benchmark datasets from previous studies, allowing for meaningful comparisons with existing methodologies and providing a standardized evaluation framework.
Data Sources
For this study, a mix of synthetic and real datasets was utilized to evaluate the effectiveness of the proposed TS-GWO algorithm. The synthetic workload comprised 1000 tasks generated using a uniform distribution, with task lengths ranging from 1000 to 20,000 machine instructions (MI). Additionally, we incorporated real-world datasets from the ‘Parallel Workload Archive,’ specifically the HPC2N and NASA Ames iPSC/860 datasets. Detailed information about both the synthetic and real workloads is provided in Tables 4 and 5.
Experimental Repetition and Parameters
To ensure the reliability of our results, each experiment was conducted independently and repeated 30 times. The average values from these iterations were then reported. The specific settings for the algorithms used in this investigation are outlined in Table 6. This approach allowed for thorough assessments of the TS-GWO algorithm’s performance in comparison to other scheduling methodologies under various workload conditions.
Performance Metrics
To evaluate the TS-GWO algorithm’s effectiveness in task scheduling within fog-cloud computing environments, we focused on two primary performance metrics: makespan and energy consumption. These metrics are mathematically defined as follows:
Makespan Definition
Makespan is defined as the total time required to complete all allocated tasks across the available fog and cloud computing nodes. This metric is essential for ensuring an even workload distribution and minimizing the overall task completion time. Mathematically, it is represented as:
$$\begin{aligned} Z = \text{Max} \left( \frac{1}{C_k} \sum _{i=1}^n \sum _{j=1}^m P_j \cdot x_{ij} \right), \end{aligned}$$
where \(n\) represents the total number of tasks, \(m\) denotes the total number of computing nodes (either fog or cloud), \(P_j\) is the processing time for task \(t_i\) on computing node \(n_j\), \(x_{ij}\) is a binary decision variable indicating task assignment, and \(C_k\) is the processing capacity of computing node \(k\). The operator \(\text{Max}()\) identifies the maximum completion time across all nodes. This metric aims to minimize the completion time for the most loaded node.
Energy Consumption Definition
Energy consumption quantifies the total energy utilized by all computing nodes while executing the assigned tasks. This metric is critical for assessing resource efficiency and is mathematically expressed as:
$$\begin{aligned} E = \sum _{i=1}^n \sum _{j=1}^m E_j \cdot x_{ij}, \end{aligned}$$
where \(E_j\) indicates the energy consumption per unit time for node \(n_j\) during task processing. The summation aggregates the energy consumed across all tasks and nodes, underscoring the algorithm’s capacity to minimize overall energy expenditure, which is vital for energy-efficient fog-cloud systems.
Evaluation Constraints
The evaluation of these metrics is conducted under specific constraints to ensure effective and valid task scheduling:
1. Task assignment: Each task \(t_i\) must be assigned to exactly one computing node:
$$\begin{aligned} \sum _{j=1}^m x_{ij} = 1, \quad \forall i \end{aligned}$$
2. Node capacity: The total workload allocated to a node must not go beyond its processing capacity:
$$\begin{aligned} \sum _{i=1}^n P_j \cdot x_{ij} \le C_k, \quad \forall k \end{aligned}$$
3. Non-negativity: The decision variable must adhere to:
$$\begin{aligned} x_{ij} \ge 0, \quad \forall i, j \end{aligned}$$
These constraints establish the foundation for evaluating the TS-GWO algorithm’s efficiency in optimizing task scheduling in fog-cloud environments, focusing on both computational effectiveness and energy consumption.
Investigation Goals
The primary objective of this research is to minimize overall energy consumption while concurrently reducing makespan, thereby enhancing system efficiency.
Results Presentation and Analysis
This section elaborates on the detailed analysis of the evaluation outcomes derived from the TS-GWO algorithm, focusing on its performance in comparison to various benchmarked algorithms across multiple workload scenarios.
Comparative Performance Analysis
The TS-GWO algorithm underwent a thorough comparative analysis against several leading algorithms, including AHA, GJO, Atomic Orbital Search (AOS), AOA, MPA, Dynamic Jellyfish Simulated Disruption (DJSD), and the Chameleon Swarm Algorithm (CSA). Table 6 outlines the parameter configurations for both TS-GWO and the comparison algorithms. To maintain consistency, common parameters such as iteration count (1000) and population size (50) were retained across all tests, with each experiment replicated 30 times, and average results calculated. Additionally, the parameter \(\phi\) was consistently set to 0.7.
Performance Evaluation Across Datasets
The efficacy of the TS-GWO algorithm was assessed across various datasets and practical applications, with performance curves illustrated in Figs. 2, 3, and 4. Specifically, Figure 2 depicts the performance curve for synthetic workloads, where TS-GWO consistently outperforms all other algorithms in every instance. Figure 3 further illustrates TS-GWO’s excellence on the NASA Ames iPSC/860 dataset. Meanwhile, Figure 4 displays TS-GWO’s performance across different task volumes (ranging from 1000 to 5000) for the HPC2N workload, consistently exceeding the performance of the seven other techniques. With respect to fitness function values, TS-GWO ranks highest among its competitors, with GWO achieving the best overall performance, followed by AHA and AOS.
Comparison of Makespan
In terms of makespan, Figs. 5, 6, and 7 present comparative results between TS-GWO and other algorithms. Figure 5 clearly indicates TS-GWO’s average makespan superiority over the GJO algorithm and others within synthetic datasets. Figure 6 further confirms TS-GWO’s dominance regarding makespan on the NASA Ames iPSC workload. Similarly, Fig. 7 verifies TS-GWO’s leading performance across the HPC2N workload. The average improvements in makespan across varying workloads are considerable, with enhancements ranging from 9.89% to 40.91% for synthetic datasets, 4.02% to 34.94% for NASA iPSC workloads, and 2.91% to 46.15% for HPC2N workloads, when compared with other algorithms.
Energy Consumption Analysis
Figures 8, 9, and 10 provide a detailed comparison of total energy consumption across the algorithms. In every case, TS-GWO demonstrates the lowest energy consumption, surpassing other algorithms in both synthetic and real-world datasets. Particularly, Figure 8 emphasizes TS-GWO’s superior energy efficiency on synthetic datasets. Likewise, Figure 9 illustrates its energy efficiency within the NASA Ames iPSC workload, and Figure 10 further corroborates TS-GWO’s leading energy consumption performance on the HPC2N workload. The average reductions in energy consumption are noteworthy, with TS-GWO achieving decreases ranging from 7.94% to 28.57% for synthetic workloads, 3.54% to 14.62% for NASA iPSC workloads, and 2.16% to 9.11% for HPC2N workloads when compared to alternative methods.
Algorithm Performance Insights
The enhancements in makespan and other parameters associated with our TS-GWO approach can be attributed to its refined capability to balance exploration and exploitation through the modified GWO algorithm. The newly introduced operators in TS-GWO facilitate improved search space exploration, resulting in more optimal task-to-node allocations. This advancement leads to reduced makespan and enhanced energy efficiency, especially under the dynamic conditions of fog-cloud environments, where task and resource distributions frequently fluctuate.
Considerations for Future Optimization
While TS-GWO has demonstrated promising outcomes across a variety of datasets, including both synthetic and real-world scenarios such as NASA Ames iPSC and HPC2N workloads, it is particularly suitable for environments where task scheduling prioritizes both makespan and energy consumption. For scenarios with highly unpredictable workloads or significantly larger systems, further refinement or adjustments to the algorithm may be necessary.
Challenges and Future Directions
However, TS-GWO could encounter difficulties in exceptionally large-scale situations with intricate task interdependencies, where the computational expense of fitness evaluations may become significant. Moreover, the algorithm’s performance may be sensitive to specific parameter tuning, potentially necessitating domain-specific adjustments. Future work will aim to address these challenges by exploring multi-objective optimization and hybrid approaches capable of better managing such complex environments.
Conclusion
In conclusion, the results affirm that TS-GWO significantly enhances both makespan and energy consumption when benchmarked against established scheduling algorithms across diverse workload scenarios. TS-GWO consistently achieves lower makespan and energy consumption, thereby optimizing task completion time and resource utilization more effectively. These findings endorse TS-GWO as a robust optimization technique for fog-cloud computing environments, where performance and energy efficiency are of paramount importance. Furthermore, the experimental analysis points to the potential for further optimization by integrating TS-GWO with complementary algorithms, such as AHA and GJO, to improve search capabilities and generate even more optimal solutions across various scenarios. The results underscore TS-GWO’s promise for practical implementation and future research applications in distributed computing environments.
