Cloud computing is an extremely important infrastructure used to perform tasks over processing units. Despite its numerous benefits, a cloud platform has several challenges preventing it from carrying out an efficient workflow submission. One of these is linked to task scheduling. An optimization problem related to this is the maximal determination of cloud computing scheduling criteria. Existing methods have been unable to find the quality of service (QoS) limits of users- like meeting the economic restrictions and reduction of the makespan. Of all these methods, the Heterogeneous Earliest Finish Time (HEFT) algorithm produces the maximum outcomes for scheduling tasks in a heterogeneous environment in a reduced time. Reviewed literature proves that HEFT is efficient in terms of execution time and quality of schedule. The HEFT algorithm makes use of average communication and computation costs as weights in the DAG. In some cases, however, the average cost of computation and selecting the first empty slot may not be enough for a good solution to be produced. In this paper, we propose different HEFT algorithm versions altered to produce improved results. In the first stage (rank generation), we execute several methodologies to calculate the ranks, and in the second stage, we alter how the empty slots are selected for the task scheduling. These alterations do not add any cost to the primary HEFT algorithm, and reduce the makespan of the virtual machines’ workflow submissions. Our findings suggest that the altered versions of the HEFT algorithm have a better performance than the basic HEFT algorithm regarding decreased schedule length of the workflow problems.
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Introduction
Cloud computing works on a “pay for each use” system where clients access the cloud services without having full knowledge of the distribution policies and hosting specifics [1‐3]. This provides global on-request access to a shared pool of assets such as storage space, computing servers, and web facilities for a reduced time to shop for enterprises and determine the logical findings [4]. Clients can access these assets steadily with no stress and no need to communicate with the facility provider [5, 6]. The aim of cloud infrastructure is to provide an easy-to-use workspace for dynamic applications.
The workspace can be obtained when various computer hardware are integrated with software package services. These facilities allow clients to transmit their submissions in cyberspace through the indication of their execution, accessibility, and Quality of Service (QoS) necessities [7]. As a result of the different configuration, deployment, and arrangement necessities of such submissions, the approaches for asset management and task scheduling becomes basic in the development of the efficiency and effectiveness of the cloud framework [8, 9]. In a distributed framework, all the jobs may be imagined as executing the various tasks in it. These tasks are classified into dependent and independent tasks. While independent tasks can be performed concurrently by several Virtual Machines (VMs), dependent tasks have to be planned through the fulfilment of their precedence relationships. This can be presented as a Directed Acyclic Graph (DAG) where the graph vertices or nodes represent tasks, and edges represent links between the tasks [10, 11]. It is compulsory to perform tasks with precedence restrictions in a scheduling order that decreases the schedule makespan. NP-Complete is the discovery of the maximal results for a task scheduling challenge [10].
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Task scheduling issues can be classified into two primary classes: the deterministic and non-deterministic scheduling. The deterministic (compile-time) scheduling is sub-divided into the heuristics-based [12, 13] and Guided Random Search-Based (GRSB) [14‐16]. Deterministic task scheduling is also referred to as static scheduling. The GRSB algorithms (Genetic Algorithms) cost more than heuristics-based scheduling algorithms because the algorithms need more iterations to generate an enhanced schedule. The heuristics-based algorithms on the other hand, provide approximate solutions in record time. They can be categorized as duplication-related [17, 18], clustering-based [19, 20], and list-based [21‐23]. The duplication-based heuristics have higher time complexity, while clustering-based heuristics are suitable for homogeneous frameworks.
In this paper, we considered list-based heuristics because of their decreased duration and efficiency in delivering a shorter makespan. They work in two primary stages for task scheduling. In the first stage, calculation of rank is done for individual tasks, after that arranged in a descending order. In the second stage, we schedule the task with the highest rank value on the available machine. The Heterogeneous Earliest Finish Time (HEFT) procedure is the most popular among its counterparts for heterogeneous computing because of its high performance trade-off and low costs [24].
The following are the main contributions of this study:
We design and propose three altered versions of the HEFT algorithm for rank calculation and processor selection, and to reduce the duration for the task scheduling.
We lay out the challenge of task scheduling on heterogeneous machines and the cloud framework-related features for efficiently managing the specified tasks on the available VMs through the inclusion of the dependency restrictions among the tasks.
We analyse and compare the proposed algorithms with the basic HEFT algorithm, the AVCT (Average Computation Cost) algorithm on arbitrarily created DAGs of real-world applications.
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The novelty of the proposed method lies in the different methodologies in the two stages of the HEFT algorithm. In the first stage (rank generation), we execute several methodologies to calculate the ranks, and in the second stage, we alter how the empty slots are selected for the task scheduling. These alterations do not add any cost to the primary HEFT algorithm, and reduce the makespan of the virtual machines’ workflow submissions. From the computational analyses and experiments we carried out, we observed the significant differences between the performance of the basic HEFT algorithm (AVCT approach) and our proposed altered versions MXCT (Maximum Computation Cost), MNCT (Minimum Computation Cost), and AVBS (Average Computation Cost and Best Empty Slot), regarding the schedule makespan that was produced. This implies that the scheme used affects the schedule length. We also observed that using the average value scheme for rank calculation and selection of the first empty slot is not always the best option. Our findings indicate that our proposed improved versions perform better than the basic HEFT algorithm regarding the decreased schedule length of the workflow problems running on the virtual machines.
The rest of this paper is organized as follows: Section 2 reviews the related literature. Section 3 briefly introduces multiprocessor task scheduling, and describes the problem model. Section 4 explores the HEFT algorithm and the proposed methodology. Section 5 discusses the experimental results. Finally, Section 6 concludes the paper.
Literature review
The authors in [5] proposed a community-based cloud framework to manage emergencies. Its aim is to coordinate and oversee different organizations and combine large amounts of heterogeneous data in order to deploy logistics and personnel to search and rescue. The framework can also be utilized in the assessment of damage. In [6], to make clear the fundamentals of cloud computing, the authors explained the features of the areas which distinguish cloud computing from other research areas. They mainly compared cloud computing to grid computing and gave insights to the essentials of both concepts. The authors in [7] proposed a toolkit which allows the simulation and modelling of application provisioning and cloud computing systems. The aim was to achieve resource performance and application workload models under different user and system configurations. In [8], the authors provided a brief but comprehensive overview into speech bifurcation, both into series and single words with unrestricted speech, and presented a methodology which converts vocal signals into text. The authors in [9] proposed a game theoretic framework for the management of dynamic cloud services, including allocation of resources and assignment of tasks, with the aim of providing reliable cloud services. The proposed framework would assist cloud service providers in the management of their resources in a cloud computing environment.
In [10], the authors presented an algorithm for scheduling of tasks that makes use of the standard deviation of the estimated task execution time on the resources available in the computing environment. This approach considers the heterogeneity of the task and significantly reduces the execution time of a specific application. The authors in [11] proposed improved versions of algorithms specifically for heterogeneous systems used for compilation of time list scheduling where the priorities of the tasks are computed. In [14], the authors examined the dynamic scheduling of tasks in a multiprocessor system in order to obtain a viable solution making use of genetic algorithms integrated with popular heuristics. The experimental results showed that the genetic algorithm can used for task scheduling to meet deadlines. The authors in [15] designed a genetic evolution-based algorithm to find an optimal solution for task scheduling in a multiprocessor system in record time. In [16], the authors provided a comprehensive overview of genetic algorithms, its techniques, tools and research results which would allow the algorithms to be applied to real-world problems in different fields. The authors in [12] presented two novel algorithms for heterogeneous processors with the goal of attaining speedy scheduling time and high performance. The experimental results revealed that the proposed algorithms performed better than existing algorithms in terms of quality and cost of schedules.
In [13], the authors proposed an algorithm for scheduling tasks in a multicore processor system which significantly decreases the recovery time in case the system fails. The proposed algorithm is based on a check pointing method. The authors in [17] proposed a cutting-edge duplication-based algorithm to reduce the schedule makespan and delay of the task execution. The proposed algorithm schedules tasks with the lowest redundant duplications. In [18], the authors presented a list scheduling algorithm to consider the heterogeneity of communication and computation. They also proposed a novel approach for priority computation which considers the difference in performances in the target computing system making use of variance. The authors in [23] proposed a ranking algorithm based on the parent–child relationship and the priority assignment stage of the HEFT algorithm designed for task scheduling in a multiprocessor system. The proposed algorithm works on the keywords’ density, the age of the webpage, and the amount of node successors.
The problem model
Multiprocessor task scheduling
Previously, various researchers have proposed several list scheduling procedures to resolve the task scheduling issue. The HEFT algorithm [12] estimates the tasks’ ascendant rank values with the average communication and computation cost. The Standard Deviation Based Task Scheduling (SDBATS) [10] uses the standard deviation of transmission and computational expenses to approximate ascendant rank values. The Critical Path on a Processor (CPOP) [12] adds the descendant and ascendant rank values to create an important track and precedence column. During each stage of the DAG, the Performance Effective Task Scheduling (PETS) [25] includes the average computation cost, data transmission and reception cost to fix the tasks’ rank values. The Duplication based Heterogeneous Earliest Finish time (HEFD) [18] uses task variance as a feature of heterogeneity to approximate the transmission and computation costs among tasks. Predict Earliest Finish Time (PEFT) [24] is created on the look-forward technique, and approximates the descendent tasks through the calculation of an Optimistic Cost value Table (OCT). The OCT is a 2D array whose columns and rows indicate the number of processors and tasks, respectively. Each element in the OCT (\({t}_{i}\),\({p}_{j}\)) shows the optimum of the shortest ways of \({t}_{i}\) offspring tasks to the leaving node, noting that machine \({p}_{j}\) is nominated for task \({t}_{i}\). All these algorithm calculations rely on standard deviation or the average of task weights on accessible machines. They do not include the framework heterogeneity. The most recent effort shows how standard deviation includes task and heterogeneity on existing machines. The various task scheduling algorithms and their limitations, tools, and parameters were analyzed in [26, 27].
We believe that the HEFT algorithm’s efficiency can be improved by using three versions of the basic HEFT algorithm. This paper proposes two schemes of the first stage (rank calculation), and a different approach for selection of the empty slot. We examined the schedules makespan generated by each version and regarded the minimum length makespan as the result. Although it slightly increases the algorithm’s costs, it is a trade-off between time complexity and performance. Our evaluation illustrates that the proposed versions produce high value schedules in terms of higher efficiency and decreased schedule length.
The model and objective function
The model of the scheduling structure consists of a target computation architecture, a submission (application), and scheduling standards. A problem can be indicated as a (DAG) = G (T, E, R, C) (see Fig. 1), where \(T = \left\{ {t}_{i},i = \mathrm{0,1},2,...,n-1\right\}\) is a set of n tasks [28‐30]. Symbol E indicates a set of edges between tasks \({E = \{ e}_{i,j}, i <j \}\), and \({e}_{i,j}\) represents the precedence limitations between two linked tasks. Tasks\({t}_{i}\),\({t}_{j}\) ∈ T, which are connected to each other, signifying the precedence limitation of task \({t}_{j}\) being dependent on task \({t}_{i}\) for its operation. It illustrates that task \({t}_{i}\) results will be applied as the input value for task \({t}_{j}\), and \({t}_{j}\) cannot begin its implementation before\({t}_{i}\). The task \({t}_{j}\) is the heir of \({t}_{i}\) and \({t}_{i}\) is the predecessor of \({t}_{j}\). Here, \(R\) signifies a 2D matrix of size\(v\times m\), and \({r}_{ij}\) in \(R\) denotes the estimated operating time of \({v}_{i}\) on \({j}^{th}\) processor. A matrix \(CmC(t\times t)\) represents the communication cost between any two tasks \({t}_{i}\) and\({t}_{j}\). In the graph below, a task with no ancestor is referred to as an entry task, and a task that has no descendant is referred to as an exit (leaving) task.
Fig. 1
A model DAG
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A cloud framework consists of a set \(VM = \{ {vm}_{i} where i = \mathrm{0,1},2,\dots .m-1 \}\) of m VMs that self-regulate and are linked over a high-rate network as illustrated in Fig. 2. The Data Transfer Frequency (DTF) may change because of the modified network bandwidth of cloud architecture. DTF can be written as an \(m \times m\) two-dimensional array, and among any two VMs as\(DTFm\times m\). The Probable Execution Cost (PEC) can be indicated by an extra 2D array \(PECn\times m\) to carry out a task \({t}_{i}\) on a VM \({vm}_{j}\), where \(0 <= i<= n-1\) and \(0 <= j <= m- 1.\) The PEC builds on the VM’s speed of computation and can be different for each VM.
Fig. 2
Task scheduling in a cloud-based framework
×
The communication cost between \({vm}_{x}\) and \({vm}_{y}\) depends on two aspects. The first is the processors’ installed frequency on both sides of communications. The second is the frequency’s correspondence cost value. We assume that each VM workstation can transmit to other workstations of a different VM with no conflict on the transmission channel. We also assume that tasks planned on the similar VM have no cost of communication among them.
The aim of the task arrangement challenge is to organize all the tasks of a given submission to machines for the application’s completion time to reduce, fulfilling all the precedence limitations.
Methodology
Review of the HEFT algorithm
The HEFT algorithm is designed to schedule the DAG tasks into heterogeneous processors. The HEFT procedure has two basic stages: the rank generation and the processor selection stages. In the first stage, HEFT carries out a calculation of ranks for all the tasks and prioritizes them according to a descending order of their rank values. It is initiated by assigning weights to each DAG node and edge for rank calculation, based on the average communication and computation cost.
In the second stage, HEFT chooses the tasks based on their priority values and schedules each nominated task on the most suitable processor, which can decrease the schedule length of the task. HEFT also arranges the tasks in an empty slot between two previously planned tasks on a processor if the precedence constraints are observed. The HEFT algorithm looks for an empty slot on a processor until it finds one that can carry the computation cost of the chosen task.
HEFT procedure makes use of average communication and computation costs as DAG weights for calculation of ranks, and selection of processor. The first empty slot is always considered for the task scheduling. In some cases, however, the average cost of computation and selection of the first empty slot may not be a good solution. Consider the sample DAG in Fig. 3. The cost of probable execution of every task on three different VMs is shown in Table 1. The edges of the sample DAG are labelled with the average cost of communication.
Fig. 3
Model task graph (using 10 tasks)
Table 1
Probable Execution Cost (PEC) matrix
Task
VM1
VM2
VM3
T1
10
6
9
T2
10
23
23
T3
10
9
7
T4
18
17
18
T5
5
2
23
T6
7
5
16
T7
17
9
17
T8
40
16
19
T9
18
9
8
T10
26
10
24
×
In this example, if prioritization of tasks is done using the average cost of computation of all three VMs (as in the basic HEFT), then the scheduling order would be \({T}_{1},{T}_{2},{T}_{3},{T}_{4}, {T}_{6},{T}_{8},{T}_{5},{T}_{10},{T}_{7},{T}_{9},\) and the schedule length would be 98. Figure 4 illustrates this. Assume the assigning of priorities is done using the optimal value of the cost of computation over the three VMs on which a task may be executed. In such a situation, the task scheduling order would be \({T}_{1},{T}_{2},{T}_{3},{T}_{4}, {T}_{6},{T}_{8},{T}_{5},{T}_{10},{T}_{9},{T}_{7},\) and the schedule length would be 96. Figure 5 illustrates this. This is lesser than the schedule length obtained by the basic HEFT algorithm. Similarly, if priorities are assigned using the minimum value of the cost of computation over the three VMs on which a task may operate, and then the task scheduling length and order would be the same as found in the basic HEFT algorithm. This is illustrated in Fig. 6.
Fig.4
Scheduling of DAG with original HEFT algorithm. (Use of Average Computation Cost in Rank Calculation & Schedule length is 98)
Fig.5
Scheduling of DAG with modified HEFT Algorithm. (Use Of maximum Computation Cost in Rank Calculation & Schedule length is 96)
Fig.6
Scheduling of DAG with modified HEFT Algorithm. (Use of minimum computation cost in rank calculation & schedule length is 98)
×
×
×
Conversely, if the processor selection stage is altered, the schedule length obtained may change. Here, the calculations of ranks are done using the average computation cost value. In the above example, if we choose an empty slot in which a task has the lowest finish time instead of the initial slot, the schedule length would go down to 89 as task \({T}_{5}\) is now scheduled on VM2 (22 to 27, see Fig. 7) instead of VM1 (24 to 26 in case of the basic HEFT, see Fig. 4). We find that the average cost of computation value for rank calculation and selection of the first empty slot for scheduling of tasks are not the best choices. The schedule lengths gotten may change.
Fig.7
Scheduling of DAG with modified HEFT algorithm. (Use Of min schedule length idle slot in processor selection & Schedule length is 89)
×
The proposed methodology for cloud environment
We propose the altered versions of the basic HEFT algorithm to acquire improved results for task arrangement challenges in the cloud environment. Figure 8 illustrates this. In the first stage (rank generation), we execute a distinct methodology, and in the second stage (resource selection), we alter the mode of selection of empty slots for task scheduling. These modifications do not incur any additional cost compared to the basic HEFT algorithm. The changes we propose in each stage are explained below.
Fig. 8
The complete HEFT algorithm
×
Rank generation stage
In this stage, each task’s precedence should be decided with the descendant or ascendant rank value. The formulas below calculate the task’s upward rank:
If Task \({T}_{i}\) is an exit task, the rank of task \({T}_{i}\) is defined by the Rank Function:
where \({w}_{i}^{k}\) is the computation amount of task \({T}_{i}\) on resource \(k\) and \(1\le k\le n\), \(suc({T}_{i})\) is the set of the direct successors of task \({T}_{i}\) and \(avg({comm}_{i,z})\) is the average cost of communication between the tasks \({T}_{i}\) and \({T}_{z}\). Here, \(f\) represents a function which could be the maximum, minimum or average value of the cost of computation. As the rank is calculated recursively from the exit node, it is referred to as the Upward Rank value.
If Task \({T}_{i}\) is an entry task, the rank of Task \({T}_{i}\) is defined by the Rank Function:
where, \(pre({T}_{i})\) is the group of direct predecessor of Task \({T}_{i}\). After calculating the each task rank, a task list is created through the arrangement of the tasks according to their descending order of \({Rank}_{up}\).
The Resource Selection Stage.
In this stage, we propose a novel approach to determine the empty slot for the selected task. Here, the search for an appropriate empty slot for a task on a resource starts when all the ancestors of Task \({T}_{i}\) transmit the required input data to that resource. The search continues until an empty slot which can hold the cost of computation of Task \({T}_{i}\) and in which the selected Task \({T}_{i}\) has the lowest finish time is found. In Fig. 8 complete algorithm of HEFT is presented.
Results and discussion
In this paper, we created a system that complements the basic HEFT algorithm, and improves the processor selection and prioritization of task processes. Input fed into the system includes the cost of communication, the Probable Execution Cost Matrix, the DAG showing dependencies, and the number of VMs and tasks. To assess the performance of our algorithm, we generated varied scheduling problems and attempted to solve them with the altered versions of the HEFT algorithm, as well as the basic HEFT algorithm.
We designed an automated system to make scheduling issues of different sizes. This is done to prevent partiality when offering values of different parameters. Our system assigns the parameters to random values in suitable ranges. We created problems for our experiments with the following features:
Size of the problem (the number of tasks) which ranges from 50 to 80 with an interval of 5.
The number of each task’s successor with the exception of the exit task which is an arbitrary number that ranges from 0 to 10.
The task implementation time, this is an arbitrary number which ranges from 1 to 20.
The task communication time, this is an arbitrary number between 1 and 50.
The amount of VMs is considered as either 4 or 5.
In all the DAGs, the tasks’ ranks are calculated using the upward rank calculation formula.
Investigation on the rank generation stage
To calculate a particular value for the method \(f\) in Rank Function, we use three techniques:
(i)
AVCT (Average Computation cost) approach: This returns the average task cost of computation over every VM. It is used in the basic HEFT algorithm.
(ii)
MXCT (Maximum computation cost) approach: This returns a maximum task cost of computation over every VM.
(iii)
MNCT (Minimum computation cost) approach: This returns a minimum task cost of computation over every VM.
In all the approaches, the first empty slot which can hold the task cost of computation is studied (as in the basic HEFT). We operate the basic HEFT algorithm (AVCT approach) and our proposed approaches (MNCT and MXCT approach) on 100 different problems with different Problem Identification Numbers (PIN) 800 to 899 for problem size 80. The experimental results reveal that for 33% of problems, all the algorithms have equal length of schedule. For the remaining 67%, the MXCT approach provides equal length of schedule in 36%, better length of schedule in 39%, and worse length of schedule in 25% of the cases compared to the AVCT approach. The differences in the schedule lengths gotten from the AVCT and MXCT algorithms are illustrated in Fig. 9.
Fig. 9
Variations in schedule length obtained from the AVCT approach and MXCT approach
×
Similarly, for the remaining 67% of the problems, the MNCT approach provides equal length of schedule lengths in 27%, better length of schedule in 40%, and worse schedule lengths in 33% of the cases in comparison to the AVCT approach. The differences in the schedule lengths gotten from the AVCT and MNCT algorithms are illustrated in Fig. 10. Table 2 compares the three approaches.
Fig. 10
Variations in schedule length obtained from the AVCT approach and MNCT approach
Table 2
Comparison of AVCT, MXCT and MNCT algorithms
Problem Percentage
Approaches
Outcomes
33%
AVCT
Equal Schedule Length
MXCT
MNCT
67%
MXCT Vs AVCT
36%
Equal Schedule Length
39%
MXCT Gives better Schedule Length
25%
MXCT Gives worse Schedule Length
MNCT Vs AVCT
27%
Equal Schedule Length
40%
MNCT Gives better Schedule Length
33%
MNCT Gives worse Schedule Length
×
From our analysis, we observed that there are noteworthy differences between the basic HEFT algorithm’s performance (AVCT approach), and the altered versions (MNCT and MXCT). We also observed that using an average value scheme for rank calculation is not always the best choice.
Investigation on the resource selection stage
We used two approaches to select an empty slot for task scheduling:
(i)
AVCT approach (the basic HEFT algorithm-average cost of computation and the first empty slot).
(ii)
AVBS (average computation cost and best empty slot) approach: This approach uses the average cost of computation to calculate the ranks and selects an empty slot where the selected task has the lowest finish time.
We took 100 sample problems of each size ranging from 50 to 80 with an interval of 5. Table 3 shows how we ran both algorithms on sample problems, and how the results were analysed. We observed that that AVBS algorithm has a better performance than the AVCT algorithm. The results from the experiment shows that the AVBS algorithm has a reduced average length of schedule in 86% problem sets and slightly greater average schedule length in 14% problem sets in comparison to the AVCT algorithm.
Table 3
Comparison of the AVCT and AVBS algorithms
Problem Size
Number of Resources
AVCT algorithm (Average of Hundred problems)
AVBS Algorithm (Average of hundred problems)
50
4
425.50
425.14
55
4
457.34
457.32
60
4
491.12
490.94
65
4
548.24
548.26
70
4
574.66
574.18
75
5
623.21
622.02
80
5
665.97
665.61
Conclusion
In cloud computing, scalable resources are offered as services to clients through the Internet. Thus, a cloud service provider has more clients to attend to in the cloud computing architecture. As a result of this, task scheduling is one of the biggest challenges in establishing a functional and efficient cloud computing environment. In this paper, we proposed different versions of the heuristic-based algorithm Heterogeneous Earliest Finish Time (HEFT) which carries out task scheduling and allocates resources in the cloud computing environment. On comparison of our proposed approach to other frameworks in terms of schedule length, we discovered that our approach performs better. We observed that the original HEFT algorithm ‘s efficiency can be enhanced by choosing the best result from each approach ‘s schedules. Although this may lead to the algorithm having a higher cost, it is a trade-off between cost and performance. We may further consider the Nature-inspired optimization algorithm-based scheduling for more effective task scheduling in the cloud environment. The existing work can be extended for dynamic task scheduling in the future.
Acknowledgements
This work was supported by UTM Research Fellow (No.00P27), the National Natural Science Foundation of China (No.61862051), the Science and Technology Foundation of Guizhou Province (No.[2019]1299, No.ZK[2022]449), the Top-notch Talent Program of Guizhou province (No.KY[2018]080), the Natural Science Foundation of Education of Guizhou province (No.[2019]203) and the Funds of Qiannan Normal University for Nationalities (No. qnsy2019rc09). The Educational Department of Guizhou under Grant NO. KY[2019]067.
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