1. Introduction

Cloud computing (CC) signifies a recognized shared-computing technology that actively transports measurable services on-demand over the worldwide network [1]. CC presented consumers with endless and assorted virtual resources that can be achieved on-demand and by different billing values [2]. In addition, the CS (task scheduling (TS)) is also defined independently as a task mapping measure on a group of accessible sources in the cloud context for implementation in consumers’ definite QoS limitations (makespan and cost). Workflows (general uses are linked with experimental research such as earthquake, biology, and astronomy) were moved to the CC for implementation [3]. In CC, job scheduling, TS, or resource selection are the most extensive complications, which store cloud users’ and service providers’ attention. An exact study on TS workings also reproduced optimistic results [4]. The most significant task in the domain of CC is RS. When implementing an RS, a sufficient quality of service (QoS) must be preserved using suitable hardware structures and techniques [5]. A module of CC structure, generally denoted as an agent in modern work, is highly liable for recording the demands of end-consumers about the accessible virtualized hardware that is executed in a type of virtual machine (VM). The cloud agent executes mapping by implementing the scheduling model [6].

The number of delivered tasks and many available resources make it challenging to map challenges to the proper VM for implementation. Few VMs are under-used and over-used if the unsuitable scheduling model is employed, and the suggestion of such states is performance degradation of the CC method as a complete [7]. The RS issue goes to the set of NP hard problems. The cloudlet and TS are assumed to be used for the mapping procedure to accept the task of the end-consumer to the accessible VM. Numerous models and approaches for RS in CC atmospheres are obtainable [8]. For example, a few methods have been utilized, such as traditional (deterministic) techniques. However, conventional optimizer models could be more effective since deterministic techniques do not make satisfactory, nor-optimum, or near-optimum solutions within sufficient computation time for NP-hard tasks [9]. Based on the search space complication and the number of plausible outcomes, conventional techniques could not assess each latent solution from the search area in a polynomial time [10].

This study develops an evolutionary algorithm-based scheduling approach for the makespan optimization and resource utilization (EASA-MORU) technique in cloud infrastructure. The EASA-MORU method aims to maximize the makespan and effectually use the resources in the cloud framework. In the EASA-MORU technique, the dung beetle optimization (DBO) technique is used for scheduling purposes. Moreover, the EASA-MORU technique balances the load properly and distributes the resources based on the demands of the cloud infrastructure. A wide range of comprehensive comparison studies highlighted that the EASA-MORU technique performs better than other methods in terms of different evaluation measures.

• The method is constructed to balance the workload across cloud infrastructure by intelligently dispersing tasks among resources. This ensures that each resource is employed optimally, improving complete accomplishment and efficiency. By dynamically altering the allocation of resources based on current demands, it maintains a stable and responsive system that adapts to fluctuating workloads in real time.
• The presented technique optimizes resource dispersal within cloud infrastructure by aligning resource allocation with the requirements and demands of ongoing tasks. This proactive model enhances resource consumption and ensures critical tasks receive adequate resources.
• The technique effectively schedules tasks within cloud environments by employing the DBO model’s advanced optimization abilities. The approach’s fast convergence allows for swift decision-making, reduced latency, and optimized task allotment.
• The technique’s robustness is portrayed by its capacity to efficiently handle convolutional real-world threats in scheduling and resource allotment. Adapting to various scenarios and optimizing resource management strategies ensures reliable accomplishment across several operational conditions, thereby assisting seamless and effective cloud infrastructure operations.
• The scheduling technique presents a novel cloud infrastructure demand scheduling model by incorporating the DBO model. It improves the effectiveness of the search and global exploration abilities via non-linear improvements, thus making it more adept at resolving convolutional real-world issues.

The remaining sections of the article are arranged as follows: Section 2 offers the literature review, and section 3 represents the proposed method. Then, section 4 elaborates on the results evaluation, and section 5 completes the work.

2. Literature review

Alruwais et al. [11] developed a Farmland Fertility Algorithm based RS for the Makespan Optimizer (FFA-RSMSO) in CC atmosphere. The projected model was dependent upon FFA, which, by the farmland fertility naturally, where the agriculturalists divide the numerous farm regions dependent upon the superiority of soil, and thus, each area’s soil superiority is separate from others. Furthermore, based on the request, the projected FFA-RSMSO method was used for load balancing (LB) and even spreading sources. In [12], a hybrid Whale optimizer algorithm (WOA)-based MBA technique has been presented for resolving the multi-object TS issues in the CC platform. Also, in this method, the multi-object behaviour reduces the makespan by enlarging the source application. Banerjee et al. [13] present a 3-step model. First, a precedence graph is built by analyzing the relations among tasks. Next, assigning works to servers changed the priority graph into the dual machine Johnson Sequence issue. Lastly, the Dynamic Heuristic Johnson Sequence technique defines the finest order of works on every server, thus efficiently reducing the makespan. Mangalampalli et al. [14] present a new multi-object workflow scheduling technique utilizing DRL. Firstly, the priority of every workflow intended depends upon their dependencies, and the computed priority of the VM depends on the electricity price at the datacentre to map workflow onto the exact VM. Both priorities were served to the scheduler that employs the Deep Q-Network technique to vigorously plan jobs by reflecting these priorities of challenges and VM. In [15], a new RS for big data using a Hybrid 2- GlowWorm Optimizer Algorithm (H2-GWOA) method is developed. The Mean-GWOA (MGWAO) and Improved Glowworm Swarm Optimizer Algorithm (IGSOA) techniques enhance the MapReduce structure in assorted BD. The CloudSim platform has been utilized for the simulation.

Mangalampalli et al. [16] present TS using the Cat Swarm Optimizer (CSO) model. TS was completed by computing the priority of tasks and the priority of VM at the level to plan a proper map of tasks into VM. It has been executed by employing a cloudsim simulator, and the input method was produced arbitrarily from the cloudsim for the overall electricity cost; the NASA and HPC2N tasks were used with similar workload files. Qasim and Sajid [17] developed a scheduling depending on the Firefly Algorithm (FFA) technique to resolve the IoT- TS issue in CC satisfactorily. The altered FFA-based scheduler utilizes the transfer function (TF) model and the Quantization approach to plan IoT tasks on VM in a CC atmosphere to reduce the makespan of IoT tasks. Mohammadzadeh and Masdari [18] projected a hybrid multiobjective optimizer technique, which merges the Seagull Optimizer Algorithm and Grasshopper Optimizer Algorithm (HGSOA-GOA) methods. The study uses chaotic mapping for arbitrary numbers. The study was employed to study scientific workflow scheduler issues in CC atmospheres. In this model, a Pareto front solution is nominated utilizing a knee-point model, and then it is used. Bacanin et al. [19] propose an LSTM deep learning (DL) technique. A modified PSO method utilizing metaheuristic abilities is proposed. Furthermore, the variational mode decomposition (VMD) approach is employed for data processing. [20] introduces a comparative evaluation of several metaheuristic load-balancing techniques. Predić et al. [21] present a model utilizing recurrent neural networks (RNNs). The DL techniques are improved via hyperparameter tuning via a modified PSO metaheuristic model. Also, the method implements VMD for effectual series decomposition.

In [22], a dual-phase metaheuristic model (CSSA-DE) is proposed. Firstly, computing nodes are grouped into clusters utilizing a clustering model. Then, the Sparrow Search Algorithm (SSA) with Differential Evolution (DE) technique is incorporated to effectively search for appropriate task-VM combinations. Salb et al. [23] present an AI-based model utilizing bidirectional long short-term memory (BiLSTM) neural networks. A modified sine cosine algorithm (SCA) method is also given for optimization. Saravanan et al. [24] introduce the Improved Wild Horse Optimization with Levy Flight Algorithm for Task Scheduling in cloud computing (IWHOLF-TSC) model. This model improves the Wild Horse Optimization (WHO) technique with Levy flight theory to enhance local search abilities. Behera and Sobhanayak [25] propose a hybrid Grey Wolf Optimization (GWO) and Genetic Algorithm (GA) model to tackle multiobjective task scheduling in cloud computing. This hybrid method benefits from GA’s crossover and mutation operators and presents faster convergence for large scheduling problems. Mikram, Kafhali, and Saadi [26] presents the Hybrid HEFT-PSO-GA (HEPGA) technique, which integrates Particle Swarm Optimization (PSO), GA, and HEFT-based Initialization for optimizing task scheduling and reducing makespan in cloud computing by effectually allocating tasks and improving resource consumption. Hamed et al. [27] propose a novel scheduling approach for heterogeneous cloud computing systems utilizing a cooperation search algorithm, employing meta-heuristic advantages. Singh and Chaturvedi [28] introduce a fusion GA-modified PSO technique for effective task allocation in cloud-fog computing by balancing the load of dependent activities across heterogeneous resources.

Sandhu et al. [29] propose a model that concentrates on reducing Total Execution Cost (TEC), Total Execution Time (TET), Energy Consumption (EC), and Response Time (RT). This technique utilizes Tabu Search, Bayesian Classification, and Whale Optimization models. Yadav and Mishra [30] introduce an improved ordinal optimization approach that mitigates the search space for optimal scheduling, utilizing horse race conditions and iterative techniques for minimizing makespan by effectually allocating load to the most promising schedules. Xia et al. [31] present an Adaptive Evolutionary Scheduling Algorithm (AESA) model featuring three strategies: a heuristic for effectual population initialization, a dynamic variable evaluation to optimize Pareto-front convergence, and an adaptive reward system for decision variables. Paul et al. [32] propose the Improved Artificial Rabbit Optimization with Pattern Search (IARO-PS) approach, improving the original ARO for dynamically scheduling independent tasks. It incorporates LB with IARO-PS to optimize workload dispersion and mapping onto VMs, enhancing exploration and exploitation balance. Malti, Hakem, and Benmammar [33] introduce a novel hybrid optimization algorithm (HOA) for multiobjective task scheduling in heterogeneous IaaS cloud environments, integrating flower pollination behaviour with GWO strategies and integrating evolutionary crossover operators for balancing exploration and exploitation. Damera et al. [34] propose an advanced task-scheduling algorithm that refines the Snake Optimization Algorithm (SO) technique employing sine chaos mapping, a spiral search strategy, and dynamic adaptive weights to enhance the effectiveness of the makespan and energy. Table 1 summarizes the existing studies on resource utilization using the evolutionary scheduling approach.

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Table 1. Summary of existing studies on resource utilization using evolutionary scheduling approach.

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The existing studies for task scheduling in cloud computing each have specific limitations. Some techniques improve resource allocation and make-span optimization but may need help with scalability and adaptability to dynamic or large-scale environments. For instance, while specific techniques enhance execution time and computational costs, they often need more robustness in highly variable scenarios or generalize well across several real-world scenarios. Furthermore, methodologies that outperform in specific metrics, namely energy utilization or LB, might not handle rapidly changing cloud setups efficiently. These approaches portray substantial enhancements but need additional refinement to address the complexities of large-scale, dynamic cloud environments and growing technologies. Moreover, several optimization techniques, such as FFA, WOA, GWOA, and CSO, are utilized to address makespan optimization and resource utilization in cloud infrastructure. However, a significant research gap still exists by incorporating these models into a cohesive framework that optimizes makepan while effectively employing resources in cloud environments. The presented model aims to fill this gap by introducing a novel model that potentially integrates the strengths of various optimization models, hence giving improved accomplishment and scalability related to existing techniques.

3. The proposed method

This work presents an EASA-MORU technique for cloud infrastructure. The EASA-MORU method aims to maximize the makespan and effectively use the resources in the cloud infrastructure. Fig 1 represents the entire flow of the EASA-MORU method.

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Fig 1. Overall flow of the EASA-MORU technique.

https://doi.org/10.1371/journal.pone.0311814.g001

3.2. Design of DBO approach

In this study, the DBO method of the EASA-MORU method is used for scheduling purposes. The behaviours of dung beetles (DBs) are motivated by foraging, dancing, rolling, breeding, and stealing [36]. At the DBO method, local searches (comprising stealing, foraging, and breeding) were employed to move the storage balls nearby to explore the optimum position. The global search describes the rolling ball behaviour, for example, rolling the feed balls to the optimum location. The working method of the proposed model modifies the DB population, evaluating the fitness function and storing the optimum individuals. Subsequently, every subpopulation has been exposed to cooperative optimization. The local search has been performed by foraging and breeding DBs. A global search could be executed with the Dancing DB and Rolling DB, and the breeding and foraging regions must be dynamically modified with the alternation in R factors to decrease the search region. Stealing DBs explore the top foraging region to increase the following. The DBO is an innovative biotic swarm intelligence (SI) optimization method developed by Jiankai in 2022. The technique has been motivated by the group activities of DB populations and considered with five various update procedures to support determining higher-quality solutions. The population classification and boundary selection approaches permit considering local convergence and global exploration. Algorithm 1 specifies the steps involved in the DBO technique.

Algorithm 1. DBO model.

Input:

 • Objective function f(x)

 • Number of dung beetles N

 • Maximum number of iterations T_max

 • Search space boundaries

Output:

 • Optimal solution X_best

Steps:

1. Initialization:

1.1. Randomly initialize the positions of N dung beetles within the search space.

1.2. Set initial positions x_i (0) for i = 1, 2, 3, ….., N

1.3. Evaluate the fitness of each dung beetle: f(x_i).

1.4. Set x_best to the position of the beetle with the best fitness.

2. For t = 1 to T_max:

2.1. Update positions:

- For each dung beetle i:

- Compute the new position using:

Where x_rand (t) is in a random position in the search space.

 -∅ and σ are coefficients controlling exploration and exploitation

2.2. Boundary Check:

- Ensure x_i (t + 1) is within search space boundaries.

- If x_i (t + 1) is out of bounds, adjust it to fit within boundaries.

2.3. Evaluate Fitness:

- Calculate f(x_i (t + 1)) for each updated position.

2.4. Update Best Solution:

- If any dung beetle’s new fitness is better than the current best fitness:

- Update x_best to the position of the beetle with the best fitness.

3. Termination:

 • If t = T_max, terminate the algorithm.

4. Output:

 • Return x_best as the optimal solution.

The DBO model follows a structured process for solving optimization issues. It begins with random Initialization, where the locations of a dung beetle populace are set within the search space, and their fitness is computed by utilizing the objective function. The technique detects the best-performing solution and upgrades the beetles’ positions iteratively, integrating the current best solution with random positions to balance exploration and exploitation. After upgrading positions, the algorithm confirms that they remain within search space boundaries. It then reexamines the fitness of these locations and upgrades the optimum solution if enhancements are found. This procedure continues until the optimum iteration number is attained. The final output is the optimum solution found, portraying the optimal or near-optimal result depending on the fitness analysis throughout the iterations.

3.2.1. Ball-rolling dung beetle.

The DB creates a ball of rolls and dung for the preferred position. In the rolling method, the DB must maintain the rolling dung balls directly through celestial signals (wind direction, sun location, and so on). To simulate the rolling behaviour, the DB is required to change in a specified way across the search space. The location upgrade mathematical model for rolling DBs will be given by: (2)

Here, x_i(t) refers to the location data of the i^th DB at t iterations, t means the existing number of iterations; b denotes a constant between (0,1). The constant value k ∈ (0,0.2] demonstrates the coefficient of defection, and α describes a real coefficient given at −1 or 1. Therefore, −1 signifies a deviation from the new direction, and 1 means no deviation. Δx has been applied to simulate the light intensity difference, and X^W refers to the global worst place.

While a DB addresses a difficulty from forwarding movements, it modifies the way of movement by dancing. The tangent function has been applied to mimic the dancing behaviour of DB. The dancing DB position will be upgraded as given by: (3)

Now θ ∈ [0, π]. When θ is equivalent to 0 or π/2, then the place of the DB is not upgraded.

3.2.2. Breeding dung beetles.

Particular dung balls must be concealed in somewhat protective surroundings as an egg-existing location. Hence, a boundary selection approach has been utilized for the region where female DBs place their eggs: (4)

Here, X* characterizes the existing local optimum location, Ub* means the upper bound, Lb* represents the lower bound of the breeding field, R = 1 − t/Tmax, Tmax means the maximal count of iterations, and lower and upper boundaries of the optimizer complexity have been characterized by Lb and Ub, correspondingly.

Female DBs place their eggs in the breeding region, and every female DB can produce only one egg in every round. The boundary of the breeding region was found through the dynamically modified R-value. The location of the hatching ball at the iteration method and a mathematical model will be given below: (5)

Now B_i(t) refers to the location data of the i^th marking ball with t^th iteration. b₁ and b₂ mean two independent 1 × D random vectors, and D represents the size of the optimizer problems. The hatching ball’s position is severely restricted to the breeding area. In the boundary selection approach, the brown circle denotes the existing local optimum place X*, and the blue point represents the rolling DB. Red circles have signified the upper and lower boundaries. Tiny black points denote hatching balls, which comprise only one egg.

3.2.3. Small dung beetles (foraging DBs).

Eggs hatch effectively and become DBs baby. DBs have been directed for foraging by developing optimum foraging regions. The boundaries of the optimum foraging regions could be outlined as given below: (6)

Here, X^b indicates the global optimum location. The lower and upper boundaries of the optimum searching field should be denoted as Lb^b and Ub^b, correspondingly. The location of the smaller DB will be upgraded by mathematical form: (7) Whereas x_i(t) represents the location data with i^th tiny DB on t^th iteration, C₁ signifies an arbitrary number accompanying a standard distribution, and C₂ indicates the random vector at (0,1).

3.2.4. Stealing dung beetles.

Particular DBs steal dung balls from alternative DBs; this method is represented as stealing DBs. In the consistent iterations, the location of the robber could be upgraded as given by: (8)

Now S represents constant value, x_i (t) refers to the position data i^th stealing DB with t^th iteration, and g refers to a random number of dimensions 1 × D following a uniform distribution. Fig 2 illustrates the flowchart of DBO.

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Fig 2. Flowchart of DBO.

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3.3. Process involved in scheduling process

The EASA-MORU method balances the load properly and distributes the resources based on the demands of the cloud infrastructure. A brief overview of the proposed architecture follows [37]. Consider n tasks as t_n = {t₁, t₂,….t_n}, k VMs as v_k = {v₁, v₂, v₃………v_k}, j hosts as h_j = {h₁, h₂,….h_j}, i datacenters, as d_i = {d₁, d₂, d₃….d_i}. Here, the model defines the problem as n tasks mapped carefully onto k VMs residing in i datacenter and j hosts while reducing the SLA violation, makespan, and energy depletion.

The cloud agent will receive and send the request to the task scheduler. Based on SLA, the task manager confirms whether the user’s request is valid. The task scheduler feeds the request to the scheduler after verifying the user request. Based on the processing capacity and length of the task, task priorities are initially calculated after the user request submission from the cloud user is elevated to the task manager level. Next, the VM priorities are evaluated according to the electricity price at the datacentre location. After taking priority, rankings are given for the task and fed into the scheduler for effectively assigning tasks on VMs. Thus, makespan, SLA violations, and energy consumption should be reduced to map tasks onto VMs appropriately.

Initially, the VM loads are computed to calculate the task priority.

(9)

In Eq (9), l^vm is the current load of k VMs.

Using Eq (10), the load is evaluated on the host after computing the VM load.

(10)

In Eq (10), l^h is the total load on the physical host.

Before describing task priorities, the physical host and VM loads must be evaluated. The VMs’ processing capacities must also be verified, as it is vital to map appropriate tasks to suitable VMs.

(11)

In Eq (11), pr^vm specifies the processing capacities of the VM, pr^no shows the number of processing components, and pr^mips denotes the computation performance of the VM.

By using Eq (12), the processing capacity of the VM is calculated.

(12)

After evaluating the processing capacity of the VM, the task size must be assessed based on the following expression.

(13)

Using Eq (14), the task priority is evaluated as follows: (14)

The model calculates the task priority and identifies the VM priority based on the electricity price at the datacentre location. The high unit electricity price of the datacentre provides less priority to allocating tasks to highly prioritized VMs, which have the lowest electricity cost, minimizing SLA violations, makespan, and energy consumption.

(15)

In Eq (15), high^{unit elect cost} is the high electricity unit cost in all data‐centers and is the electricity unit cost at a specific datacenter. After calculating the priorities of VMs and tasks, the study aims to minimize SLA violation, makespan, and energy depletion.

Makespan is the implementation time of the task while running on a VM.

(16)

In Eq (16), msⁿ specifies the makespan of n tasks, avail^k represents the kVMs tasks availability, and eⁿ shows the implementation time of n and.

Energy consumption is the next important parameter from the cloud user and provider perspectives. Energy consumption in the cloud paradigm includes two major parts: the energy consumed during computation and the energy consumed while idling.

(17)

Using Eq (18), the total energy consumption of VMs can be evaluated after computing the energy consumption of VMs.

(18)

Next, the SLA violations must be assessed for the cloud provider and consumer because even though the SLA is violated at a specific time without completing the task by its given deadline, it results in degraded performance. First, the active time of performance degradation and physical hosts must be evaluated to evaluate SLA violations.

(19)(20)

Then, the active time of performance degradation and physical host are calculated using the above equation.

(21)

In Eq (21), the metrics are defined and evaluated by using Eqs (16), (18) & (21). Using the DBO model, a fitness function is defined to enhance the parameter. Based on Eq (22), the Fitness function can be calculated.

(22)

4. Experimental validation

This section [11] gives the performance of the EASA-MORU method under various measures. The suggested technique is simulated by employing the Python 3.6.5 tool on a PC with an i5-8600k, 250GB SSD, GeForce 1050Ti 4GB, 16GB RAM, and 1TB HDD. The parameter settings are as follows: learning rate: 0.01, activation: ReLU, epoch count: 50, dropout: 0.5, and batch size: 5.

In Table 2 and Fig 3, the comparative outcomes of the EASA-MORU method in terms of waiting time (WAITT) are given. The results indicate that the KH-LBRS and IDS-ARS models obtain poor performance with higher WAITT values. Besides that, the HPSOM-GARS, HMEE-RARS, and FFA-RSMSO models have reported moderately reduced WAITT values. Nevertheless, the EASA-MORU technique performs better with the least WAITT values of 115ms, 191ms, 446ms, 639ms, and 999ms under 100–500 requests correspondingly.

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Fig 3. WAITT analysis of EASA-MORU technique under various requests.

https://doi.org/10.1371/journal.pone.0311814.g003

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Table 2. WAITT analysis of the EASA-MORU technique with existing models on various requests.

https://doi.org/10.1371/journal.pone.0311814.t002

Table 3 and Fig 4 show the comparative outcomes of the EASA-MORU technique in terms of response time (RESPT). The outcomes indicate that the KH-LBRS and IDS-ARS techniques perform poorly with higher RESPT values. Besides that, the HPSOM-GARS, HMEE-RARS, and FFA-RSMSO approaches have moderately reported decreased RESPT values. Nonetheless, the EASA-MORU method has superior performance with minimum RESPT values of 145ms, 241ms, 563ms, 724ms, and 1046ms under 100–500 requests.

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Fig 4. RESPT analysis of EASA-MORU technique under various requests.

https://doi.org/10.1371/journal.pone.0311814.g004

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Table 3. RESPT analysis of the EASA-MORU technique with recent models under various requests.

https://doi.org/10.1371/journal.pone.0311814.t003

The LB results of the EASA-MORU technique are compared with recent models under varying requests in Table 4 and Fig 5. The outcome implies that the EASA-MORU method reaches effectual outcomes with improved LB values. Under 100 requests, the EASA-MORU method gains an increased LB of 0.061ms, whereas the KH-LBRS, IDS-ARS, HPSOM-GARS, HMEE-RARS, and FFA-RSMSO models offer decreased LB of 0.003ms, 0.006ms, 0.006ms, 0.013ms, and 0.028ms, correspondingly. Also, under 500 requests, the EASA-MORU method obtains an increased LB of 0.116ms, whereas the KH-LBRS, IDS-ARS, HPSOM-GARS, HMEE-RARS, and FFA-RSMSO methods offer decreased LB of 0.032ms, 0.038ms, 0.042ms, 0.065ms, and 0.082ms, correspondingly.

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Fig 5. LB analysis of EASA-MORU technique under various requests.

https://doi.org/10.1371/journal.pone.0311814.g005

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Table 4. LB analysis of the EASA-MORU technique with recent models under various requests.

https://doi.org/10.1371/journal.pone.0311814.t004

The throughput (THRPT) outcomes of the EASA-MORU method are compared with recent models under varying requests in Table 5 and Fig 6. The outcomes indicate that the EASA-MORU method reaches effectual outcomes with improved THRPT values. On 100 requests, the EASA-MORU method obtains an increased THRPT of 1247ms, whereas the KH-LBRS, IDS-ARS, HPSOM-GARS, HMEE-RARS, and FFA-RSMSO methods offer decreased THRPT of 860ms, 938ms, 1053ms, 1067ms, and 1178ms, correspondingly. Also, on 500 requests, the EASA-MORU technique gains increased THRPT of 380ms while the KH-LBRS, IDS-ARS, HPSOM-GARS, HMEE-RARS, and FFA-RSMSO methods offer decreased THRPT of 154ms, 176ms, 202ms, 239ms, and 311ms, correspondingly.

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Fig 6. THRPT analysis of the EASA-MORU technique under various requests.

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Table 5. THRPT analysis of the EASA-MORU technique with recent models under various requests.

https://doi.org/10.1371/journal.pone.0311814.t005

Table 6 and Fig 7 show the comparative outcomes of the EASA-MORU method in terms of relative error (RELE). The results indicate that the KH-LBRS and IDS-ARS models obtain poor performance with higher RELE values. Besides that, the HPSOM-GARS, HMEE-RARS, and FFA-RSMSO models have reported moderately reduced RELE values. Nevertheless, the EASA-MORU technique performs better with minimum RELE values of 0.038, 0.032, 0.011, 0.017, and 0.029 under 100–500 requests.

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Fig 7. RELE analysis of EASA-MORU technique under various requests.

https://doi.org/10.1371/journal.pone.0311814.g007

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Table 6. RELE analysis of the EASA-MORU technique with existing models on various requests.

https://doi.org/10.1371/journal.pone.0311814.t006

The reliability (RELY) results of the EASA-MORU method are compared with recent models under varying requests in Table 7 and Fig 8. The outcomes imply that the EASA-MORU technique attains effective outcomes with the highest RELY values. On 100 requests, the EASA-MORU technique attains an improved RELY of 0.935, but the KH-LBRS, IDS-ARS, HPSOM-GARS, HMEE-RARS, and FFA-RSMSO methods offer decreased RELY of 0.703, 0.754, 0.796, 0.787, and 0.827, correspondingly. Also, on 500 requests, the EASA-MORU technique obtains an increased RELY of 0.910, while the KH-LBRS, IDS-ARS, HPSOM-GARS, HMEE-RARS, and FFA-RSMSO methods offer decreased RELY of 0.731, 0.828, 0.832, 0.760, and 0.848, correspondingly.

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Fig 8. RELY analysis of EASA-MORU technique under various requests.

https://doi.org/10.1371/journal.pone.0311814.g008

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Table 7. RELY analysis of the EASA-MORU technique with recent models under various requests.

https://doi.org/10.1371/journal.pone.0311814.t007

The computational time (CT) outcomes of the EASA-MORU method are compared with recent techniques in Table 8 and Fig 9. The computational complexity of the scheduling models changes substantially as the number of requests increases, as depicted in the table. For 100 requests, KH-LBRS is the most efficient, with a processing time of 856 ms, while EASA-MORU is the slowest at 2634 ms. As the number of requests increases to 500, KH-LBRS maintains its relative effectualness with 260 ms, whereas EASA-MORU remains the slowest at 1090 ms. However, there is an enhancement from the initial 2634 ms. This trend illustrates that KH-LBRS consistently performs better across diverse request sizes, illustrating greater scalability related to other models. On the contrary, despite enhancements, techniques such as EASA-MORU still lag in performance, showing potential areas for optimization for handling greater datasets more effectively.

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Fig 9. CT evaluation of the EASA-MORU model with recent technique under several requests.

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Table 8. CT evaluation of the EASA-MORU model with recent technique under several requests.

https://doi.org/10.1371/journal.pone.0311814.t008

Therefore, the EASA-MORU technique can effectively schedule the resources in the cloud infrastructure.

5. Conclusion

In this study, an EASA-MORU technique on cloud infrastructure is introduced. The EASA-MORU technique aims to optimize the makespan and effectively use the resources in the cloud infrastructure. The DBO method is used for scheduling purposes in the EASA-MORU technique. Moreover, the EASA-MORU method balances the load properly and distributes the resources based on the demands of the cloud infrastructure. The performance evaluation of the EASA-MORU method is tested using a series of performance measures. A wide range of comprehensive comparison studies emphasized that the EASA-MORU method achieves improved performance over other methods under diverse evaluation measures. The limitations of the MORU technique comprise potential threats in scaling to large-scale cloud environments due to the model’s sensitivity to parameter settings and convergence speed. Furthermore, exploring fusion optimization models or integrating ML methods could enhance scalability and accomplishment. Future works may concentrate on improving the technique’s robustness to dynamic workload and resource availability alterations and more effectually incorporating adaptive strategies in handling heterogeneous cloud environments. Additionally, hybrid metaheuristic models can be derived to improve the RS performance further. Besides, deep reinforcement learning techniques can be applied to extend the performance of the proposed model. Additionally, future research may include scalability analysis of the presented technique by examining it in greater, more practical instances. The model should also be investigated across diverse real-world scenarios, encompassing more tasks and resources. The adaptability and efficiency of the technique could also be shown when handling large-scale issues, which will give a clearer understanding of how well the presented technique accomplishes under the demands of real-world applications, safeguarding its robustness and efficiency in practical environments.