1 Introduction

The cloud environments involve numerous requests that arise from varied geographical channels concurrently. These requests are randomly assigned to different cloud providers. This ensures the unequal load assignment at a specific node that is few nodes are overloaded. Whereas, few nodes are under-loaded. This unequal load might degrade the system performance. To solve this, correct Load Balancing (LB) is significant. The study [1] reviewed various approaches by a comparative analysis of LB in the cloud. It affords an extensive opportunity for investigators to develop effective LB algorithms for the cloud environment [2]. The survey has been carried out by considering algorithms like heuristic-based LB (Round Robin algorithm, Improved Max–Min algorithm, Balanced Reduce algorithm and others.), metaheuristic based LB algorithm (Firefly algorithm, Honey Bee algorithm, Artificial Bee colony and others) and hybrid-based LB algorithms (Genetic Algorithm with Tabu search and so on). As LB is a strategy of detecting under-loaded and overloaded nodes, the article [3] explored a study that relies on the modern LB algorithms evolved particularly to fit the cloud environment. Taxonomy has been introduced for the LB algorithm. The simulation has been undertaken in the CloudSim simulator to assess the performance of the algorithms used in this study. These approaches should be clearly understood for future research. The proposed algorithms have to be implemented in real-time along with comparative evaluation [4]. Similarly, the paper [5] discussed various LB algorithms for cloud environments in a systematic way in accordance with a taxonomy. It has been found that irrespective of the significance of the network bandwidth in this environment, the high rate of network traffic led to degradation in the efficient usage of networking elements. This results in serious issues like data loss, communication delay and network failure. Thus, many effective LB algorithms have to be developed to use the network bandwidth in an effective way [6]. Additionally, the paper [7] introduced a hybrid LB strategy named Throttled and Equally Spread Current Execution. This approach has been utilized to reduce the time for response, enhance the services, minimize the cost of the machine and avoid bottleneck issue. In the same way, an improved scheduling algorithm has been proposed in this article [8]. This algorithm relies on the Particle Swarm Optimisation (PSO) algorithm. It intended to schedule huge tasks without affecting the performance of the system. Effective outcomes have been attained. Yet, the proposed methodology failed to consider certain objective functions like energy consumptions or cost. Moreover, this algorithm has to be altered to work as a concurrent workflow scheduling [9]. Thus, the present study intends to optimize the Virtual Machines (VM) by hybrid Lateral Wolf and Particle Swarm Optimization so as to avoid overloading and under-loading of VMs, thereby performing concurrent scheduling.

The major contributions of this study are listed below.

  • To determine the optimized Virtual Machines by the proposed hybrid Lateral Wolf and Particle Swarm Optimization (LW-PSO) for efficient Load Balancing.

  • To minimize the response time of the task and perform parallel scheduling by the proposed hybrid algorithm.

  • To analyze the system performance with respect to various parameters (average load, average response time, average turnaround time, CPU utilization, runtime and memory utilization) to evaluate its efficiency.

1.1 Paper Organisation

The paper is organized as follows.

Section I discusses the basic concepts of Virtual Machine, Task scheduling and Load Balancing in cloud computing environment. This is followed by section II that discusses the review of the various existing systems for LB in cloud. Then, section III explores the proposed hybrid method to accomplish concurrent LB. The results obtained through the proposed method is discussed in section IV. Finally, the overall study is summarized in section V.

2 Review of existing work

Various methodologies used by the existing system for Load Balancing (LB) in cloud computing are discussed in this section.

Task scheduling in an effective way is a major issue in the cloud computing environment. The study [10] has proposed a method to dynamically balance the load in a cloud environment via a combination of Modified Particle Swarm Optimization (MPSO) and an improved Q-learning algorithm named QMPSO. Actually, the combination process was done by adjusting the velocity of MPSO via gbest and pbest depending on the actions of Q-learning. This algorithm results in an improvement in makespan, throughput and energy utilization. On the other hand, LB also reduces waiting time for the tasks comparatively when executed separately as per this study. Future work is proposed to carry out load balancing among other tasks in a dynamic way. Moreover, the primary tasks in a virtual system are to schedule tasks effectively. The upcoming study aids with a proposed method for static task scheduling depending upon particle swarm optimization (PSO). Here, the tasks are independent and cannot be assigned properly. Thus, the LB technique is used to improve the performance of the PSO method. The results show improvement in resource utilization by 22% and a decrease in the makespan by 33%. The future work intends to consider cost reduction and fault tolerance capability [11]. Hence, it is clear that the Cloud environment is using task scheduling and load balancing for optimal file sharing. The article [12] has proposed a fuzzy-based multi-dimensional resource scheduling model in order to sustain the efficiency of resource scheduling in a cloud environment. The model was tested via simulations created by cloud simulators and showed effective results of 7% for an increase in resource scheduling and a 35% increase in the time factor. The future work was to propose a resource scheduling in privacy-aware resources with load balancing by considering success rate and response time [13].

Now-a-days, green cloud computing is facing certain issues like high energy cost and low efficiency. To avoid those issues, the following study [14] has given a global optimization algorithm known as resource-aware load balancing clonal algorithm focusing on task scheduling in order to deal with energy consumption in green cloud computing. The results prove that this algorithm performs effectively and exploration and exploitation factors were enhanced and balanced well. The future work is to have different energy-efficient approaches applicable for large data centres. Cloud computing is concentrating recently on the allocation of resource management efficiently. The paper [15] has introduced a method of combining fuzzy logic, evolutionary algorithms and task scheduling techniques in order to improve resource allocation in a cloud environment along with maintaining LB [16]. This method was quite effective in response time, task execution time and less energy consumption. Future works depend upon creating evolutionary algorithms in task schedulers and using bounding techniques for LB maintenance. Similarly, the article [17] has proposed PSO based scheduling algorithm via load balancing. Here the tasks are very diverse in the area. The proposed method has proven to be effective when compared to traditional methods. Yet, the study lacks real-time implementation. Cloud technology is currently facing optimization problems along with LB. In order to resolve this issue, this study [18] has proposed a Modified Adaptive Neuro-Fuzzy Inference System (MANFIS) for handling dynamic LB. MANFIS is introduced by using the Fire-Fly algorithm. The results are up to the mark and satisfying by utilizing resources properly. Reinforcing the same concept is yet to be done. Additionally, the paper [19] has provided an approach known as the hybrid fruit fly optimization technique depending on the improvement of optimal resource utilization and reduced energy consumption along with reduced cost in the cloud. The experiment has resulted in efficient outcomes compared to existing LB algorithms. Future work was proposed to work with the QoS factor and balancing workflows in cloud computing.

Now-a-days, Mobile Cloud Computing (MCC) has become a trend, but these are also facing LB issues. As a way to avoid those issues, the following study [20] has proposed a strategy of Krill Load Balancer (Krill LB). They concentrate on VMs by increasing the throughput of the networks up to the level. This algorithm is depending upon factors like speed, task, cost and weight. This method has proved to work effectively against Honey Bee Behaviour Load Balancing (HBB-LB), Kill herd, Round Robin algorithms. Moreover, cloud computing is considered to be flexible and scalable and available at low cost. However, major issues come across these environments like LB and task scheduling. Thus, the study [21] is proposing a novel algorithm MGGS (modified genetic algorithm (GA) combined with greedy strategy). This method is used for task scheduling and uses a fewer number of iterations. The results showed that MGGS performs well compared to others. The future work is to implement a stochastic service system to improve the cloud resource environment. Correspondingly, the paper [22] has proposed to concentrate on CPU bound requests so as to avoid LB. The requests are divided into CPU-bound and I/O bound request. This is attained by using the CloudSim tool. The results are much effective in comparison to round-robin, honey bee, Naïve Bayesian approaches. Implementing this approach in geographical clouds having dispersed data centres is proposed in future work. The allocation of cloud resources accordingly is a major constraint in the cloud system. In order to support the above-said issue, the article [23] concentrated on LB and QoS methods performed in the cloud environment. The work observed Qos management applications along with their performance challenges and different models available using different tool kits available. The end results were effective. There are scopes for research opportunities in the area of LB in the cloud environment.

Another type of approach for handling load balancing is suggested in the article [24]. They are Capacity Based Deadline LB algorithm which is proposed to overcome the problem of LB. This algorithm ensures that customer needs are satisfied with minimal cost. The results are stated that this algorithm overcomes all hurdles and are effective than other competitive algorithms. Yet, it did not consider the QoS parameters and workflow applications for LB. Since cloud computing has grown out largely, the LB issue can be overlooked by larger approaches. Hence, the study [25] has proposed an algorithm named Region Rerouting Load balancing (RRRL) for dealing with the loading capacity issues. This approach achieved its aim with minimal latency and high throughput. The future work is to establish this algorithm in cloud servers across geographical regions. Cloud manufacturing has caught more attention recently. To make it successful, issues like scheduling and service selection (SOSL) has to be taken care of. To support this, the paper [26] has proposed a genetic algorithm implementing both Cloud Manufacturing Queuing Systems (CMfgQS) and the LB heuristic algorithm based on task process time (LBPT). This code is generally applied to larger data resulting in an effective outcome. Several more heuristics and Metaheuristics algorithms have to be compared accordingly in the near future. Likewise, the study [27] has proposed two hybrid metaheuristic algorithms. It used fuzzy logic with the PSO algorithm (TSDQ-FLPSO). Subsequently, it used simulated annealing with the PSO algorithm (TSDQ-SAPSO). The proposed algorithm has provided maximum results for high dimensional problems along with great advantage of time, queue length, cost and resource utilization. LB is focusing on managing workloads by distributing resources among computers. So as to achieve that, the paper [28] introduced a combination of Firefly and Improved Multi Objective PSO technique abbreviated as (FIMPSO). The former is used to perform Search Space (SS) minimization and latter is used to find the improvised response. The results shows that hybrid algorithms results with maximum utilization of CPU up to 98%, memory utilisation (93%), 67% of reliability and throughput of 72%. This has improved the results comparing to other methods. Parallel method are suggested to overcome the issue of LB. One such approach has been proposed based on PSO [29]. The results of this paper gives a strong optimal results than others methods. The outcomes are simple, easily accessible and gives better solutions. LB and scheduling based applications setbacks are approached in various ways. Among them, the following approach as proposed in the paper [30] employed a hybrid algorithm based on gravitation search and non-dominated sorting genetic algorithm (GSA and NGSA). The results are proved effective in proposed algorithm’s efficiency. Future work was to solve power consumption in cloud data centres and implementing green cloud computing. Resources can also be allocated using the study discussed in [31] as it has proposed allocation of resource using modified cloud resource provisioning algorithm aided by optimization technique and OCRP algorithm. The result of this paper reduced the optimal cost. In addition, it used low memory usage compared to other techniques. Yet, this study have to consider various parameters to confirm its efficacy further.

3 Proposed Methodology

The study proposed a hybrid Lateral Wolf and Particle Swarm Optimization (LW-PSO) to find the optimized VM so that tasks can be assigned to all the VMs by avoiding overloading and under-loading. The task scheduling and LB are performed in a cloud environment by implementing the proposed hybrid algorithms. This is carried out by various processes and is given in the below Fig. 1.

Fig. 1
figure 1

Overall flow: lateral Wolf Based PSO Optimization for Load Balancing on Cloud Computing

Full size image

At first, the user request is taken as a task queue on VM and provided to the VM Manager. Then, the VMs are created. Subsequently, the active VMs are uploaded with tasks. By using the PSO optimization, the parameters are initialized. This is followed by initializing the particle with position and velocity to solve the target problem. After this, the fitness value is updated by LW operation. In LW, the starting population is initialized and the fitness is evaluated. The search agent is then updated in a lateral manner to find the fitness value of the search agents. Finally, the best fitness value is saved. The best particle,

position and velocity is updated to obtain the optimal solution. Thus, the high load VMs are optimized using the proposed hybrid LW-PSO by assigning tasks to low loaded VMs, thereby performing LB. The proposed system is also analyzed with respect to various performance measures, namely runtime, average load, CPU utilization, average turnaround time, average response time and memory utilization to evaluate its effectiveness.

3.1 Particle Swarm Optimization (PSO)

PSO is an optimization and meta-heuristic technique employed to optimize an issue by iteratively attempting to enhance a candidate resolution in accordance with the given quality measure. It rectifies an issue by possessing a candidate solution populations (particles). Then, it moves these particles round the Search Space (SS) based on precise mathematical formula over the position as well as the velocity of the particle. The movement of an individual particle is inclined by its local best-identified position. On the other hand, it is directed towards the best-identified positions in SS. This is then updated as optimal positions and is expected for moving the swarm to optimal solutions. This particular algorithm does not utilize the gradient corresponding to the issue that is being optimized. This means that it does not need the optimization issue to be diverse as needed by classific optimization techniques like quasi newton and gradient descent methodologies. This study uses PSO to obtain the optimal solution for LB and task scheduling which are the main issues in the cloud environment.

At first, the position and velocity of the particle is initialized as per Eqs. 1 and 2.

$$\mathrm{Position}: {\mathrm{X}}_{\mathrm{i}}=\left({\mathrm{x}}_{\mathrm{i},1} , {\mathrm{x}}_{\mathrm{i},2} , \dots , {\mathrm{x}}_{\mathrm{i},\mathrm{n}}\right)\upvarepsilon {\mathrm{R}}^{\mathrm{n}}$$
(1)
$${\mathrm{Velocity}:\mathrm{ V}}_{\mathrm{i}}=({\mathrm{v}}_{\mathrm{i},1} , {\mathrm{v}}_{\mathrm{i},2} , \dots , {\mathrm{v}}_{\mathrm{i},\mathrm{n}})\upvarepsilon {\mathrm{R}}^{\mathrm{n}}$$
(2)

Subsequently, the velocity of the particle is computed by Eqs. 3 and 4.

$${\mathrm{V}}_{\mathrm{i}}\left(\mathrm{k}+1\right)=\mathrm{Inertia}+\mathrm{cognitive}+\mathrm{social}$$
(3)
$${\mathrm{V}}_{\mathrm{i}}\left(\mathrm{k}+1\right)=\upomega \times {\mathrm{V}}_{\mathrm{i}}\left(\mathrm{k}\right)+ {\mathrm{c}}_{1} \times {\mathrm{random}}_{1} \times \left({\mathrm{PBest}}_{\mathrm{i}}- {\mathrm{x}}_{\mathrm{i}}\left(\mathrm{k}\right)\right)+ {\mathrm{c}}_{2} \times {\mathrm{random}}_{2} \times \left({\mathrm{GBest}}_{\mathrm{i}}- {\mathrm{x}}_{\mathrm{i}}\left(\mathrm{k}\right)\right)$$
(4)

Here, \(\mathrm{w},{\mathrm{c}}_{1},{\mathrm{c}}_{2}\mathrm{ are the constants }\), \({\mathrm{random}()}_{1},{\mathrm{random}()}_{2}\mathrm{ indicates the random variable}\).

After updation, the position and velocity of the particle is given by Eqs. 5 and 6.

$${\mathrm{X}}_{\mathrm{i}}\left(\mathrm{k}+1\right)= {\mathrm{X}}_{\mathrm{i}}\left(\mathrm{k}\right)+{\mathrm{V}}_{\mathrm{i}}(\mathrm{k }+1)$$
(5)
$${\mathrm{X}}_{\mathrm{i}}\left(\mathrm{k}+1\right)=\mathrm{ Inertia}+\mathrm{cognitive}+\mathrm{social}$$
(6)

The pseudo-code corresponding to PSO algorithm is given below.

figure c

All the particles are initialized. The fitness value (FV) for each of the particles is computed. When the computed FV is better when compared to the optimal FV in history, this particular FV is set as a new FV. Finally, all the particles that possess the best FV are selected. The velocity of these particles are computed and later updated. This process continues until maximum iterations, or minimum error is obtained.

3.2 Lateral Wolf (LW)

The LW algorithm imitates the hunting mechanism and leadership hierarchy of a grey wolf. Four kinds of grey wolves, namely alpha, omega, beta and delta are applied to simulate this leadership hierarchy. Additionally, three main hunting steps are implemented to accomplish optimization. These steps include searching the prey, encircling and attacking it. The proposed LW has recently evolved as an effective meta-heuristic optimization method. It has the ability to solve unimodal issues, works effective for complex functions, thereby eluding local minima. It also has a superior exploration capacity for multi-modal issues.

In addition, the encircling process of the mathematical model is given by Eqs. 7 and 8.

$$\mathrm{d }= \left|{\mathrm{cx}}_{\mathrm{p}}(\mathrm{t}) -\mathrm{ x}(\mathrm{t})\right|$$
(7)
$$\mathrm{x}(\mathrm{t }+ 1) = {\mathrm{x}}_{\mathrm{p}}(\mathrm{t}) -\mathrm{ ad}$$
(8)

Here \(\mathrm{t}\) denotes the current iteration count, \(\mathrm{a and}\) \(\mathrm{c}\) denotes the coefficient vectors, \({\mathrm{x}}_{\mathrm{p}}\) is the prey position vector and \(\mathrm{x}\) denotes the LW’s position vector. Here the \(\mathrm{a and}\) \(\mathrm{c}\) vectors are computed by Eqs. 9 and 10.

$$\mathrm{a }= 2.\mathrm{f}.{\mathrm{r}}_{1} -\mathrm{ a}$$
(9)
$$\mathrm{c }= 2.{\mathrm{r}}_{2}$$
(10)

Here \(\mathrm{f}\) is linearly minimized from two to zero via iteration. The random vectors are given by \({\mathrm{r}}_{1}\) and \({\mathrm{r}}_{2}\) within the range of (0, 1).

To perform mathematical simulation of the LW behaviour, an assumption is made that the beta, delta and alpha (availability of best solution) are effectively informed regarding the potential prey’s location. The three of the effective solutions attained is stored, other agents are enforced to update their corresponding positions in accordance with the locations of the best agent. This association is given by the below equations.

$${\mathrm{d}}_{\mathrm{\alpha }} = \left|{\mathrm{c}}_{1}{\mathrm{x}}_{\mathrm{\alpha }}(\mathrm{t}) -\mathrm{ x}\right| , {\mathrm{d}}_{\upbeta } = \left|{\mathrm{c}}_{2}{\mathrm{x}}_{\upbeta }(\mathrm{t}) -\mathrm{ x}\right| , {\mathrm{d}}_{\updelta } = \left|{\mathrm{c}}_{3}{\mathrm{x}}_{\updelta }(\mathrm{t}) -\mathrm{ x}\right|$$
(11)
$${\mathrm{x}}_{1} = {\mathrm{x}}_{\mathrm{\alpha }} - {\mathrm{a}}_{1}({\mathrm{d}}_{\mathrm{\alpha }}) , {\mathrm{x}}_{2} = {\mathrm{x}}_{\upbeta } - {\mathrm{a}}_{2}({\mathrm{d}}_{\upbeta }) , {\mathrm{x}}_{3} = {\mathrm{x}}_{\updelta } - {\mathrm{a}}_{3}({\mathrm{d}}_{\updelta })$$
(12)
$$\mathrm{x}\left(\mathrm{t}+1\right)= \frac{{\mathrm{x}}_{1}+ {\mathrm{x}}_{2}+ {\mathrm{x}}_{3}}{3}$$
(13)

The pseudo-code corresponding to LW algorithm is given below.

figure d

The size of the problem and the size of the population is taken as input. At first, the grey wolf's population are initialized. Then, the FV of agent grading and search agents are computed. Subsequently, the present position of the search agent is updated when \(\mathrm{t}1\) is less than the maximum iteration count as per step 2. Finally, the best FV \(\mathrm{Pg}1\_\mathrm{best}\) is updated.

3.3 Lateral Wolf Based Particle Swarm Optimization (LW-PSO)

In this study, the Particle Swarm Optimization and Lateral Wolf are hybrid for LB in the cloud environment. The PSO has various merits like easy implementation, simple concept, computational efficiency and robustness in terms of parameter control. Due to these merits, it is efficient than other methods. Thus, this study employed this particular algorithm to determine the optimized VM so as to schedule tasks, thereby minimizing overloading and under-loading accordingly. On the other hand, a solution is required to minimize the probability of PSO to trap into Local Minimum (LM). In this study, LW is employed to assist the PSO algorithm in minimizing this LM issue, thereby performing efficiently in combination with PSO to schedule the tasks in the cloud environment. The LW algorithm has the ability to avoid these threats by directing few particles to particular positions (partially enhanced by the LW algorithm) without directing them to some random position. Additionally, the LW algorithm has the capacity to perform task scheduling and LB in parallel, it needs only minimum memory, easy implementation and faster convergence which shows its effectiveness for implementation in this study.

The fitness value is computed by hybrid LW-PSO through the computations shown in Eqs. 14 and 15.

$${\text{In the Position Update X}}_{\mathrm{i}}\left(\mathrm{k}+1\right)= {\mathrm{X}}_{\mathrm{i}}\left(\mathrm{k}\right)+{\mathrm{V}}_{\mathrm{i}}\left(\mathrm{k }+1\right)+ {\mathrm{d}}_{\mathrm{\alpha }} = \left|{\mathrm{c}}_{\mathrm{n}}{\mathrm{x}}_{\mathrm{w}}(\mathrm{t}) -\mathrm{ x}\right|$$
(14)

Here \(\mathrm{w}-\mathrm{wolves }\), \(\mathrm{n}-\mathrm{number}\).

$${\text{In the Position Velocity X}}_{\mathrm{i}}\left(\mathrm{k}+1\right)=\mathrm{ Inertia}+\mathrm{cognitive}+\mathrm{social x}\left(\mathrm{t}+1\right)+ \frac{{\mathrm{x}}_{1}+ {\mathrm{x}}_{2}+ {\mathrm{x}}_{3}\dots +{\mathrm{x}}_{\mathrm{n}} }{\mathrm{n}}$$
(15)

The pseudo-code of the proposed LW-PSO is given below.

figure e

The particles are initialized and iteration is performed by considering the maximum iteration count and the size of population count fixed by the user. Subsequently, the position and velocity of the present particle are updated. The LW algorithm is hybrid with PSO to avoid local minima and step 2 is implemented. Then, the positions of wolves are updated concurrently. This is continued until the position of the present particle is similar to the mean of the three optimal wolves' position.

4 Results and Discussion

The proposed LW-PSO is hybrid to perform Load Balancing (LB) in an efficient way. The obtained results from the implementation of this methods are discussed in this section.

4.1 Experimental Setup

The proposed system utilized a simulation environment named CloudSim using python language. This simulation tool permits the ability to explore the workflows as well as hosts.

4.2 Performance and Comparative analysis

The performance of this method is also analysed by comparing the proposed method with the existing methods with respect to average response time, memory utilization, average load, CPU utilization, average turnaround time and runtime.

The performance of the proposed system is assessed in terms of runtime by comparing it with Enhanced Bee Colony Algorithm (EBCA-LB) and existing methods. The obtained results are shown in the below Table 1.

Table 1 Analysis of the proposed and existing system [32] with respect to runtime
Full size table

The VM speed and task length are the two significant parameters to assign tasks to all the resources. Here various tasks are assigned. When 100 tasks are assigned, the Hybrid Enhanced Bee Colony Algorithm (EBCA-LB) takes 77.9 s, Hybrid Honey Bee Behaviour Load Balancing (HBB-LB) takes 28.5 s, and the existing method takes 23.5 s. Whereas the runtime of the proposed system is found to be 20.25 s when 100 tasks are assigned. Similarly, when various tasks are assigned, like 150 tasks, 200 tasks, 250 tasks, 300 and 400 tasks, the runtime of the proposed system is found to be low than the existing methods [32]. It is graphically shown in the below Fig. 2.

Fig. 2
figure 2

The runtime of the existing [32] and the proposed method

Full size image

The execution time of the proposed and existing methods [32] for individual tasks are computed. It is found that the runtime of the proposed system is low when 100, 150, 200, 250, 300 and 400 tasks are assigned. This indicates that the runtime of the proposed system remains low than the existing system even when more tasks are assigned.

In addition, the proposed method is also analysed by comparing it with other existing methods like Hybrid Job Scheduling Algorithm (HJSA) and Task Scheduling Load Balancing Ant Colony Optimization (TSLBACO) in terms of runtime to evaluate its efficiency further. The results obtained are given in the below Table 2.

Table 2 Analysis of the proposed and existing methods [32] with respect to runtime
Full size table

More tasks are assigned to VMs. The performance of the proposed and existing HJSA and TSLBACO [32] are analysed to find the efficient algorithm that determines the optimized VM and assigns tasks to them accordingly in minimum time. When 200 tasks are assigned, the runtime of the existing method is 0.5 s, the existing HJSA takes 0.61 s, and TSLBACO takes 0.63 s. On the other hand, the proposed system takes only 0.45 s. Likewise, the proposed system shows minimum runtime in comparison to other mentioned methods when 400, 600, 800 and 1000 tasks are assigned. Typically, as the tasks increase, the running time is more. But, here, the proposed method takes only minimum time for execution even when huge tasks are assigned. It is graphically shown in the below Fig. 3.

Fig. 3
figure 3

Comparison of the proposed and existing methods [32] with respect to runtime

Full size image

The proposed and existing HJSA, TSLBACO are assessed by assigning more tasks to VMs. The ability of each of these algorithms to find the optimized VM is examined when tasks are increased. The analytical results reveal that the proposed method takes minimum runtime for execution than existing methods. Due to the computational efficiency of PSO and parallel LB capacity of LW, the proposed hybrid LW-PSO accomplished minimum runtime proving its efficacy.

The proposed method is also assessed with respect to average load, response time, average turnaround time, CPU utilization and memory utilization. The obtained results are shown in the below Tables 3, 4 and 5.

Table 3 Analysis of the proposed and existing methods [28] with respect to average response time
Full size table
Table 4 Analysis of the proposed and existing methods [28] with respect to CPU utilization
Full size table
Table 5 Analysis of the proposed and existing methods [28] with respect to memory utilization
Full size table

It is found that the existing RR method shows an average load of 0.43 s, an average turnaround time of 41.98 ms and 30.5 s as average response time. Similarly, the existing Round Robin (RR), First Come First Service (FCFS), Short jobs First (SJF), Improved PSO (IPSO), Firefly IPSO (FF-IPSO) and Firefly Improved Multi-objective PSO (FIMPSO) shows high average load, response time and turnaround time. It is graphically shown in the below Figs. 4, 5 and 6.

Fig. 4
figure 4

Analysis of the proposed and existing methods [28] in terms of average load

Full size image
Fig. 5
figure 5

Analysis of the proposed and existing methods [28] in terms of average turnaround time

Full size image
Fig. 6
figure 6

Analysis of the proposed and existing methods [28] in terms of average response time

Full size image

From Fig. 4, it is clear that the proposed hybrid LW-PSO shows a minimum average load in comparison to the existing FCFS, RR, SJF, IPSO, Firefly, FF-IPSO and FIMPSO. Similarly, the average turnaround time of the proposed and existing methods are compared and it is graphically shown in Fig. 5.

From the Fig. 5, it is found that the proposed method shows minimum turnaround time in comparison to the existing RR, FCFS, SJF, IPSO, Firefly, FF-IPSO and FIMPSO. Additionally, the average response time is also computed for the proposed method and it is compared with the mentioned existing methods to find its efficacy. The response time is a significant factor in the cloud environment. The results corresponding to this are shown in Fig. 6.

The proposed system takes less time to respond to each user request thereby proving the system efficiency. This response time is also minimum when compared to the traditional methods. This outstanding performance of the proposed method makes it effective. Generally, hybrid methods take more time. But, the proposed hybrid algorithms have more computational efficiency. This makes them work faster.

The proposed hybrid LW-PSO is assessed in terms of CPU and memory utilization for different task types. It is shown in the Table 4.

Various kinds of tasks like small, large, medium and extra-large are considered. The existing Random method- RD utilized CPU only to a minimum extent in all kinds of tasks. Similarly, the CPU utilization of all the other existing methods namely Weighted Round Robin (WRR), Diffusive Load Balancing (DLB), Load Balancing Bayes and Clustering (LB-BC), Load balancing Resource control (LB-RC), IPSO-Firefly and FIMPSO are analysed by comparing with the proposed method. It is found that the proposed method efficiently utilized CPU at a maximum rate of 74% for small tasks, 82% for medium tasks, 98% for large tasks and 101% for extra-large tasks. It is graphically shown in the below Fig. 7.

Fig. 7
figure 7

Analysis of the proposed and traditional methods [28] with respect to CPU Utilization

Full size image

The above Fig. 7 shows that the proposed method performs effective CPU utilization in comparison to other existing methods. Usually, as the tasks increases the CPU cannot be efficiently used. But, when the proposed hybrid LW-PSO is implemented, it has the ability to effectively perform CPU utilization which makes it suitable for load balancing in cloud system. The proposed methodology is also analysed in terms of memory use as shown in Table 5.

Similarly, the proposed system is compared with the traditional algorithms to find its efficiency with regard to memory utilization. Various kinds of tasks as small, large, medium and extra-large are considered. The analytical outcomes explore that the proposed method uses 63% of memory for small tasks, 76% of memory for medium tasks, 86% of memory for large tasks and 90% of memory for extra-large tasks. This memory usage is efficient for proposed than existing methods as shown in Table 5. This means the proposed hybrid method efficiently uses memory for all the task types. It is graphically shown in the Fig. 8.

Fig. 8
figure 8

Analysis of the proposed and traditional methods [28] with respect to memory Utilization

Full size image

The proposed system shows efficient memory utilization in comparison to the conventional techniques. As the task increases, the efficiency of the memory utility remains steady for the proposed method than the existing method. This proves that the proposed method is consistent than the existing method even when more tasks are assigned for the VMs. It still has the ability to find the optimized VM and perform effective LB which response fast to the user request. Further, the parameter initialization for the proposed method are shown in Table 6.

Table 6 Parameter initialization
Full size table

The study [33] employed hybrid ant colony and lion optimization for solving the issues of task scheduling in cloud system. Though the study showed better outcomes it considered only minimum parameters such as imbalance degree, makespan time and response time. This minimum parameter is insufficient to prove its efficiency. The present study considered various significant parameters for analysis like runtime, average load, memory utilization, average response time, average turnaround time and CPU utilization. The analytical results are found to be efficient for the proposed system with regard to all the six significant parameters. This proves that the proposed hybrid LW-PSO is suitable to solve the tasks scheduling challenges in cloud environment.

5 Conclusion

In this study, the Lateral Wolf-Particle Swarm Optimization (LW-PSO) has been proposed for solving the task scheduling issues in cloud system by finding the optimized Virtual Machines (VMs). An analysis is performed by considering significant parameters like average load, CPU utilization, average turnaround time, runtime and average response time and memory utilization. The results explored that the proposed method is efficient than the existing methods as it reduces the average load, response time and turnaround time. The proposed method effectively used memory and CPU in comparison to the traditional methodologies. Though the tasks are increased and the types of tasks are complex, the proposed hybrid LW-PSO accomplished effective results in minimum time by assigning tasks to VMs by avoiding overloading and under-loading. This performance is found to be outstanding than the conventional techniques. Thus, this study will assist to perform optimal Load Balancing (LB) of VMs thereby avoiding the task scheduling issues.