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Mathematical Model and Statistical Assessment of Non Linear 

Scheduling Optimization in Cloud Environment using 

Improved Cuckoo Search Algorithm 

 

Shilpa Maheshwari1, Sunil Gupta2, Surendra Singh Choudhary3 

1Research Scholar, School of Computer and System Sciences, Jaipur National University, Jaipur-302017, 

Rajasthan (India) 

2Professor, School of Computer and System Sciences, Jaipur National University, Jaipur-302017, Rajasthan 

(India) 

3Professor, Department of Computer Sciences, Sri Balaji College of Engineering & Technology, Jaipur-

302013 Rajasthan (India) 

Email: agiwal.shilpa@gmail.com1, sunilg95@rediff.com2, ssc_jaipur@yahoo.com3 

 

 

Article History: 

Received: 08-02-2024 

Revised: 20-04-2024 

Accepted: 05-05-2024 

Abstract:  

 The scheduling optimization subject is indeed one of the most effective 

solutions in cloud system area to ensure the high systems performance and resource 

usage. The novelty presented in this study is a mathematical model that draws on an 

Improved Cuckoo Search Algorithm as a scheduling non-linear optimizer for the cloud 

computing environment. The model under consideration takes into account the 

underlying complications as well as the varying nature of the use of cloud resources, 

primarily addressing the latency issue with priority given to the increase of the 

throughput. Improved Cuckoo Search (ICS) Algorithm, developed on 'cuckoo search' 

algorithm, uses adaptive step size and probabilistic switching, which, in turn, ensure 

that the solution space is both being properly examined and exploited. The applications’ 

utilization of the scheduling mathematical model is based on an elaborately designed 

theoretical background representing the task as a non-linear optimization problem that 

meets all the specific constraints and objectives important in cloud computing. 

Statistical reassessment involves the comparison of the proposed model with standard 

benchmarks. The proposed model superiority is evident in terms of convergence speed, 

solution quality and robustness against diverse workloads, as shown in varied tests. The 

findings of this research contributes to the field by deriving a specialized tool commonly 

used by the cloud service provider in designing resource scheduling, enhancing the 

service delivery and operational efficiency. 

Keywords: Optimized Scheduling, Cloud Computing, Cuckoo Search Algorithm, Task 

Allocation, Resource Utilization, Performance Analysis. 

 

1. INTRODUCTION 

The cloud computing has led to a radical change in the current computing space as the 

computing resources are now available on a pay-as-you-go basis over the internet enabling 

on-demand access to shared configurable resources. This paradigm shift has become a major 

driver of the ability for organizations to scale operations dynamically, reduce infrastructure 



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costs, and increase flexibility in deploying applications and services. Managing resources 

efficiently, in cloud computing, starts with effective task scheduling, so as to achieve the 

best utilization of resources and good performance of the system. 

Resource scheduling in the cloud involves assigning the appropriate computing tasks to 

either virtual machines or to VMs so that their execution time is minimized, throughput 

maximized and resources used optimally. However, the stp of optimal task scheduling is full 

of challenges owing to cloud environments being dynamic, fluctuating workload demads 

and the manifold objectives such as minimum latency and energy savings. 

Among the scheduling algorithms, floating schedules, including Round Robin and First 

Come First Serve, lacking adaptability and optimization properties, are of no help in dealing 

with the complexities of cloud computing environments. As a result, smart scheduling 

techniques that can dynamically re-schedule tasks based on workload changes and distribute 

resources effectively are becoming more and more necessary. 

This paper proposes a new method that enhances task scheduling in cloud computing 

systems using the cuckoo optimisation algorithm. The developed algorithm mimics the 

adoptive behavior of cuckoo species to broadly explore the search space to achieve best task 

scheduling configurations efficiently. Through the inclusion of the enhancements of the 

classic cuckoo search algorithm, which are featuring more convergence speed and solution 

quality, we aim at tackling the drawbacks of the existing scheduling algorithms and ensuring 

a stable performance of this approach in various cloud computing scenarios. 

Cloud computing consists of convergence and simultaneous execution of multiple activities 

for achieving various objectives such as performance improvement, make-span reduction, 

throughput increase, cost minimization, and resource utilization optimization. Hence, the 

importance of the implementation of scheduling system increases in the process of optimal 

distribution of tasks among the available resources [1]. In this particular setting, we suggest 

that implementation of an intelligent scheduling system should be made through the use of 

cuckoo search and simulated annealing. 

1 Objective function for optimization: 

𝑓(𝑥) − min∑  

𝑛

𝑖−1

𝑤𝑖 ⋅ 𝑥𝑖 

2 Constraint for resource allocation: 

∑ 

𝑛

𝑖−1

𝑟𝑖 ⋅ 𝑥𝑖 ≤ 𝑅 

3 Non-linear constraint for task execution: 

∑ 

𝑛

𝑖−1

𝑡𝑖 ⋅ 𝑥𝑖
2 ≤ 𝑇 



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4 Definition of latency: 

𝐿 −∑  

𝑛

𝑖−1

𝑙𝑖 ⋅ 𝑥𝑖 

5 Throughput maximization: 

max(
1

∑  𝑛
𝑖=1   𝑡𝑖 − 𝑥𝑖

) 

6 Cuckoo Search random walk: 

𝑥𝑖
(𝑡+1)

− 𝑥𝑖
(𝑡)

+ 𝛼 ⊗ Levy⁡(𝜆) 

7 Levy flight distribution: 

𝐿(𝑠) −
𝜆Γ(𝜆)sin⁡(𝜋𝜆/2)

𝜋

1

𝑠1+𝜆
, 𝑠 > 0 

8 Probability of switching to a new solution: 

𝑝 −
1

1 + exp⁡(−Δ𝑓/𝑇)
 

9 Adaptive step size adjustment: 

𝛼new − 𝜌 ⋅ 𝛼old  

10 Objective function for makespan minimization: 

𝑓(𝑥) − max
𝑛

𝑖−1
 ∑  

𝑚

𝑗−1

𝑥𝑖𝑗 ⋅ 𝑡𝑖𝑗 

11 Load balance measure: 

𝐿𝐵 −
max
𝑛−1

𝑖+1
 ∑  0

𝑖=1  𝑥𝑖𝑗 ⋅ 𝑡𝑖𝑗

𝑚 −∑  𝑚
𝑗−1  ∑  𝑛

𝑖=1  𝑥𝑖𝑗 ⋅ 𝑡𝑖𝑗
 

12 Energy consumption model: 

𝐸 =∑  

𝑛

𝑖−1

∑ 

𝑚

𝑗−1

𝑥𝑖𝑗 ⋅ 𝑒𝑖𝑗 

13 Reliability constraint: 

𝑅 −∏ 

𝑛

𝑖−1

(1 − 𝑟𝑖)
𝑥1 ≥ 𝑅min 

 

 



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14 Cost function for cloud resources: 

𝐶 −∑  

𝑛

𝑖−1

𝑐𝑖 ⋅ 𝑥𝑖 

15 Constraint for deadline satisfaction: 

∑ 

𝑛

𝑖−1

𝑥𝑖 ⋅ 𝑑𝑖 ≤ 𝐷 

16 Statistical mean of completion time: 

𝜇 −
1

𝑛
∑  

𝑛

𝑖−1

𝑡𝑖 ⋅ 𝑥𝑖 

17 Variance of completion time: 

𝜎2 −
1

𝑛
∑  

𝑛

𝑖−1

(𝑡𝑖 ⋅ 𝑥𝑖 − 𝜇)2 

18 Probability of task migration: 

𝑃migrate −
1

1 + exp⁡(−𝛿𝑓)
 

19 Cost efficiency ratio: 

CE −
 Perfarmamse 

 Cost 
 

20 Quality of Service (QoS) indicator: 

 QoS − 𝜔1. Performance − 𝜔2. Cost  

21 Availability of cloud system: 

𝐴 − 1 −∏ 

𝑛

𝑖−1

(1 − 𝑎𝑖) 

22 Scalability function: 

𝑆(𝑛) −
𝑓(𝑛)

𝑓(1)
 

23 Response time for a request: 

𝑅𝑡 −∑  

𝑛

𝑖−1

1

1 + 𝑒−(𝑡𝑖−𝑛
 

 

 



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24 Utilization of a resource: 

𝑈 −
∑  𝑎
𝑖,1  𝑥𝑖 ⋅ 𝑡𝑖

𝑇𝑖
 

Theoretical analysis of the given mathematical equations revolves around the optimization 

of scheduling tasks in a cloud environment, where various parameters like resource 

allocation, task execution time, and system performance are crucial. 

Objective Function for Optimization: The equation 𝑓(𝑥) −min∑𝑖−1
𝑛  𝑤𝑖 ⋅ 𝑥𝑖 defines the 

objective function aiming to minimize the weighted sum of variables 𝑥𝑖. In a cloud 

computing context, this could represent minimizing the total cost or resource usage, where 

𝑤𝑖 are the weights (e.g., costs or resources) associated with each task 𝑥𝑖. 

Resource Allocation Constraint: The equation ∑𝑖−1
𝑛  𝑟𝑖 + 𝑥𝑖 ≤ 𝑅 ensures that the total 

resources used by all tasks do not exceed the available resources 𝑅. Here, 𝑟𝑖 represents the 

resource requirement for each task. 

Non-linear Constraint for Task Execution: The non-linear equation ∑𝑖−1
𝑛  𝑡𝑖 ⋅ 𝑥𝑖

2 ≤ 𝑇 might 

represent a scenario where the resource usage or task completion time grows non-linearly 

with an increase in the task size or number. 

Latency Definition: Latency 𝐿 − ∑𝑖−1
𝑛  𝑙𝑖 ⋅ 𝑥𝑖 is defined as the sum of individual latencies 𝑙𝑖 

for tasks, crucial for evaluating the responsiveness of the cloud system. 

Throughput Maximization: Maximizing throughput max (
1

∑𝑖−1
𝑛  𝑡1⋅𝑥𝑖

) focuses on optimizing 

the system to handle the maximum number of tasks in a given time, where 𝑡𝑖 represents the 

time taken for each task. Cuckoo Search Algorithm: These equations represent components 

of the Cuckoo Search optimization algorithm, including the random walk using Levy flight 

distribution and adaptive step size. This algorithm is used for finding the optimal solutions 

by mimicking the behavior of cuckoo birds. 

System Performance Metrics: Equations relating to makespan minimization, load 

balancing, energy consumption, reliability, cost, and deadline satisfaction are pivotal for 

assessing the performance and efficiency of the cloud scheduling system. 

Statistical Assessments: These equations involve calculating the mean and variance of 

completion times, migration probabilities, and cost-efficiency ratios, providing insights into 

the statistical performance of the scheduling system. 

Quality of Service and System Metrics: These equations assess the quality of service 

(QoS), system availability, scalability, response time, and resource utilization, which are 

critical for evaluating the effectiveness and user satisfaction of the cloud service. 

In summary, these equations collectively form a comprehensive mathematical model to 

analyze and optimize scheduling in cloud environments, focusing on efficiency, 

performance, and resource utilization. 



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The consideration of several features including processing time, cost, execution time, 

makespan, and power consumption will form an optimal strategy for cloud task scheduling. 

The metaheuristic approach, which has been applied in many studies [2], [3], has been 

widely used to address this optimization problem. While Cuckoo search (CS) and SA also 

use random solutions and iteratively improve them, they differ in their approaches. SA that 

is a single solution search scheme has been hybrided with other optimization methods to 

improve its performance in getting rid of the local optima problems. Nonetheless, CS has 

one important limitation, which is the possibility of premature convergence and slow 

convergence rates. So, Abed-alguni and Alkhateeb suggested six modifications to the CS 

algorithm, which significantly exceeded the benchmark functions results that were achieved 

by the original CS approach [4]. 

Only lately, deep reinforcement learning is infused into cloud computing for the real-time 

resource scheduling optimization [5]. Wang et al. came out with the multi-objections 

workflow scheduling method based on Deep-Q-network (DQN) to obtain uncorrelated 

equilibrium solutions on the cloud platform. Their proposed model performed better than 

the existing ones in the study [6]. This demonstrates the significance of conducting future 

work and development in the area of scheduling and load balancing of cloud environment. 

Although metaheuristic methods are widely used and they are very promising, there still left 

some issues for us to solve the problem of optimal solutions in this field. Therefore, it 

stresses the need for future research supporting the ongoing process of coming up with better 

ideas. 

2. PROBLEM FORMULATION 

In the cloud Computing environment, STEs (Service Task Elements) are efficiently allocated 

to available Processing Elements (PEs) spread across data centers to achieve maximum user 

fulfillment. Each PE is marked by its own speed of executions as well as energy 

consumption. Jobs in the application is represented as a Directed Acyclic Graph (DAG), 

denoted as G(V, E), where V denotes the set of vertices that represent tasks and E denotes 

the set of edges that represent task dependencies. 

In this model, all PES are considered as homogenous and parallel and we assume non-

preemption. The main aim is to distribute efficiently the user workloads on the PEs across 

several data centers in the cloud for throughput and makespan minimization. 

Makespan = max {vmjtime; j=1,2,3,4….,m} (1) 

Throughput = ΣTi (ETi) (2) 

ETi = Tlen / CPvm (3) 

Here, Tlen denotes the length of the task and CPvm represents the capacity of the virtual 

machine (VM). CPvm is calculated as the product of the VM's processing speed (P) and the 

number of CPUs  

 



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(Q): CPvm = P * Q (4) 

Thus, the formulas offer the foundation for the assessment and enhancement of cloud-based 

application functionality, taking into account the parameters including the task execution 

times, VM capacities, and the system throughput, on the whole. The scheduling algorithms 

should be designed in such a way that they capture these metrics and provide the best 

resource utilization and user satisfaction. To continue, optimizing throughput and makespan 

in cloud application scheduling requires finding a method of task allocation to PEs which 

result in the minimum makespan and maximum throughput simultaneously. This goal can 

be attained by carefully analyzing task dependencies, PBE capabilities and resource 

availability across numerous data centers. 

The makespan metric gives the overall completion time of the workload as a whole, which 

allows scheduling efficiency to be evaluated. Minimizing the makespan, the system will also 

have timely completion of tasks which will result to enhanced user satisfaction and system 

performance.However, throughput is a measure of the rate of task completion in a given time 

window. Thoughput maximization is of utmost importance for enhancing system 

performance and resource utilization as it implies system efficiency to process works 

productively. 

VMs are assigned to each task and the time spent in execution of the task, determined by its 

length and the capacity of the assigned VM, directly affects both makespan and 

throughput. System optimization of task scheduling is achieved by minimizing the execution 

time and the evenly distributing resource usage across PEs, thus, leading to improved overall 

performance. 

Besides, the capacity of VMs depends on their processing speed and the number of CPUs 

which is very crucial in deciding the productivity of system in executing tasks. The system 

can efficiently use resources by assigning tasks to VMs of right capacities and in this way 

avoid bottlenecks and increase overall throughput. 

Effective throughput and makespan optimization in cloud application scheduling becomes 

challenging because of the many things to consider like task dependencies, PE capabilities, 

and resource availability. Achieving better resource utilization, enhanced performance, and 

user satisfaction can be done by using efficient scheduling algorithms and metric decisions, 

such as makespan and throughput. 

3. PROPOSED METHODOLOGY 

 The Cuckoo Search (CS) algorithm, suggested by Xin-She Yang and Susah Deb in 2009, is 

a new algorithm that is inspired by a certain cuckoo species that lay their eggs in other birds’ 

nests. This technique outperforms other optimization algorithms such as Particle Swarm 

Optimization (PSO) and Genetic Algorithm (GA), making it applicable for solving broad 

class of optimization problems [Yang and Deb, 2014]. Computation approaches guided by 

nature such as CS, imitate natural phenomena to solve rigid optimization problems. 

The CS algorithm represents each possible solution as a cuckoo egg, and candidate solutions 

would be the nests. The algorithm operates based on three idealized rules: cuckoos lay one 



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egg at a time and randomly allocate them to the selected nests and higher-quality eggs are 

passed to the subsequent generations, while the hosts have a probability of discovering alien 

eggs or they can also rebuild their own nests. 

Unlike the traditional evolutionary algorithms, CS mimic the foraging behavior of cuckoos 

and embeds Levy flight characteristics for global exploration. The algorithm applies random 

moves with the purpose of finding efficient solutions and ultimately converging to high-

quality solutions rapidly. Nevertheless, the drawback of the original CS strategy is the slow 

convergence time and the oscillations which make the approach not suitable for all 

situations. 

In an attempt to circumvent these limitations, the ICS algorithm was then 

developed. Compared to the original CS which adopts random initialization and updates 

based on Levy flight, ICS however introduces modifications to achieve convergence and 

stability. Equation shows the CS update mechanism, where agents take steps towards best 

option. Pseudo-code of CS algorithm is shown in so that implementation and understanding 

is facilitated. 

𝑑𝑖+1
𝑘 = 𝑑𝑖

𝑘 + 𝛼 ⋅
|𝑢|

𝑣1/𝛽
⋅ (𝑑best − 𝑑𝑖

𝑘)                                            (5) 

where I is the generation number (i=,1,2,......it), k is the order of searching agents in the 

swarm (k=1,2,....ss), ss is the swarm size, is the step size (which can be determined 

depending on the problem, though it is generally recommended that =1), and u and v are 

matrices with uniform distribution - their values can be determined . 

𝑢 ≈ 𝑁(0, 𝜎𝑢
2) and 𝑣 ≈ 𝑁(0, 𝜎𝑣

2)                                                                                                (6) 

where the variance of 𝑢 and 𝑣 can be obtained from : 

𝜎𝑢 = (
Γ(1+𝛽)⋅sin⁡(𝜋⋅𝛽/2)

Γ(
1+𝛽

2
)⋅𝛽⋅2

(
𝛽−1
2

)
)  and 𝜎𝑣 = 1                                                                              (7) 



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Figure 1: Implementation process flow 

 

Figure 2: Proposed Hybrid Algorithm 

 



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Figure 1 describes the basic implementation process of Cuckoo Search Algorithm. It outlines 

the steps of a Cuckoo Search (CS) optimization algorithm. The CS algorithm is inspired by 

the brood parasitism of some cuckoo species. Figure 2: Hybrid Algorithm Flowchart 

illustrate a hybrid algorithm that combines features of the annealing function with a task 

scheduling process. This algorithm used for efficiently scheduling tasks in cloud computing. 

The flowchart depicts a Grey Wolf Optimizer (GWO) enhanced with a Cuckoo Search 

algorithm. This indicates a novel approach to combining the hunting strategy of grey wolves 

with the parasitic behavior of cuckoos for optimizing schedules in cloud computing. The 

new hybrid algorithm of the Grey Wolf Optimizer (GWO) with Cuckoo Search Algorithm 

(CSA) develops a powerful method for the solving of complex optimization needs. This 

integrative approach utilizes the advantages of both algorithms in order to compensate for 

their individual drawbacks and maximize the overall search capacity. 

The grey wolf’s optimization (GWO) adapts the social structure and hunting strategy of 

these animals. It has a reputation for efficiently converging on preliminary solutions which 

is beneficial to its exploitation. On the flip side, this fast alignment could be a bottleneck as 

it can result into premature convergence and local optima getting trapped. 

To cope with this, the CSA steps up. The obligatory brood parasitism of some cuckoo species 

serves as the source of inspiration for the CSA. It introduces a random way by Levy flights 

that provides a mechanism of overcoming local optima by updating the locations (solutions) 

with a certain probability, which is unrelated to the search path. This advantage accelerates 

the global search process and improves the exploration of the searching space. 

The position update equation for CSA is used to amend the position of the grey wolves in 

the hybrid CSA-GWO algorithm. Through this update, not only the exploitations are 

improved but also both of them have a balance, which is vital for the algorithm 

efficiency. Wolves' positions, convergence accuracies, and velocities are changed by means 

of the CSA equation thus, the separation of search agents is done better. This approach 

(hybrid method) is compared to other meta-heuristic methods to check its efficiency. The 

analysis, comparison and statistics show that the CSA-GWO hybrid leads to better design 

parameters, which provides a robust and fine effective solution to the optimization problem. 

By combining the high convergence capabilities of GWO with the vast exploration potential 

of CSA, the hybrid algorithm promises a more reliable and versatile solution to optimization 

problems [9]. 

4. PERFORMANCE EVALUATION 

Here we use CloudSim 3.0.3 for the modeling of cloud computing environment. The 

experimentation has VM deploying across five data centers which has 140 VMs and each 

data center can host up to three hosts. The workload, called Cloudlets, is of the size of from 

1000 to 3000 Million Instructions. The VMs are configured with the processing elements of 

2 to 4 that are used to test the performance. 

The plan of our implementation is to solve the cloud scheduling problem, which is referred 

to as NP-hard problem, by using the meta-heuristic algorithm for task scheduluing 



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optimization. We represent each scheduling solution as an vector, where each component is 

associated to a VM number where tasks are assigned, allowing to assign multiple tasks to 

the same VM. 

The simulation environment is designed to manage up to 1000 tasks with each VM with 

memory size of 512 MB and bandwidth of 1000 Mbps. The workload of each job ranges 

within 1000 million instructions to 3000 million instructions. The data centers operate their 

virtual machines under both of the space-shared and time-shared policies to maximize 

resource usage efficiency. 

We do different tests for varying parameter ranges to measure the efficiency of the proposed 

hybrid grey wolf- cuckoo search algorithm (GWO-CSA). The performances of HCSA is 

contrasted with conventional optimization algorithms like PSO (Particle Swarm 

Optimization), ACO (Ant Colony Optimization), and a load-balancing variant of PSO (PSO-

ALBA). Performance measures, such as makespan and throughput, are for the evaluation. 

Table 1. Result on 50 VMs 

No. of 

Tasks 

GWO-CSA 

(Makespan, 

Throughput) 

PSO-ALBA 

(Makespan, 

Throughput) 

PSO (Makespan, 

Throughput) 

ACO (Makespan, 

Throughput) 

100 15.5, 4.4 17.04, 3.98 25.32, 3.14 28.55, 2.97 

200 39, 4.2 52.01, 3.9 109, 1.88 117.15, 1.54 

300 72, 3.25 104.96, 2.89 176.19, 1.72 198.9, 1.6 

400 115, 3.1 175.95, 2.3 271.5, 1.63 279.56, 1.38 

500 163, 2.6 264.96, 1.91 561.5, 0.91 454.29, 1.16 

600 222, 2.3 371.98, 1.63 579.7, 1.03 667.71, 0.89 

700 290, 2.05 497.03, 1.4 945.23, 0.74 955.52, 0.73 

800 370, 1.85 647.99, 1.23 834.54, 0.95 1103.58, 0.72 

900 455, 1.85 818.99, 1.09 1032.28, 0.87 1167.71, 0.77 

1000 550, 1.65 1010, 0.99 1554.21, 0.64 1625.86, 0.61 

 

The results provided by the study as encapsulated in Tables 1 and 2 indicate that GWO-CSA 

exceeds the comparison algorithms. The results from the simulation show that GWO-CSA 

is not only effective in optimizing the task scheduling, but also provides additional benefit 

in the whole cloud computing environment in terms of performance and efficiency. 

Table 2. Results on Different Virtual Machines and Tasks 

No of 

Tasks 

VMs GWO-CSA 

(Makespan, 

Throughput) 

PSO-ALBA 

(Makespan, 

Throughput) 

PSO 

(Makespan, 

Throughput) 

ACO 

(Makespan, 

Throughput) 

100 40 12.5, 6.3 20.71, 4.82 37.32, 2.67 43.72, 2.87 

200 50 20, 6.1 51.99, 3.9 105.5, 1.89 116.51, 1.71 

300 60 35, 6.0 88.15, 3.44 197.32, 1.52 213.11, 1.4 

400 70 55, 5.0 122.6, 3.26 222.62, 1.79 258.22, 1.54 

500 80 80, 4.7 189.3, 2.64 319.05, 1.56 347.72, 1.43 



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600 90 110, 4.0 210.3, 2.85 428.01, 1.4 449.02, 1.33 

700 100 145, 3.8 257.38, 2.75 484.34, 1.44 549.54, 1.27 

800 110 180, 3.4 333.3, 2.4 510.88, 1.56 655.93, 1.21 

900 120 225, 3.3 362.8, 2.48 687.09, 1.3 822.36, 1.09 

1000 140 275, 3.25 421.09, 2.37 663.96, 1.5 809.22, 1.23 

 

Figure 3: Analysis of Throughput for Different Tasks and VM 

 

Figure 4: Analysis of Make span for Different Tasks and VM 

 

Figure 5: Throughput Comparison for 50 VMS 

 



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Figure 6: Makespan Comparison for 50 VMS 

Figure 3: Analysis of Throughput for Different Tasks and VM illustrates the throughput 

achieved by different algorithms as the number of tasks increases. The algorithms being 

compared include a Grey Wolf Optimizer with Cuckoo Search Algorithm (GWO-CSA), a 

Particle Swarm Optimization with Artificial Bee Colony (PSO-ALBA), a standard Particle 

Swarm Optimization (PSO), and an Ant Colony Optimization (ACO). Generally, as the 

number of tasks increases, the throughput for each algorithm decreases. This suggests that 

as the workload grows, the efficiency of processing tasks diminishes. GWO-CSA appears to 

maintain the highest throughput across the task range, indicating that it may be the most 

efficient algorithm among those tested. 

Figure 4: Analysis of Make span for Different Tasks and VM shows the makespan for 

different algorithms as the number of tasks increases. Again, the same set of algorithms is 

compared. As expected, the makespan increases with the number of tasks for all algorithms, 

but the rate of increase varies. The GWO-CSA algorithm shows a more gradual increase in 

makespan, indicating better scalability with the increased workload compared to the other 

algorithms. 

Figure 5: Throughput Comparison on 50 VMs narrows the performance evaluation of the 

algorithms to a specific scenario with 50 VMs. It provides a focused comparison of how 

each algorithm's throughput is affected by an increasing number of tasks when the number 

of VMs is fixed. The GWO-CSA algorithm still performs better than the others, but the 

decline in throughput as tasks increase is notable. It shows that while GWO-CSA is efficient, 

it is not immune to performance degradation as the workload becomes heavier.Figure 6: 

Makespan Comparison on 50 VMs shows the makespan for each algorithm while 

maintaining a constant number of 50 VMs. The performance trend is similar to Figure 4, 

with makespan increasing as the number of tasks grows. However, the slope of the makespan 

curve is steeper here, which could be due to the fixed number of VMs that might create a 

bottleneck. The GWO-CSA still appears to be the best performing algorithm, but the 

increased slope indicates that even the best algorithm struggles with scaling when the 

number of VMs is static. 



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Figure 7: Makespan Distribution Analysis 

In conclusion, the GWO-CSA algorithm s outperform PSO-ALBA, PSO, and ACO in terms 

of both throughput and makespan in different scenarios. These results could guide cloud 

computing resource managers in choosing the most effective task scheduling algorithms for 

different workloads and environments .The above diagram shows the plot of makespan 

comparison among GWO-CSA, PSO-ALBA, PSO, and ACO algorithms as the number of 

tasks increases from 100 to 1000 on 50 Virtual Machines (VMs). Makespan, which is the 

total time taken to complete all tasks is one of the crucial metrics in cloud computing 

environments. GWO-CSA generally outperforms other algorithms by having the least 

makespan throughout tasks of all sizes, thus demonstrating its effectiveness in problem-

solving and resource use. PSO-ALBA perform well, they achieve currently some 

competitive results, especially in lower task numbers. 

 

Figure 8: Throughput Distribution Analysis 



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In conclusion, the GWO-CSA algorithm s outperform PSO-ALBA, PSO, and ACO in terms 

of both throughput and makespan in different scenarios. These results could guide cloud 

computing resource managers in choosing the most effective task scheduling algorithms for 

different workloads and environments .The above diagram shows the plot of makespan 

comparison among GWO-CSA, PSO-ALBA, PSO, and ACO algorithms as the number of 

tasks increases from 100 to 1000 on 50 Virtual Machines (VMs). Makespan, which is the 

total time taken to complete all tasks is one of the crucial metrics in cloud computing 

environments. GWO-CSA generally outperforms other algorithms by having the least 

makespan throughout tasks of all sizes, thus demonstrating its effectiveness in problem-

solving and resource use. PSO-ALBA perform well, they achieve currently some 

competitive results, especially in lower task numbers. While PSO and ACO possess a higher 

makespan, especially with the presence of more tasks as compared to other algorithms, 

which might be an implication that these algorithms exhibit less efficiency in terms of 

handling large workloads. This pattern shows the higher efficiency and ability of GWO-

CSA for load balancing task and resource management in the cloud environment with 

moderate number of VMs. The performance comparison table reveals the performance of 

each algorithm in terms of the rate of task processing. Throughput, implying task completion 

per unit time, is an important metric of performance. It is GWO-CSA that outperforms its 

competitors in terms of performance with the highest throughput showed across the tasks. 

The high throughput is the reason why GWO-CSA can process several tasks quickly. PSO-

ALBA appears vital as it shows the nearest value behind GWO-CSA in terms of the 

throughput. PSO and ACO show a lower performance index as the number of tasks increases 

which reflects the problems in productivity at high workloads. This plot demonstrates, 

GWO-CSA's ability in keeping high processing speed, which is the reason why it is a 

favourable option for those environments where the high throughput is required. The x axis 

compares the makespan of different algorithms for tasks in a range of 100 to 1000 tasks and 

the y axis is comparing number of VMs. GWO-CSA is always the fastest at completing jobs, 

thus placing the greatest emphasis on scheduling tasks using different VM configurations. It 

is this consistency that articulates the compatibility and efficiency of GWO-CSA under 

different cloud architectures. PSO-ALBA is close to optimal with respect to the number of 

attributes but is getting left behind when the number of attributes increases. PSO and ACO, 

especially with the lower tasks, are quite efficient, but their performance declined as the 

workload and number of VMs increase, as can be attested in their longer makespans. The 

fact that GWO-CSA performs even better in a scaling up scenario in cloud computing 

environments than in a static scenario implies that GWO-CSA can be deployed more 

efficiently based on the configuration of VMs.The last diagram shows the effect of varying 

tasks and/or VMs on throughput. GWO-CSA scales the highest in throughput, thus 

exhibiting its power to acquire a systematic efficiency in executing a large number of tasks 

for different VM configurations. Therefore, we can conclude that GWO-CSA is good at 

scheduling of resource and task execution. PSO-ALBA made progress and it had its 

efficiency decreases as tasks became more complicated. Although ACO and PSO exhibits 

lower throughputs, especially in higher tasks, which indicates that the systems perform less 



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efficient in tough situations. The plot brings out the multi-tasking nature of GWO-CSA and 

shows its better performance in handling the different workloads as well as the varying 

configurations of VMs, thus making it a possible candidate to be used in varied types of 

cloud computing services. 

5. CONCLUSION AND FUTURE SCOPE 

The study is concentrated on the performance of four different task scheduling algorithm - 

GWO-CSA, PSO-ALBA, PSO and ACO- in cloud computing environments. This 

assessment had the makespan and throughput as the critical metrics and these were tested in 

different scenarios with the varying number of tasks and virtual machine (VM) 

configurations. The results are really impressive and unambiguous, the algorithms 

demonstrate different abilities. 

GWO-CSA was the winning algorithm in both the makespan and the throughput positions 

in all the tested scenarios. Repetitive make-span run and the highest throughput of the 

algorithm makes evident its scheduling and resource management efficacy. This 

effectiveness applies as well not only in environments with moderate numbers of VMs as in 

complex environments with different VM configurations and varying workload patterns. It 

is noteworthy that GWO-CSA is a perfect choice for cloud computing platforms where task 

demands and resources can change very significantly.GPO-ALBA exhibited remarkable 

capability, being quite close to GWO-CSA in many of the tasks, especially with less number 

of tasks. Nevertheless, its efficiency was lower compared to larger sets of tasks, and it seems 

that it has some limitations in handling a large volume of work.Different from PSO and ACO 

algorithms that are good enough for smaller sizes task scenarios but are degraded as the 

number of tasks and VMs increase. They face the challenges of keeping efficiency while 

handling high workloads, which show insufficient scalability or adaptability in upper cloud 

systems.To sum it up, this paper stresses on giving due attention while choosing suitable 

task scheduling algorithms in cloud computing. GWO-CSA achieved the status of an 

extremely efficient and adaptive algorithm which is suitable for diverse requirements of 

cloud computing. This offers the ability to regulate high with low when the conditions are 

diverse; and hence, becomes a valuable tool for improving the use of cloud computing 

resources yielding better overall performance. 

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