1 Introduction

Scheduling tasks on cloud-based VMs for efficient client-level service performance is a multidomain task, that involves the design of task pattern analysers, capacity optimization units, task map** units, correlation evaluation layers, task dependency analysis models, etc. A typical task-to-VM scheduling model evaluates the correlation between the task’s requirements and capacity of the VM [1] and uses Eq. 1 to identify a matching VM for a given task,

$$C=MAX\left(\frac{\bigcup_{i=1}^{N\left(VM\right)}{f}_{c}\left(V{M}_{i}\right)}{\bigcup_{j=1}^{N(T)}{f}_{r}({T}_{j})}\right)$$
(1)

where \(N\left(VM\right) \mathrm{and} N(T)\) represents the number of VMs, and the number of tasks, while \({f}_{c} \mathrm{and} {f}_{r}\) represents the capacity evaluation function for VM, and the requirement evaluation function for individual tasks. These functions are modeled such that the capacity of the VM has a close correlation with the respective requirements of underlying tasks. A CNN-based task map** model is depicted in Fig. 1, wherein an optimized dynamic scheduler (ODS) is optimized via CNN based classification process.

Fig. 1
figure 1

A CNN based task to VM map** engine for real-time deployments

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The process utilizes resource monitoring statuses which include the capacity of VMs, deadline of tasks, make-span of tasks, and mutual dependency of tasks to estimate a map** plan between underlying VM and task configurations. The capacity of VMs is evaluated via Eq. 2,

$$Cap\left(VM\right)=\frac{BW}{Max(BW)}+\frac{Mem}{Max(Mem)}+\frac{MIPS}{Max(MIPS)}$$
(2)

where, \(BW, Mem, \& MIPS\) represents bandwidth, memory availability, and processing capacity in millions of instructions per second, while \(Cap(VM)\) represents the capacity of individual virtual machines. Similarly, the task requirements are evaluated via Eq. (3),

$${T}_{r}=\left|\frac{MS}{Max(MS)}+\frac{D}{Max(D)}\right|*\frac{MS\left(D\right)}{Max\left(MS\left(D\right)\right)}\dots$$
(3)

where, \(MS, D \& MS(D)\) represents make-span, deadline, and make-span dependency delays for each of the tasks, while \({T}_{r}\) represents its computational requirement levels. Based on these evaluations, the CNN model can classify each task requirement into relevant map** VM types, which assists in improving scheduling performance. Similar models [2,3,4] are briefly reviewed in the next section of this text, wherein their contextual nuances, applicative advantages, functional limitations, and deployment-specific future scopes are discussed under various scenarios. Based on this discussion, it was observed that existing models are either highly complex or do not consider task and VM dependencies while performing the map** process. Moreover, most of these models are highly context-sensitive, and cannot be applied to large-scale scheduling applications. To overcome these issues, Sect. 3 discusses the design of a novel hybrid bioinspired model for task-and-VM-dependency and deadline aware scheduling via dual service level agreements. This model was evaluated in terms of cloud utilization, task diversity, resource provisioning delay, and energy consumption levels in Sect. 4, where it is compared with various state-of-the-art methods. This article concludes with some thought-provoking comments on the model offered, as well as some ideas for enhancing the model's overall effectiveness across a range of usage scenarios.

1.1 Core contributions

  • Hybrid bioinspired model The proposed model aims to enhance task scheduling in cloud systems by combining the strengths of LCA and GWO. The LCA component handles task scheduling by considering task dependencies and assigning tasks to suitable VMs. The GWO component then optimizes the scheduling results obtained from the LCA by exploring the search space further and refining the schedule.

  • Deadline aware and task-and-VM-dependency aware scheduling The suggested model considers several variables, including task duration, deadline, task dependencies, VM capacity, and energy consumption. The model aims to enhance real-time task and cloud settings as well as scheduling performance across various use cases by including these factors in the fitness function used by the optimization algorithms.

  • Dual service level agreements (SLAs) To increase task and requesting-user variety, the method makes use of a task-based SLA mechanism. Additionally, it builds a VM-based SLA model that alters the VM's internal characteristics to support various task types. The model aims to improve scheduling effectiveness in real-time cloud environments by taking deadline awareness, task-level dependency awareness, and VM-level dependency awareness into account for different scenarios.

  • Performance evaluation Using diverse task datasets from different parallel workload archives, the paper compares the performance of the proposed model to that of other models that are already in use. According to the evaluation results, the suggested model performs better than other models in terms of task diversity, resource provisioning speed, cloud utilization, and energy usage levels. This demonstrates the proposed model's potential applicability to real-time cloud deployments.

1.2 Organization of the paper

The paper begins with an abstract that provides a concise summary of the study's objectives, methodology, and key results. The introduction section establishes the context and motivation for the research, highlighting the limitations of existing models for task scheduling in VM-based cloud systems. It presents the research problem and outlines the objectives of the study. Following that, the review section offers a comprehensive analysis of related literature, discussing existing approaches and their strengths and weaknesses. This section also introduces bioinspired optimization algorithms and their relevance to task scheduling. The proposed model section describes in detail the hybrid bioinspired model that addresses task and VM dependencies while considering deadlines. It explains the integration of the league championship algorithm (LCA) and grey wolf optimization (GWO), along with the formulation of the fitness function that incorporates various factors. The results section presents the experimental findings, including the datasets used, performance metrics, and a comparison with other models. It discusses the implications of the results and highlights the advantages of the proposed model. Finally, the conclusion and future scope section summarizes the contributions of the research, reflects on the strengths and limitations of the proposed model, and suggests areas for future research and improvement. It concludes with a statement on the significance of the proposed model in real-time cloud deployments.

2 Literature review

A wide variety of task scheduling models are proposed by researchers, and each of them varies in terms of their internal operating characteristics. For instance, work in [5, 6] proposes the use of geo-distributed data analytics, and a self-adapting task scheduling model, for the estimation of high-density data patterns while map** tasks to different cloud configurations. But these models are not scalable, and thus cannot be used for heterogeneous task types. To overcome this limitation, work in [7] proposes the use of multiple device co-processing of data-parallel kernels, which assists in deploying the model for task scheduling under distributed scenarios. This model is capable of predicting task patterns, which assists in improving capacity pre-emption for different VM types. Similar models are discussed in [8,9,10], which propose the use of joint task scheduling and containerizing (JTSC), genetic algorithm with mobility aware task scheduling (GAMTS), and deep neural network scheduling (DNNS), for estimation of multiple task types under real-time environments. These models are useful for deploying scheduling techniques for large-scale use cases. Extensions to these models are discussed in [11,12,13], which propose the use of non-pre-emptive stochastic co-flow scheduling (NPSCS), energy, time, and rent cost (ETRC) optimization, and whale optimization algorithm (WOA) which assists in improving its performance for inter-related task sets. These models are highly functional when applied to low-complexity scenarios, and thus can be used to mitigate issues in presence of scheduling faults. Due to this characteristic, they can be deployed for large-scale scheduling applications.

Models that propose the use of energy-efficient scheduling [14], profit sensitive spatial scheduling (PS3) [15], multi-task deep reinforcement learning (MTDRL) [16], novel multi-objective evolutionary algorithm based on decomposition (NMOEA) [17], dynamic voltage and frequency scaling (DVFS) [18], and elastic task scheduling scheme (ETSS) [19], that assists in tracking task pattern analysis, and deployment of SLA specific operations, which assists in enforcing application-level constraints. But these models are not useful for dynamic task sets, thus they are further extended via the work in [20], which proposes the use of the dynamic and resource aware load balanced scheduling model (DRALBM), which assists in improving its performance continuously changing task scenarios. To further optimize their performance, work in [21,22,23] proposes the use of an Energy-efficient dynamic scheduling scheme (EDSS), deep neural networks (DNN), and task scheduling and microservices based computational offloading (TSMCO), which aims at incorporating high-density feature extraction under real-time scheduling scenarios. These models are highly complex, and thus cannot be used for real-time applications. To overcome this issue, work in [24,25,26] proposes the use of parallel processing, deep reinforcement learning (DRL), and earliest deadline first (EDF) scheduling models, that can be used for high-speed applications. These models are capable of incorporating low-complexity processing techniques, which assists in improving their real-time performance. This work is further extended in [27, 28], which discusses the integration of task duplication, and particle swarm optimization (PSO) with idle time slot-aware rules, which assists in the minimization of execution costs, under mutually dependent task sets. A cost-effective model work in [30, 31] proposes the use of replication. But these models are either highly complex to deploy for real-time cloud tasks or do not consider task and VM dependencies while performing the map** process. These models also showcase a high level of context sensitivity, and thus cannot be used for large-scale scheduling applications. To overcome these issues, the next section discusses the design of a novel hybrid bioinspired model for task-and-VM-dependency and deadline aware scheduling via dual service level agreements. The model was validated under multiple real-time datasets and was compared with various state-of-the-art methods, which assists in validating its performance under real-time deployments (Table 1).

Table 1 Review of existing models
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Based on this review, the following are the gaps of existing methods,

  1. 1.

    Taking task and VM dependencies into account: Current models for task scheduling in cloud systems based on virtual machines frequently fail to take task and VM dependencies into account. The proposed model incorporates task and VM dependency awareness in an effort to close this gap. Further study may examine more sophisticated methods to model and optimize task and VM dependencies, taking into account complex scenarios and interactions between various tasks and VMs.

  2. 2.

    Scalability and real-time scheduling: The proposed model shows improvements in scheduling performance; however, its scalability in massive cloud environments and real-time scheduling scenarios needs more research. To ensure effective and timely scheduling decisions, research could concentrate on improving the model's scalability and responsiveness to dynamic workload changes.

  3. 3.

    Energy efficiency and sustainability The suggested model takes energy use into account when scheduling operations are performed, which helps to lower energy consumption. The sustainability and environmental impact of the model could be improved, though, by further research into energy-efficient scheduling techniques like dynamic power management and workload consolidation. The hybrid bioinspired model combines the league championship algorithm (LCA) and grey wolf optimization (GWO), two optimization algorithms and strategies. While these algorithms are used, it may be possible to explore additional bioinspired algorithms or optimization strategies to improve the scheduling performance. The efficacy of various optimization algorithms and their combinations for task scheduling in VM-based cloud systems could be further investigated.

  4. 4.

    Evaluation and benchmarking The proposed model was compared to other models using diverse task datasets, according to the paper. The detailed comparison methodologies, benchmark datasets, and evaluation criteria are not provided. By taking into account additional performance metrics, utilizing standardized benchmark datasets, and contrasting it against a wider range of existing models, future research could concentrate on providing a more thorough evaluation of the proposed model.

  5. 5.

    Real-world implementation and deployment Although the proposed model exhibits encouraging results in the paper, additional study may examine its real-world implementation and deployments. This would entail taking into account the constraints and difficulties faced by real-world cloud systems, assessing the model's viability and efficiency across various cloud platforms, and resolving any implementation issues that may arise for real-time scenarios.

3 Research methodology

After referring to existing scheduling models, it was observed that they are either highly complex to deploy for real-time cloud tasks or do not consider task and VM dependencies while performing the map** process. Most of these models also showcase a high level of context sensitivity, and thus cannot be used for large-scale scheduling applications. To overcome these issues, this section discusses the design of a novel hybrid bioinspired model for task-and-VM-dependency and deadline aware scheduling via dual service level agreements. The flow of the model is depicted in Fig. 2, wherein it can be observed that the proposed model uses a combination of grey wolf optimization (GWO) with the league championship algorithm (LCA), to perform efficient scheduling operations.

Fig. 2
figure 2

The overall flow of the proposed hybrid bioinspired model for the efficient scheduling process

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These optimization techniques model a fitness function that incorporates task make-span, task deadline, mutual dependencies with other tasks, the capacity of VMs, and energy needed for scheduling operations. This assists in improving its scheduling performance for multiple use cases. To perform these tasks, the model initially deploys a task-based service level agreement (SLA) method, which assists in enhancing task and requesting-user diversity. This is followed by the design of a VM-based SLA model, that reconfigures the VM's internal characteristics for the incorporation of multiple task types. The model also integrates deadline awareness along with task-level and VM-level dependency awareness, which assists in improving its scheduling performance under real-time task and cloud scenarios.

Based on the model design depicted in Fig. 2, it can be observed that the model initially collects task and VM information from their respective sources, and then applies a task-based service level agreement (SLA) model which assists in sequencing tasks based on a context-based criterion. The following process is used to perform this task,

  • Arrange all tasks chronologically as per their request timestamps, and track the user (client) from which the task request has arrived for scheduling purposes

  • Define a task SLA time (\({T}_{SLA}\)), and User SLA time (\({U}_{SLA}\)), and perform the following process,

    • For each set of tasks, evaluate the SLA interval (\({I}_{SLA}\)) via Eq. (4),

      $${I}_{SLA}=t\left(i+1\right)-t\left(i\right)\dots$$
      (4)

      where, \(t\) represents the timestamp of the task, while \(i\) represents the task number that has to be scheduled.

    • Shift this task to the end of the list if \({I}_{SLA}>{T}_{SLA}\)

  • For each user, check the user number for each task, and evaluate user-level SLA interval (\(I{U}_{SLA}\)) via Eq. (5),

    $$I{U}_{SLA}=t\left(i+1\right){\left.\right|}_{U}-t\left(i\right){\left.\right|}_{U}\dots $$
    (5)

    where \(t\left(i\right){\left.\right|}_{U}\) represents the task timestamp for the \({U}^{th}\) user that has requested for scheduling operations.

  • Shift this task to the end of the list if $${IU}_{SLA}>{U}_{SLA}$$

    This process is repeated for all tasks, and all users, which assists in enforcing task-level and user-level SLA for input scheduling requests. Based on the resulting task sets, a GWO Model is activated, which assists in deciding the configuration of VM-based input task requests. This model works via the following process,

  • Initialize the following optimization parameters of GWO,

    1. o

      Maximum iterations allowed for optimization (\({N}_{i}\))

    2. o

      Maximum Wolves to be used for optimization (\({N}_{w}\))

    3. o

      The selected learning rate for the optimization process (\({L}_{r}\))

    4. o

      The current capacity of all VMs (\(C(VM)\))

  • To initialize the process, mark all the optimizer Wolves into the 'Delta' category

  • Evaluate each iteration, and scan all Wolves via the following process,

    • Check if Wolf’s current category is not ‘Delta’, then skip it and go to the next Wolf in sequence

    • Else, modify Wolf's configuration via the following process,

      • Stochastically modify the capacity of each VM via Eq. 6,

        $$C{\left(VM\right)}_{New}=C\left(VM\right)+STOCH\left(-{L}_{r}, {L}_{r}\right)\dots $$
        (6)

        Where, \(STOCH\) determines a stochastic process, which is used to generate numbers between the given range sets.

      • The value of capacity \(C(VM)\) is evaluated for every VM, via Eq. 7 as follows,

        $$C\left(VM\right)=\sum_{i=1}^{{N}_{PE}}\frac{B{W}_{i}}{Max\left(BW\right)}+\frac{MIPS}{Max\left(MIPS\right)}+\frac{RAM}{Max\left(RAM\right)}\dots$$
        (7)

        where, \({N}_{PE}\) represents the Number of Processing Elements present with the VM, while, \(MIPS, BW \& RAM\) represents the processing speed of the VM in millions of instructions per second, its bandwidth, and the RAM available with the VM for scheduling purposes.

      • Based on this capacity, estimate cloud utilization factor (\(CUF\)) for the entire configuration via Eq. 8,

        $$CUF=\frac{\sum_{i=1}^{{N}_{VM}}C{\left(VM\right)}_{i}}{\sum_{j=1}^{{N}_{T}}CR{\left(T\right)}_{j}}\dots$$
        (8)

        where \({N}_{VM} \& {N}_{T}\) represents the number of VMs, and the number of tasks to be executed on the VMs respectively, while \(CR(T)\) represents the computational requirements of the task, which are evaluated via Eq. 9,

        $$CR\left(T\right)=\frac{MS}{Max(MS)}+\frac{DL}{Max(DL)}\dots$$
        (9)

        where, \(MS \& DL\) represents the make-span and deadline of the task respectively, which are combined for evaluation of task scheduling optimizations.

    • Evaluate this value for each Wolf, and then estimate the iteration threshold via Eq. 10,

      $${f}_{th}=\sum_{i=1}^{{N}_{w}}CU{F}_{i}*\frac{{L}_{r}}{{N}_{w}}\dots$$
      (10)

  • At the end of each iteration, reconfigure Wolves via the following process,

    1. o

      Mark Wolf as ‘Alpha’, if \(CUF>2*{f}_{th}\)

    2. o

      Else, mark Wolf as ‘Beta’, if \(CUF>{f}_{th}\)

    3. o

      Else, mark Wolf as ‘Gamma’, if \(CUF>{L}_{r}*{f}_{th}\)

    4. o

      Else, mark Wolf as ‘Delta’, and continue the optimization process

This process is repeated for all iterations, and the final configuration of the VM is evaluated based on the highest fitness of wolf and is used for the scheduling process. these configurations along with task sequences are given to a league championship algorithm (LCA), which assists in optimizing its performance for real-time use cases. This LCA Model works via the following process,

  • Initially set up all LCA parameters as follows,

    1. o

      Number of Leagues (\({N}_{l}\))

    2. o

      Number of Seasons (\({N}_{s}\))

    3. o

      The learning rate for the model (\({L}_{r}\))

    4. o

      Number of VMs that contest in the league (\({C}_{VM}\))

  • Initially generate all leagues via the following process,

    1. o

      Stochastically generate VM sequences and map tasks to each of the VMs. Based on this map** evaluate VM score (\({s}_{i}\)) via Eq. 11,

      $${s}_{i}=\frac{\sum {S}_{task}}{\sum C(VM)}+\frac{\sum B{W}_{task}}{\sum B}+\frac{\sum {RAM}_{task}}{\sum R}+\frac{\sum {DL}_{task}}{\sum {N}_{PE}*\frac{R}{B}}\dots$$
      (11)

      where \({S}_{task}, B{W}_{task}, RA{M}_{task}, and D{L}_{task}\) represent task size, bandwidth needed to schedule task, RAM needed for scheduling, and deadline of the task, while \(R, B and C\) represents RAM and Bandwidth of the VMs, which are used for the scheduling process.

    2. o

      Perform this task twice, and select the VM that has the minimum score via Eq. 12,

      $${s}_{out}=Min\left(\bigcup {s}_{i}\right)\dots$$
      (12)

  • Repeat this process for all leagues, and identify configurations with minimum score levels.

  • Now, iterate through all seasons, and check all leagues via the following process,

    • Select two stochastic leagues, and compare their score levels.

    • Mark the league with a higher score level as 'Winner', while modifying other leagues via the following process,

      • Stochastically replace \({L}_{r}*{N}_{VM}\) VM sequences in the underlying league with VM sequences from the ‘Winner’ league via Eq. 13,

        $$S\left(New\right)=S\left(Winner\right)\dots$$
        (13)

        Where, \(S\left(New\right) \& S\left(Winner\right)\) represents stochastically replaced VM sequences from the 'Winner' league to the target league, thereby assisting in the deployment of an incremental learning process.

      • Repeat this process for all seasons, and continuously modify league configurations.

At the end of the final season, identify the league with a minimum score, and use its VM sequences for scheduling tasks. Due to this, the scheduling model can map VMs to tasks via deadline and dependency awareness. The performance of this model was evaluated in terms of different statistical parameters, under real-time VM and task configurations. This performance was compared with various state-of-the-art models and can be observed in the next section of this text.

4 Result evaluation and comparative analysis

From the discussion about the proposed model, it can be observed a combination of GWO with LCA is capable of incorporating deadline awareness, SLA enforcement, and incremental optimization under dependent task types. To validate this, the proposed model was evaluated in terms of its task execution delay (D), scheduling efficiency (SE), deadline hit ratio (DHR), and energy efficiency (E) under different VM and task configurations. This performance was compared with WOA [13], MT DRL [16], and DNN [22]. To perform this comparison, configurations for different VM and task types were extracted from parallel workloads archive (PWA) which can be accessed via https://www.cs.huji.ac.il/labs/parallel/workload, and can be used with open-source licenses. These logs consist of a large number of task configurations, out of which Sandia Ross cluster logs, San Diego Supercomputer Centre (SDSC) Blue Horizon logs, Lawrence Livermore National Lab’s Linux Cluster Logs, Potsdam Institute for Climate Impact Research (PIK) IBM iDataPlex Cluster logs, and Intel Netbatch logs were used for the evaluation process.

The proposed model was evaluated using the CloudSim simulator, which assisted in the formation of virtual machines (VM), task scheduling processes and performance evaluation of different model parameters. These datasets were combined to form a total of 500 k tasks, which were evaluated on 400 VMs with standard configurations. Based on this evaluation strategy, the mean delay of execution (D) for different numbers of Tasks (NT) can be observed in Table 2.

Table 2 Task execution delay evaluated for different numbers of tasks
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Based on this evaluation and Fig. 3, it can be observed that the proposed model showcases 8.5% faster execution performance when compared with WOA [13], 5.3% faster than MT DRL [16], and 6.5% faster than DNN [22] under multiple evaluation scenarios. This is possible due to the integration of low-complexity LCA and GWO Models, that assist in the high-speed map** of tasks with VMs of different configurations.

Fig. 3
figure 3

Task execution delay evaluated for different numbers of tasks

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Based on a similar evaluation strategy, the deadline hit ratio (DHR) was evaluated via Eq. 14 as follows,

$$DHR=\frac{{N}_{{t}_{d}}}{{T}_{t}}\dots$$
(14)

where, \({N}_{{t}_{d}}\) represents the number of tasks executed under the required deadline, while \({T}_{t}\) represents the total number of tasks executed by the VMs of different configurations. The values of DHR were tabulated in Table 3 as follows,

Table 3 Deadline hit ratio evaluated for different numbers of tasks
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Based on this evaluation and Fig. 4, it can be observed that the proposed model showcases 2.5% higher DHR when compared with WOA [13], 2.4% higher DHR than MT DRL [16], and 2.6% higher DHR than DNN [22] under multiple evaluation scenarios. This is possible due to the integration of deadline awareness in both LCA and GWO Models, which assist in map** VMs with better DHR performance levels. Similarly, the scheduling efficiency is evaluated via Eq. 14 and is a measure of the computational efficiency of the scheduling (E) model under different configurations.

$$E=\frac{NC{C}_{opt}}{NCC}\dots$$
(15)

where, \(NC{C}_{opt}\) represents the optimum number of computational cycles that must be used for scheduling the tasks, while \(NCC\) represents the total computational cycles required to execute the tasks using given solutions. Based on this evaluation, scheduling efficiency is tabulated in Table 4 as follows,

Fig. 4
figure 4

Deadline Hit Ratio evaluated for different numbers of tasks

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Table 4 Scheduling efficiency for different models
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Based on this evaluation and Fig. 5, it can be observed that the proposed model showcases 9.5% higher scheduling efficiency when compared with WOA [13], 12.4% higher scheduling efficiency than MT DRL [16], and 10.5% higher scheduling efficiency than DNN [22] under multiple evaluation scenarios. This is possible due to the integration of deadline awareness along with makespan, bandwidth, and other task and VM-specific parameters in both LCA and GWO Models, that assist in map** VMs with better scheduling efficiency performance levels. Similarly, the energy needed for map** tasks to VMs was evaluated and tabulated in Table 5 as follows,

Fig. 5
figure 5

Scheduling efficiency for different models

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Table 5 The energy needed for scheduling under different numbers of tasks
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Based on this evaluation and Fig. 6, it can be observed that the proposed model showcases 24.8% lower energy consumption when compared with WOA [13], 19.4% lower energy consumption than MT DRL [16], and 3.5% lower energy consumption than DNN [22] under multiple evaluation scenarios. This is possible due to the use of low complexity LCA and GWO Models, which reduce energy requirements when evaluated for heterogeneous task scenarios. Due to these improvements, the proposed model is capable of deployment for large-scale task scheduling application use cases.

Fig. 6
figure 6

The energy needed for scheduling under different numbers of tasks

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5 Conclusion and future scope

The proposed model fuses GWO and LCA to enforce service level agreements (SLA) at both the task level and VM level, which assists in the identification of optimum map** between dependent tasks and heterogeneous VM types. The model also incorporates deadline awareness along with dependency awareness, which assists in improving the efficiency of map** for large-scale task sets. Due to these optimizations, the proposed model was able to 8.5% faster execution performance when compared with WOA [13], 5.3% faster than MT DRL [16], and 6.5% faster than DNN [22] under multiple evaluation scenarios. This allows the model to be deployed for high-speed scheduling use cases. The model was also observed to achieve 2.5% higher DHR when compared with WOA [13], 2.4% higher DHR than MT DRL [16], and 2.6% higher DHR than DNN [22], while it was also observed to have 9.5% higher Scheduling Efficiency when compared with WOA [13], 12.4% higher scheduling efficiency than MT DRL [16], and 10.5% higher Scheduling Efficiency than DNN [22] under multiple evaluation scenarios. This is possible due to the integration of deadline awareness along with makespan, bandwidth, and other task and VM-specific parameters in both LCA and GWO Models, that assist in map** VMs with better DHR and scheduling efficiency performance levels. In terms of energy consumption, the proposed model was observed to consume 24.8% lower energy when compared with WOA [13], 19.4% lower energy than MT DRL [16], and 3.5% lower energy than DNN [22] under multiple evaluations scenarios. This is possible due to the use of low complexity LCA and GWO Models, which reduce energy requirements when evaluated for heterogeneous task scenarios. Due to these improvements, the proposed model is capable of deployment for large-scale task scheduling application use cases. In the future, the model's performance must be validated on large-scale datasets and can be improved via the integration of deep learning techniques that can pre-empt task requests, and modify VM performance under large-scale scenarios. The models' performance can also be extended via the use of a hybrid fusion of different Q-Learning and incremental learning models, which can assist in tuning its performance for multiple task sets under heterogeneous cloud configurations.

5.1 Limitations of this work

  1. 1.

    Simplified model assumptions The paper does not explicitly mention the assumptions made in the proposed model. It is important to consider the simplifications or assumptions made regarding the task characteristics, VM capabilities, and system dynamics. These assumptions might not capture the full complexity of real-world cloud systems, potentially limiting the generalizability of the models.

  2. 2.

    Lack of real-world implementation and validation While the paper presents promising results based on evaluations using heterogeneous task datasets, it does not mention if the proposed model has been implemented and validated in real-world cloud environments. The absence of real-world implementation and validation might raise questions about the practical feasibility and effectiveness of the model in actual cloud deployments.

  3. 3.

    Limited comparison with state-of-the-art models The paper briefly mentions the evaluation of the proposed model against other models. However, it does not provide a detailed comparison with state-of-the-art models or existing state-of-the-art techniques in task scheduling. A more comprehensive comparison with a wider range of existing models would provide a better understanding of the advancements and contributions offered by the proposed models.

  4. 4.

    Lack of sensitivity analysis The paper does not mention conducting sensitivity analyses to assess the robustness and stability of the proposed model. Sensitivity analyses could help identify the impact of different parameters, variations in workload characteristics, and changes in system configurations on the model's performance. The absence of sensitivity analysis limits the understanding of the model's behavior under various scenarios.

  5. 5.

    Limited discussion on model complexity and overhead The paper does not explicitly discuss the computational complexity or overhead associated with implementing and executing the proposed model. The potential impact of the model's complexity on the overall system performance, scalability, and resource utilization is not addressed. Understanding the computational requirements and potential overhead is essential for assessing the practical viability of the models.

  6. 6.

    Lack of open-source implementation or reproducibility The paper does not mention the availability of an open-source implementation of the proposed model or provide detailed information on how to reproduce the experiments and results. This can hinder the reproducibility and transparency of the research, making it challenging for other researchers to validate or build upon the proposed models.