an energy efficient algorithm for workflow scheduling in...
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J Grid Computinghttps://doi.org/10.1007/s10723-019-09490-2
An Energy Efficient Algorithm for Workflow Schedulingin IaaS Cloud
Vishakha Singh · Indrajeet Gupta ·Prasanta K. Jana
Received: 17 July 2018 / Accepted: 16 August 2019© Springer Nature B.V. 2019
Abstract Energy efficient workflow scheduling is thedemand of the present time’s computing platformssuch as an infrastructure-as-a-service (IaaS) cloud.An appreciable amount of energy can be saved ifa dynamic voltage scaling (DVS) enabled environ-ment is considered. But it is important to decreasemakespan of a schedule as well, so that it may notextend beyond the deadline specified by the clouduser. In this paper, we propose a workflow schedul-ing algorithm which is inspired from hybrid chemicalreaction optimization (HCRO) algorithm. The pro-posed scheme is shown to be energy efficient. Apartfrom this, it is also shown to minimize makespan.We refer the proposed approach as energy efficientworkflow scheduling (EEWS) algorithm. The EEWSis introduced with a novel measure to determine theamount of energy which can be conserved by consid-ering a DVS-enabled environment. Through simula-tions on a variety of scientific workflow applications,we demonstrate that the proposed scheme performsbetter than the existing algorithms such as HCRO and
V. Singh · P. K. JanaDepartment of Computer Science & Engineering, IndianInstitute of Technology (ISM), Dhanbad 826004, Indiae-mail: [email protected]
Prasanta K. Janae-mail: [email protected]
I. Gupta (�)Department of Computer Science Engineering, BennettUniversity, Greater Noida, 201310, Indiae-mail: [email protected]
multiple priority queues genetic algorithm (MPQGA)in terms of various performance metrics includingmakespan and the amount of energy conserved. Thesignificance of the proposed algorithm is also judgedthrough the analysis of variance (ANOVA) test and itssubsequent LSD analysis.
Keywords Workflow scheduling ·Energy conservation ·Chemical reaction optimization ·Makespan · Cloud
1 Introduction
Workflow scheduling in cloud computing continues toattract the attention of research fraternity, as it lever-ages the full strength of distributed computing [1–10].A real world workflow application consists of a set of alarge number of interdependent tasks. Such workflowscan be represented as directed acyclic graphs (DAGs),which are executed on infrastructure as a service(IaaS) cloud to run the applications. An IaaS cloud isa deployment model used in cloud computing whichprovides computational resources to the users for exe-cuting their applications. Scheduling of workflowsis the major concern for the cloud service provider(CSP) which furnishes IaaS cloud resources to itsusers on the basis of pay-as-you-go model. Workflowscheduling consists of two phases: 1) determining theexecution order of tasks without violating any of the
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task precedence constraints and 2) finding a suitabletask-to-VM (virtual machine) mapping which consistsof assigning the VMs to the tasks to achieve an optimalschedule. This is a well-known NP-hard problem [5,11]. Many algorithms have been developed which con-sider various performance issues such as resource utili-zation, makespan, cost, fault tolerance [12] and so on.
The concept of green cloud computing [10, 13, 14]has continued to gain impetus since the last few years,as the data centers consume huge amount of energy.This in turn leads to the generation of excessive carbonfootprint, which is very harmful in the perspective ofthe environment. So, the researchers are concentratingon designing approaches to reduce energy consump-tion while scheduling workflows [15]. The use of adynamic voltage scaling (DVS) enabled environmenthas been a quantum leap in this regard [14]. DVSis an energy controlling technique for the computerprocessors which is based on fluctuating the voltageto achieve energy efficiency. Another major objec-tive of workflow scheduling is the minimization ofmakespan (i.e, the overall execution time of a givenworkflow). But both these objectives are conflictingto each other. This means that the higher is the con-sumption of energy, the lower is the makespan andvice versa. Therefore, a trade off is needed to strike abalance between makespan and energy consumption.
In this paper, we propose a workflow schedulingalgorithm that aims at maximization of energy conser-vation as well as minimization of makespan. Vari-ous researches have been carried out considering theaforementioned objectives. But some of them have notconsidered an important aspect of scheduling namely,CPU performance variability [5] (i.e., the processorsdo not work with their full efficiency all the time). Itis noteworthy that there may be a variability of 24% inthe performance of the CPU [16]. There are also manyreal world factors that affect the process of scheduling,like the VM boot time, VM shut down time, etc, whichare also left unattended by most of the researchers. Inthe proposed approach, we consider all such aspects.
Recently, a method called hybrid chemical reac-tion optimization (HCRO) [17] has been proposed forworkflow scheduling which is a combination of twoother existing algorithms namely, chemical reactionoptimization (CRO) [18] and heterogeneous earliestfinish time (HEFT) [19]. Although HCRO is quiteefficient for makespan minimization, it does not con-sider any other important objectives such as reduction
of energy consumption, effective resource utilization,load balancing and so on.
The algorithm presented in this paper is inspiredfrom HCRO. However, the proposed method is shownto be more efficient with respect to minimization ofenergy consumption and the makespan. It has alsothe following notable differences with HCRO: 1)Besides makespan, the proposed approach also con-siders energy conservation by using a DVS-enabledenvironment. 2) It includes many aspects of real-timeworkflow scheduling such as CPU performance vari-ability, VM boot time, VM shut down time, etc, whichare not considered by HCRO. 3) It incorporates a dif-ferent criteria for including the new molecules in thecurrent population, to enhance the scheduling results.The existing HCRO technique lacks all these features.We call our proposed approach as energy efficientworkflow scheduling (EEWS).
Numerous simulation experiments have been con-ducted on the proposed scheme over various bench-mark scientific workflows and the results are com-pared with HCRO and the multiple priority queuesgenetic algorithm (MPQGA) [1]. The experimentalresults show that proposed algorithm EEWS performsbetter than these techniques. The main contributionsare summarized as follows:
• An efficient scheme is proposed for workflowscheduling with the aim of maximizing energyconservation and minimizing makespan.
• We introduce a new operator called on-wallpseudo-effective collision to exploit the benefitsof swap mutation. We also build up a new methodto modify the population.
• A novel measure is proposed to calculate theamount of energy that can be conserved whilescheduling workflows using a DVS-enabled envi-ronment.
• We perform extensive simulations on the pro-posed approach for the sake of testing its effi-cacy over MPQGA [1] and HCRO [17]. We alsoperform ANOVA [20] test and LSD analysis tovalidate the performance of the proposed method.
The paper is organized as follows. Survey of the exist-ing works is presented in Section 2. In Section 3,we discuss about the various models used in the pro-posed scheme followed by problem formulation. Theoverview of existing approach HCRO is presented inSection 4. We propose our approach in Section 5 and
An Energy Efficient Algorithm for Workflow Scheduling in IaaS Cloud
illustrate its performance and comparative studies withother approaches, in Section 6. Followed by this, weexpress our concluding remarks in Section 7.
2 Related Work
Objectives like makespan minimization and energyconservation have drawn the interest of manyresearchers in the area of workflow scheduling. Themethods developed for optimization problems can bebroadly classified into two groups: heuristics andmeta-heuristics. The heuristics are problem specific and theyemphasize only on a particular portion of search spacewhich is narrowed down using some greedy approach.Whereas meta-heuristics usually span a very large partof the solution space and have good exploration capa-bilities, which is a crucial aspect that helps in findingan optimal or a near-optimal solution [21].
Many heuristics have been proposed to tackle theproblem of energy optimization along with makespanminimization in scheduling workflows. In [19], theauthors had reported a heuristic called HEFT for min-imization of makespan. In this approach, each task isalloted to that particular VM (from the available poolof VMs), which minimizes its execution time. Durilloet al. [2] have suggested an extension of the HEFTalgorithm called multi-objective heterogeneous earli-est finish time (MOHEFT) that is capable of provid-ing suitable trade-offs between makespan and energyconsumption. Sun et al. [22] have proposed an energy-efficient framework called ”Re-Stream” for resourceallocation, that considers increasing energy efficiencyand decreasing response time in real time schedulingenvironment. The Re-Stream provides an intelligentbalance between energy efficiency and response timewithin a big data computing environment. Zong etal. [23] proposed two energy-efficient duplication-based scheduling algorithms to achieve both fastperformance and energy efficiency in clusters. Thismethod strives to balance makespan and energy sav-ings judiciously by task duplication if it helps inperformance without degrading energy efficiency.Thanavanich et al. [24] proposed two energy-awaretask scheduling algorithms called enhancing hetero-geneous earliest finish time (EHEFT) and enhancingcritical path-on-a processor (ECPOP) for achievingtime and energy efficiency. Yang et al. [25] proposedan energy aware importance-ratio-based stochastic
task scheduling (EISTS) algorithm, which maintains agood balance between the optimization of makespanas well as energy consumption. They claimed thatthe algorithm achieves shorter makespan when theimportance-ratio of makespan to energy consumptionis high and lesser energy consumption when the ratiois low. Juarez et al. [26] have proposed an algorithmwhich considers makespan and energy efficiency asits objectives and gives priority to one of them byusing an energy-performance importance factor issuedeither by the resource provider or the user. But nei-ther of these approaches consider the benefits that canbe procured by using a DVS-enabled environment fordecreasing energy consumption.
Apart from this, a number of approaches have triedto optimize energy consumption in a deadline con-strained environment, while scheduling workflows.In [27–30], the authors have used a state-of-the-arttechnique called dynamic voltage scaling (DVS) foroptimizing energy consumption. Xie et al. [30] haveproposed the downward energy consumption min-imization (DECM) algorithm in which they haveconsidered the objective as minimization of energyconsumption in a deadline constrained environmentby dividing the deadline among tasks. In [27], theauthors have proposed two deadline-constrained algo-rithms namely, non-DVFS energy-efficient scheduling(NDES) and global DVFS-enabled energy-efficientscheduling (GDES). These approaches mainly focuson the energy consumed and are less concerned withmakespan, as long as the deadlines are met.
Xu et al. [4] have proposed an energy efficientresource allocation (EnReal) algorithm to minimizeenergy consumption in cloud data centers. Chen et al.[31] too have proposed a method called “EONS” withthe same motive. In [3], the authors have proposed twopre-allocation algorithms based on a strategy for effec-tive host utilization. The solutions produced by theseapproaches are appreciable in case of energy con-sumption, but simultaneously the makespan becomeslarger in order to conserve more energy.
Although time complexity of heuristic approachesis low, but they span only a small area of solutionspace due to their greedy nature. So, this led to theinclination of many researchers towards the meta-heuristic techniques. Xu et al. [1] have proposed amethod for minimizing makespan, in which geneticalgorithms (GAs) have been employed to assign prior-ity to each task and HEFT is used for task-to-processor
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mapping. This approach uses multiple priority queuesthat are generated using a heuristic based operator.Kar et al. [32] tried to minimize both makespan andenergy consumption by proposing an energy awaretask scheduler using GA. Mezmaz et al. [11] pro-posed a parallel bi-objective hybrid GA that takes intoaccount both makespan and energy consumption. Thisapproach illustrated the effective use of DVS in work-flow scheduling. Dai et al. [33] have proposed a com-bination of GA and ant colony optimization (ACO)and considered multiple constraints (makespan, cost,security and reliability) for the scheduling process.Zhao et al. [34] also proposed an approach that usesGA and ACO, along-with a novel strategy to fastenthe search for an optimal solution in terms of energyefficiency. But the GA based approaches (used inthe above methods), suffer from their inherent prob-lem of premature convergence even after successfulmodifications.
Li et al. [18] used a population based meta-heuristiccalled CRO in order to minimize makespan of thegiven workflows. In CRO, solutions are encoded asmolecules which roam around the search space tofind a suitable result. Bechikh et al. [35] proposedan approach called non-dominated sorting chemicalreaction optimization, to exploit CRO for solvingthe problems involving multiple conflicting objec-tives. Jin et al. [8] used CRO for task schedulingin grid computing. In [36], the authors have pro-posed an approach called double molecular structure-based chemical reaction optimization (DMSCRO) forreducing makespan of the given DAG. CRO is basi-cally free from premature convergence but it suffersfrom the problem of unguided mutations and ineffec-tive crossovers. Recently, Xu et al. [17] proposed amethod called HCRO for optimization of makespan,with increase in speed of convergence. This approacheradicated the issues like unguided mutations andineffective crossovers in CRO, by blending some pop-ular general purpose heuristics in the CRO operators.But HCRO is also devoid of memory like CRO, dueto which the molecules may progress towards worsesolutions. Also, they have not considered the benefitsthat can be captured using simple swap mutation.
None of the above approaches consider the realworld scheduling constraints like the boot time andshut-down time of the VMs, the processor perfor-mance variability, etc. Rodriguez et al. [5] have pro-posed a PSO based method that considered all of these
factors. But their work is directed towards minimiza-tion of the workflow execution cost, while meeting thedeadline.
The proposed method EEWS overcomes most ofthe deficiencies pointed out in the aforementionedapproaches.
3 Model and Problem Formulation
In this section, we present the cloud model, energymodel and the workflow model followed by the prob-lem formulation.
3.1 Notations and Definitions
Let us first enumerate the important notations used inthis paper and their respective definitions, as given inTable 1.
3.2 Cloud Model
Cloud providers offer a variety of heterogeneousVMs with different processing capabilities [37, 38].In the proposed work, the cloud model consists ofa set of m heterogeneous VMs denoted by R ={V M1, V M2, V M3, · · · , V Mm}. The processors ofthe physical machines on which VMs are deployed areDVS-enabled, i.e., they can work on different inputvoltages [11, 39–42] but any decrease in voltage sup-ply causes a relative decrement in processor speed asshown in Table 2. Note that the amount of decrementapplied in the input voltage is relatively much lesserthan the standard value of the input voltage itself, i.e,dV << IV . This is because the machines have asmall range of workable voltages and if the input volt-age drops below this range, a physical machine maynot work. It is also assumed that the tasks of a particu-lar workflow are scheduled at the same data center andthe transfer time required for transmitting data fromone VM to another VM is negligible with respect tothe task computation time. So, the data transfer timedoes not have a huge impact on the makespan, andhence it can be ignored.
3.3 Workflow Model
A workflow is modeled as a DAG, Wf = (T , E), asdepicted in Fig. 1, where T = {T1, T2, · · · , Tn} is a set
An Energy Efficient Algorithm for Workflow Scheduling in IaaS Cloud
Table 1 Notations and definitions
Notations Definitions
Pop Current Population
PopSize Number of molecules in the Pop
Vi ith molecule
Vbest best molecule
Tj j th task (an atom in Vi )
V Mk kth Virtual Machine
PE(Vi) Potential Energy of molecule Vi
KE(Vi) Kinetic Energy of molecule Vi
M Makespan
Mn Normalized value of M
Mmax Maximum makespan
Ec Energy conserved
Econ Energy consumed
Ecn Normalized value of Ec
Ecmax Maximum energy conserved
IV Standard input voltage
WTiLength of task Ti
Texit Last task of the DAG
f itness fitness value
D processor performance variability on scale of 0-1
ETV Mk
TjExecution time of task Tj on V Mk
spdVjDecrement in speed of processor on scale of 0-1
where Ti is running
dVj Reduction in the input voltage of processor
where Ti is running
type parameter that determines whether to perform a
single molecule or an intermolecular operator
intertype parameter that determines whether to perform an
intermolecular ineffective collision or synthesis
of n tasks and E = {E1, E2, · · · , Ee} represents a setof e edges. The weight assigned to a node indicates thenumber of instructions in MI (millions of instructions)
Table 2 Effect of reduction of voltage on processor speed
Decrement in voltage Relative decrement
(dV ) in volts in speed (spdV )
0 0
0.25 0.05
0.5 0.125
1.0 0.175
1.25 0.25
T0
T1
T4
40
20
T2
30
T3
16
24
T5
20
T6
20
T7
40
T8
20
T9
10
T10
20
Fig. 1 An example of a workflow
required to finish a given task, as given in Table 3. Anedge Ek = (Ti , Tj ) indicates the precedence relation-ship between task Ti and task Tj . In other words, ifan edge Ek = (Ti , Tj ) exists in set E, then task Ti isa predecessor to task Tj and hence the execution oftask Tj can begin only after task Ti is complete. So,the earliest start time (EST) of a task Tj can be calcu-lated by using the actual finish time (AFT) of all of itspredecessors, as given in (1).
EST (Tj ) = maxTi∈pred(Tj )
{AFT (Ti)} (1)
Also, the makespan of a given DAG can be calculatedas the time at which the execution of the last task,Texit , would be complete, i.e.,
M = AFT (Texit ) (2)
For the sake of calculation of the execution time(of given tasks), we represent the computational speedof a virtual machine V Mk as SV Mk
and performancevariability is represented as D. Weight of each nodeWTi
represents the total number of instructions in MI,required to finish a given task Ti . Thus, the time takento execute task Ti on V Mk considering decrement involtage supply by dVi and the relative decrement inVM speed as spdVi
, is given as follows.
ETV Mk
Ti= WTi
(SV Mk× (1 − D − spdVi
))(3)
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Table 3 Length of tasks inthe given DAG Task-ID T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10
Task-length(in MI) 40 20 30 16 24 20 20 40 20 10 20
3.4 Energy Model
The energy model used in this work is derivedfrom the power consumption model in complemen-tary metal-oxide semiconductor (CMOS) logic cir-cuits [11]. The energy consumed during the executionof a particular workflow is defined as follows.
Econ = β × M ×n∑
i=1
(IVi)2 (4)
where, IVi is the decremented input voltage of the VMon which task Ti is running, β is a constant related tothe device [43] and M is the makespan.
Equation (4) clearly indicates that the input volt-age is a dominant factor for determining the energyconsumption. Therefore, any change in the suppliedvoltage would influence the amount of energy con-sumed. The total energy conserved (Ec) during theexecution of a DAG is given as follows.
Ec = 2 × β × M × IV ×n∑
i=1
dVi (5)
where, IV is the standard input voltage when DVSenabled environment is not considered and dVi is thedecrement applied in voltage of the VM on which taskTi is running so that the resultant voltage is IVi , i.e.,
dVi = IV − IVi (6)
The correctness of the expression for the amountof energy conserved (Ec), is proved by the followingtheorem.
Theorem 1 If we decrease the standard input volt-age, IV , of the processors by some quantum, thenthe amount of energy conserved is given by, Ec =2×β×M×IV ×∑n
i=1 dVi , whereM is the makespan,dVi is the decrement applied in voltage of the VM onwhich task Ti is running and β is a constant.
Proof Let us assume that Econ to be the energyconsumed when there is no reduction in voltage,Econ′ be the energy consumed when a DVS enabled
environment is considered. Now, Econ and Econ′ canbe calculated using (4) and (6) as follows,
Econ = β × M ×n∑
i=1
(IV )2 (7)
Econ′ = β × M ×n∑
i=1
(IVi)2 (8)
⇒ Econ′ = β × M ×n∑
i=1
(IV − dVi)2 (9)
Ec = Econ − Econ′ (10)
⇒ Ec = 2 × β × M × IV ×n∑
i=1
dVi − β
×M ×n∑
i=1
(dVi)2 (11)
As dV << IV , we can ignore the second termin the expression given in (11) because its value isnegligible with respect to the first term. So,
Ec = 2 × β × M × IV ×n∑
i=1
dVi (12)
3.5 Problem Formulation
Minimization of makespan and maximization ofenergy conservation are the two objectives of the pro-posed scheme. As stated earlier, the physical machinesare considered to be DVS-enabled. We formulate thefitness function for our problem as follows.
3.5.1 NLP Formulation and Fitness Function
Potential Energy (PE) is a measure of the goodnessof a molecule (lower the PE, better is the correspond-ing schedule). So, the potential energy function shouldbe constructed in such a way that it evaluates thegiven molecule accurately. A potential energy functionmay be built by using one or more than one objec-tives. In our case, it comprises of two objectives, withmakespan minimization as primary and maximization
An Energy Efficient Algorithm for Workflow Scheduling in IaaS Cloud
of energy conservation as our secondary objective.These objectives can be written using (2) and (5) as,
Objective 1: Minimize M = AFT (Texit ) (13)
Objective 2: Maximize Ec = 2 × β × M × IV
×n∑
i=1
dVi (14)
It is quite evident that both the objectives conflictwith the optimization of one another. So, we formu-late the potential energy in such a way that a carefulbalance is struck between them. We use weightedsum approach for the same. In this method, we mul-tiply a weight (value) to each objective and add theirproducts. Thus, we obtain the following.
PE = γ × Mn + δ
(1 + Ecn)(15)
where, 0 < γ < 1 and δ = 1 − γ . Here, Mn is nor-malized value of makespan M and Ecn is normalizedvalue of the corresponding conserved energy Ec.
We apply normalization of the values obtained formakespan and energy conserved as they are mea-sured on different scales. Decimal scaling normaliza-tion [44] is particularly used in our approach, becauseit needs only the maximum possible values of bothmakespan and the energy conserved to normalize theresults obtained by our algorithm in each run. Thelargest value of makespan would be achieved if aschedule arises in which all the tasks are sequentiallyscheduled on the slowest VM with maximum reduc-tion in the input voltage. After finding this maximumvalue of makespan, we can find the maximum value ofenergy conserved using (5).
The given objectives can be modeled together as anon-linear minimization problem as follows:
Minimize PE = γ × Mn + δ
(1 + Ecn)(16)
subject to the following constraints:
M < Mmax (17)
0 < Ec < Ecmax (18)
γ = 1 − δ and 0 < γ < 1 (19)
The constraint (18) ensures that some amount ofenergy is always conserved, but it is never equal to itsmaximum possible value. This is because, as speci-fied in constraint (17), it would be very disagreeable toachieve the highest value of makespan in the solution.Constraint (19) represents the relationship betweenγ and δ and their range. We treat PE as a fitnessfunction in our proposed method. So fitness value,f itness = PE (refer to (16)).
4 Overview of HCRO
Here we give an overview about the molecule encod-ing along-with the generation of initial population andthe hybrid heuristic operators used in HCRO withrespect to the DAG shown in Fig. 1. The modifica-tion of basic HCRO in our proposed method EEWS iselaborated in Section 5.
4.1 Molecular Encoding
A molecule V is represented as a priority queue whichcontains the given tasks in topologically sorted order,as per the outcome of Phase-1 of HCRO. A task ina molecule is called an atom [17]. An example of amolecule is shown in Fig. 2, with respect to the DAGgiven in Fig. 1.
4.2 Initial Population
For generation of the initial population, the conceptof maximum hamming distance is used to expandthe search space in the very beginning. A moleculeis selected at random, from the population. Then, anatom is chosen from the selected molecule and its lastpredecessor and first successor are determined. Afterthis, a left (or right) rotation is performed, startingfrom the chosen atom till the atom which is just afterits predecessor (or just before its successor), in orderto satisfy the precedence constraints and obtain thelarge hamming distance simultaneously. This processis repeated until the required number of moleculesis obtained [17]. Figure 3 shows how a molecule ofinitial population is generated.
T0 T2 T3 T1 T4 T5 T6 T7 T8 T9 T10V
Fig. 2 An example of a molecule
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T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10
T0 T1 T2 T3 T4 T7 T5 T6 T8 T9 T10
First successor of T5
Maximum possible hamming distance
V
V1
Chosen atom
Fig. 3 An illustration of generation of molecules of the initial population
4.3 Hybrid Heuristic Operators
The standard operators used in CRO are combinedwith some well known heuristics to develop the hybridoperators as in [17]. Each operator acts accordingto a given set of conditions, which is based on twokey properties associated with each molecule namely,Potential Energy (PE) and Kinetic Energy (KE). ThePE corresponds to the fitness value of the moleculeand KE is used for increasing the tolerability of thealgorithm towards worse solutions (in order to expandthe search space). The algorithms of these operatorscan be found in [17].
4.3.1 On-Wall Ineffective Collision
A single molecule is chosen as a reactant. To derive achild molecule V1 from parent molecule V , as in [17],a right rotation is performed from the chosen atomtowards its last predecessor. Note that, for this opera-tion the condition PE(V1) ≤ PE(V ) + KE(V ) musthold true. An illustration is shown in Fig. 4.
4.3.2 Decomposition
This operator involves disintegration of a singlemolecule V into two new molecules V1 and V2. An
atom is chosen from the given molecule and a leftor right rotation is performed either towards its firstsuccessor or towards its last predecessor. But the con-dition PE(V1) + PE(V2) ≤ PE(V ) + KE(V ) +buf energy (buf energy is energy stored in theshared buffer) should hold true [17]. An illustration isshown in Fig. 5.
4.3.3 Inter-Molecular Ineffective Collision
This reaction involves collision of two molecules,V1 and V2, resulting in the formation of two newmolecules, V ′
1 and V ′2 using crossover operation [17].
But the condition, PE(V ′1) + PE(V ′
2) ≤ PE(V1) +PE(V2) + KE(V1) + KE(V2) should hold. Then, V ′
1and V ′
2 are compared and the one with higher potentialenergy is rejected. An illustration is shown in Fig. 6.
4.3.4 Synthesis
Synthesis is an intermolecular reaction in which twomolecules fuse to form a single molecule, usingcrossover operation, as in [17]. In synthesis, twomolecules V1 and V2 collide to produce two newmolecules V ′
1 and V ′2 such that PE(V ′
1) ≤ PE(V1) +PE(V2) + KE(V1) + KE(V2) and PE(V ′
2) ≤PE(V1)+PE(V2)+KE(V1)+KE(V2) and then the
Fig. 4 An example of on-wall ineffective collision
An Energy Efficient Algorithm for Workflow Scheduling in IaaS Cloud
Fig. 5 An example of decomposition
molecule with the lower potential energy is chosen asthe resultant molecule V ′. An illustration is shown inFig. 7.
5 Proposed Algorithm
An outline of the proposed method is given in Algo-rithm 1. In lines 4-5, we initialize the initial moleculepopulation and calculate the potential energy of eachmolecule. Then, we start the process of finding a nearoptimal solution as given in lines 6 through 28 andrepeat the same, until we reach the maximum speci-fied number of iterations. In lines 7-9, we select somemolecules randomly from the current population, andform a Parent set. Followed by this, we generate arandom number r1 in line 11. Based on the value of r1,we determine the operator which will be used in thatiteration. As given in line 12, if the value of r1 is lessthan the value of type, we use two single-moleculeoperators successively on the given molecule Vi . Oth-erwise, we use an intermolecular operator as givenin lines 18 through 22 (for which we find another
reactant molecule Vk as in line 16) based on the com-parison between the values of another random numberr2 and the input parameter intertype.
In line 24, we use a novel operator called on-wallpseudo-effective collision on Vi1 to form Vi2, as dis-cussed later in Algorithm 2. In line 25, we calculatethe potential energy of the newly generated moleculesVi1 and Vi2. Next, we compare the potential energy ofVi1 and Vi2 and run Algorithm 3 (as explained later)on the one with a lesser value. This is done to checkwhether this molecule can be included in the currentpopulation.
5.1 On-Wall Pseudo-Effective Collision
We use a new operator on the molecules of currentpopulation. The rationale behind this operator is thatsometimes over-zealousness of the hybrid operatorsused in HCRO may cause them to miss the moleculesthat can be formed by a simple swap mutation. So, theproposed operator overcomes this drawback by usingsimple (but intelligent) swap mutation. The descrip-tion of on-wall pseudo effective collision operator is
T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10
T0 T2 T3 T5 T6 T1 T4 T9 T7 T8 T10
T0 T1 T2 T3 T4 T5 T6 T9 T7 T8 T10
T0 T2 T3 T5 T6 T1 T4 T7 T8 T9 T10
Crossover point
Crossover point
V1'
V2'
V1
V2
Fig. 6 An example of intermolecular ineffective collision
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T0 T2 T3 T1 T4 T5 T7 T6 T8 T9 T10
T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10
T0 T2 T3 T1 T4 T5 T6 T7 T8 T9 T10
Crossover point
Crossover point
V'
V1
V2
Fig. 7 An example of synthesis
Algorithm 1 Energy efficient workflow scheduling.
1: procedure EEWS(Wf (T , E))2: Input: Given DAG Wf (T , E), type, intertype,KEIntial , KELossRate
3: Output: Best molecule Vbest
4: Initialize Pop5: Calculate PE of each molecule in Pop using (15) after mapping as per (20)6: while iteration �= max num iterations do7: for l = 1 to PopSize do8: Select some molecules and form a set Parent9: end for10: for each molecule Vi in Parent do11: Choose a random number r112: if r1 ≤ type then13: Vi1 = Perform on-wall ineffective collision on Vi
14: Vi1 = Perform decomposition Vi115: else16: Select another molecule Vk from Parent17: Choose a random number r218: if r2 < intertype then19: Vi1 = Perform intermolecular ineffective collision between Vi and Vk
20: else21: Vi1 = Perform synthesis between Vi and Vk
22: end if23: end if24: Vi2 = Call ON − WALL − PSEUDO − EFFECT IV E(Vi1)25: Calculate PE of Vi1 and Vi2in Pop using (15) after mapping as per (20)26: if PE(Vi1) ≤ PE(Vi2) then27: Vi = Vi128: else29: Vi = Vi230: end if31: Pop = Call REPLACE(Pop, PopSize, Vi)32: end for33: end while34: return Vbest
35: end procedure
given in Algorithm 2 along-with an illustration inFig. 8.
According to the algorithm, we randomly select anatom Ti from the given molecule and find its last pre-decessor Tj and first successor Tk (as given in lines5 through 7). Let the position of atoms Ti , Tj , Tk inthe molecule be denoted by pTi
, pTj, pTk
respectively.In line 8, a random number, say rpos, is generated
between pTjand pTk
, provided rpos is not equal topTi
. This furnishes the chosen atom with the maxi-mum number of alternatives for swapping. Then theatom present at rpos (T ′) is swapped with Ti to obtaina new molecule Vnew, as given in lines 9-10. Whetherthe molecule Vnew enters current population or not,depends on the criteria mentioned in the Algorithms 1and 3.
An Energy Efficient Algorithm for Workflow Scheduling in IaaS Cloud
T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10
T0 T1 T2 T5 T4 T3 T6 T7 T8 T9 T10
Chosen atom First successor of T5
V
V1
Last predecessor of T5
Randomly selected atom for swapping
Fig. 8 An example of on-wall pseudo-effective collision
Algorithm 2 On-wall pseudo-effective collision.
1: procedure ON-WALL PSEUDO-EFFECTIVE(V )2: Input: A molecule V .3: Output: A new molecule Vnew.4: Let Vnew ← V
5: Choose randomly an atom Ti from Vnew
6: Find the last predecessorTj of the atom Ti
7: Find the first successor Tk of the atom Ti
8: Find a random number rpos wherepTj+1 ≤ rpos ≤ pTk−1 such that rpos �= pTi
9: Let T ′ ← atom at rpos in Vnew
10: Exchange Ti ↔ T ′ in Vnew
11: return Vnew
12: end procedure
5.2 New Molecule Inclusion Plan
We propose a new scheme of including molecules inthe current population, as given in Algorithm 3. Thedecision whether the molecule formed by applyingany of the five operators should be allowed to enterthe current population, is dependent on an entirelydifferent set of conditions than those in HCRO [17].
According to the algorithm, a new molecule (Vnew)produced by using any of the five operators, is con-sidered as a potential candidate for being included inthe current population. To determine its eligibility, wefind the best (Vbest ) and the worst (Vworst ) moleculein the current population based on the measure of theirpotential energy as given in lines 6 through 12. In lines13-15, we check whether the best molecule can bereplaced in the population as well as in the buff er
(which stores the best-so-far molecule in terms ofpotential energy, so that it may not be replaced in thecurrent population). If not so, in lines 16-17, we ver-ify whether we can replace the best molecule at leastin the population (without any change in the buff er).
If this too does not take place, the new molecule iscompared to the worst, as in lines 18-19. If even thiscondition is false, we do not include the new moleculein the population. As mentioned in previous sections,KE is used to increase tolerance of the algorithmtowards those molecules which do not appear wor-thy at present, but may become important later dueto some minute modifications performed by the fiveaforementioned operators.
Algorithm 3 Replacing the current molecules.
1: procedure REPLACE(Pop, PopSize, Vnew)2: Input: Current population Pop, A new molecule
Vnew
3: Output: Modified Pop.4: Vworst ← V1
5: Vbest ← V1
6: for i = 1 to PopSize do7: if PE(Vi) ≤ PE(Vbest ) then8: Vbest = Vi
9: else if PE(Vi) ≥ PE(Vworst ) then10: Vworst = Vi
11: end if12: end for13: if PE(Vnew) ≤ PE(Vbest ) then14: replace Vbest by Vnew in Pop
15: replace Vbest by Vnew in buffer16: else if PE(Vnew) ≤ PE(Vbest ) + KE(Vbest )
then17: replace Vbest by Vnew in Pop
18: else if PE(Vnew)≤PE(Vworst )+KE(Vworst )
then19: replace Vworst by Vnew in Pop
20: end if21: Return Pop
22: end procedure
V. Singh et al.
5.3 Task-to-VM Mapping
In the second phase of scheduling, we use HEFTto perform task-to-VM mapping. Every task Ti ismapped on a suitable virtual machine V Mk usinga function Map(Ti, V Mk). The tasks (atoms) areextracted from the beginning of a given a molecule andare allocated to a particular VM (present in a pool ofavailable VMs), according to (20).
Map(Ti, V Mk) = MinV Mk∈ avail V Ms
{ETV Mk
Ti} (20)
5.4 Time Complexity Analysis
The overall time complexity of Algorithm 2 is O(n ×e) (where e is the number of edges and n is the totalnumber of tasks in the given workflow), which ismainly determined by the maximum time taken to findthe first predecessor and first successor of the givenatom, as given in lines 5-6. Regarding Algorithm 3, thetime complexity is O(PopSize), i.e, the maximumtime taken to execute lines 6-12.
The time complexity of Algorithm 1 (whichdenotes the overall approach), is derived mainly fromlines 5 through 33, as follows. Time taken to calcu-late PE in line 5 is O(n × m), where m is the numberof VMs. The time taken to execute the lines 7-9 isO(PopSize). The overall time taken to execute lines10-32 isO(PopSize×(n2+n×e+n×m+PopSize)).This is because, firstly, the time taken by opera-tors mentioned in lines 13, 14, 19 and 21 is O(n2)
each (as per [17]), secondly, as mentioned before, thetotal time required to perform line 24 is O(n × e),thirdly, time taken for performing line 25 is O(n ×m), and finally, the time required to execute line 31is O(PopSize).
Therefore, the overall time complexity of Algo-rithm 1 (which also happens to be the total timecomplexity of EEWS) is O(max num iterations ×PopSize × (n2 + n × e + PopSize)).
5.5 An Illustration
We consider given the DAG in Fig. 1 and Table 3showing the corresponding millions of instructions(MI) information of the tasks. The computationalspeed of VMs, i.e., millions of instructions per second(MIPS) is given in Table 4. Let us assume the CPUperformance variability D as 0.24, PopSize = 4 and
Table 4 VM information
VM-ID VM speed (in MIPS)
V M1 4
V M2 2.5
V M3 2
number of VMs, i.e. |R| = 3. The decrease in voltageand the consequent relative speed matrix is as givenin Table 2. We consider standard input voltage, IV =230 volts. Here we run our proposed EEWS algorithmfor three iterations.
A molecule V1 is constructed and then the remain-ing molecules are derived as discussed in Section 4.2.The initial population so formed, is given in Table 5.
Once we find the initial population, we map thetasks in each molecule to the VMs according to (20).After performing the mapping, we calculate the result-ing PE value for each molecule in the population,using (15). Now, the operators are applied on themolecules for the next three iterations. The resultsof application of these operators after the first andthe third iteration are mentioned in Tables 6 and 7respectively.
It is evident that V4 is the best molecule with PE =0.3276. The corresponding task-to-VM mapping isshown in Fig. 9.
If we compare the results of makespan, energy con-served and fitness value (PE) obtained fromMPQGA,HCRO and EEWS, as given in Table 8, it is quite clearthat EEWS outperforms both MPQGA and HCRO.
6 Simulation Studies
In this section, we test our proposed scheme EEWSthrough simulation runs and compare the results withother hybrid approaches like MPQGA and HCRO.It is important to mention here that we have mod-ified MPQGA and HCRO to entertain the objectiveof energy conservation as well. We have evaluatedthese approaches using our fitness function. The per-formance metrics considered for comparison are asfollows.
• Makespan measured in seconds, as given in (2).• Energy conserved in joules, as given in (5).• Fitness value (PE) as given in (15).
An Energy Efficient Algorithm for Workflow Scheduling in IaaS Cloud
Table 5 Initial populationMolecule Task-ID PE
V1 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 0.3346
V2 T0 T2 T3 T1 T4 T5 T6 T7 T8 T9 T10 0.3361
V3 T0 T1 T2 T3 T5 T6 T4 T7 T8 T9 T10 0.3325
V4 T0 T3 T2 T1 T4 T5 T6 T7 T8 T9 T10 0.3310
Table 6 Population afterfirst iteration Molecule Task-ID PE
V1 T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 0.3346
V2 T0 T2 T3 T1 T5 T6 T4 T7 T8 T9 T10 0.3341
V3 T0 T1 T2 T3 T5 T6 T4 T7 T8 T9 T10 0.3325
V4 T0 T3 T2 T1 T4 T5 T6 T7 T8 T9 T10 0.3310
Table 7 Population afterlast iteration Molecule Task-ID PE
V1 T0 T3 T2 T1 T4 T5 T6 T7 T8 T9 T10 0.3338
V2 T0 T2 T3 T1 T5 T6 T4 T7 T8 T9 T10 0.3341
V3 T0 T1 T2 T3 T5 T6 T4 T7 T8 T9 T10 0.3325
V4 T0 T3 T1 T2 T4 T6 T5 T7 T8 T9 T10 0.3276
Task -ID
T0 T3 T1 T2 T4 T6 T5 T7 T8 T9 T10
VM -ID
VM 1 VM 1 VM 2 VM 3 VM 1 VM 2 VM 3 VM 1 VM 2 VM 1 VM 1
Fig. 9 The mapping of best molecule to the VM pool
Table 8 Performancecomparison Performance metric MPQGA HCRO EEWS
Makespan 69.2 71.72 62.96
Energy Conserved 47348 49215 57897
Fitness value 0.3343 0.3361 0.3277
V. Singh et al.
6.1 Simulation Setup
The EEWS is simulated in Java on the Eclipse ver-sion 4.4.0 on Intel(R) Core(TM) i5-6200U CPU @2.30 GHz and 4GB RAM running on Windows 10platform. The inputs to the program are as follows:1) task lengths in MI, 2) a matrix containing VMspeed in MIPS and their performance variability onthe scale of 0 to 1, 3) a task dependency matix, 4) VMboot time and shut down time and 5) a matrix con-taining the permissible set of decrements in voltagesupply and the corresponding reduction in the speedof the processor (on the scale of 0 to 1). The mar-tix containing decrement in voltage and the relativedecrement in speed is as given in Table 9 and VMspeed and performance variability matrix is as givenin Table 10.
6.2 Datasets Used
In the simulations , we have considered five bench-mark scientific workflows [7] namely, Montage,Cybershake, LIGO Inspiral, Sipht and Epigenomicwhich comprise of 25-1000 task nodes. The corestructure of the workflows is shown in Fig. 10. TheMontage is used for astronomical purposes, the Cyber-shake is employed in the study of earthquakes, theEpigenomic and the SIPHT are used in biology andthe LIGO is employed in gravitational physics.
In the experiments, the parameters used for EEWSand HCRO are specified in Table 11. Here, KEinitial
denotes the initial kinetic energy of the molecules.KELossRate denotes the rate at which the kineticenergy decreases in order to enable convergence. Notethat the value of KEinitial is considered so becausedecimal scaling normalization is used in this approach.We also specify the parameter settings for MPQGA inTable 12 as given in [1].
Table 9 Effect of reduction of voltage on processor speed
Decrement in voltage Relative decrement
(dV ) in volts in speed (spdV )
1.5 0.2
1.7 0.3
2.0 0.5
2.2 0.6
Table 10 VM information
VM-ID VM speed Performance
(in MIPS) variability
V M1 25 0.1
V M2 21 0.1
V M3 18 0.1
V M4 15 0.1
For the sake of simulations, all the above men-tioned workflows have been divided into three groupsdepending on their number of tasks as follows:
1) Small sized workf lows, consisting of work-flow applications having 25-101 task nodes.
2) Medium sized workf lows, consisting of work-flow applications having 200-400 task nodes.
3) Large sized workf lows, consisting of work-flow applications having 800-1000 tasks.
6.3 Simulation Results and Analysis
We now present comparison results of simulationruns on EEWS, MPQGA and HCRO based on theperformance metrics as discussed before.
6.3.1 Comparison of Makespan
It is evident from Fig. 11a that EEWS provides min-imum makespan for all the workflow applications,contained in Small sized workf lows. Performanceof EEWS is appreciable as compared to MPQGA andHCRO, in the case of Medium sized workf lows
and Large sized workf lows as shown in Fig. 11b,c. EEWS lags just behind MPQGA, in case ofEpigenomic-400 and Inspiral-802.
6.3.2 Comparison of Energy Conserved
It is evident from Fig. 12a that the amount ofenergy conserved is much more in case of EEWS ascompared to both MPQGA and HCRO, for all theworkflow applications in Small sized workf lows
(shown in Fig. 12a). EEWS also performs betterthan MPQGA and HCRO for all the workflows inMedium sized workf lows, except in the case ofMontage-398, where it lags behind MPQGA by atrivial amount (shown in Fig. 12b). Performance of
An Energy Efficient Algorithm for Workflow Scheduling in IaaS Cloud
Fig. 10 Five Benchmark Scientific workflows used in the simulations: a Montage, b Cybershake, c Inspiral, d Epigenomic, and eSipht
EEWS is also comparatively better for almost allthe workflows in Large sized workflows (shown inFig. 12c), in which it lags behind HCRO in the case ofMontage-804 and MPQGA in the case of Cybershake-800, by a tad amount. Thus, we can say that EEWSgives comparatively better results than MPQGA andHCRO, for almost all sizes and types of workflowapplications, in case of energy conservation.
6.3.3 Comparison of Fitness Value
We can observe from Fig. 13a, b and c, that EEWS pro-vides better results for fitness value than bothMPQGAand HCRO, for all the workflow applications con-tained in each set namely, Small sized workf lows,Medium sized workf lows,Large sized workf lows.
Table 11 THE EEWS and HCRO parameters
Parameter Value
PopSize 500
KEinitial 0.1
KELossRate 10%
type 0.4
intertype 0.5
6.4 Analysis of Variance
To check statistical significance of the experimentalresults, we have applied ANOVA test [20]. It is astatistical analysis tool which checks whether meansof the given groups are dissimilar or not. In techni-cal terms, it determines whether we can reject the nullhypothesis (H0) which is proposed as follows,
H0 : μEEWS = μHCRO = μMPQGA (21)
Similarly, the alternative hypothesis can be defined as,
H1 : Means are not equal (22)
We have considered 10 samples of the aforemen-tioned workflows of different sizes to perform theANOVA test on all the three performance metrics (i.e.,makespan, energy conserved, fitness value). Here, we
Table 12 The MPQGA parameters
Parameter Value
The population size 500
The crossover probability 0.7
The mutation probability 0.35
V. Singh et al.
Fig. 11 Comparison of makespan for all workflow applications in: a Small sized workflows, b Medium sized workflows, and cLarge sized workflows
Fig. 12 Comparison of energy conserved for all workflow applications in: a Small sized workflows, b Medium sized workflows,and c Large sized workflows
An Energy Efficient Algorithm for Workflow Scheduling in IaaS Cloud
Fig. 13 Comparison of fitness value for all workflow applications in: a Small sized workflows, b Medium sized workflows, and cLarge sized workflows
show the results of ANOVA test for Sipht workflowwith 1000 task nodes. The degree of freedom (df ),mean, F-statistic, P-value and F-critical for makespan,energy conserved and the fitness value are demon-strated in Tables 13, 14 and 15 respectively. For reject-ingH0, P-value must be lesser than the selected α level(=0.05). Also, the value of F-critical must be lesserthan that of F-statistic. As per the results obtained,as given in Tables 13–15, we reject the null hypoth-esis for all the performance metrics (i.e., makespan,conserved energy and fitness value). In other words,we accept the alternative hypothesis, i.e., means ofthree groups are not equal. Hence, we assert that
the performance gain achieved by EEWS is not bychance.
Next we perform post-hoc least significant dif-ference (LSD) analysis on the results obtained afterANOVA test, for determining whether EEWS is betterthan HCRO and MPQGA. For this, taking two groupsat a time, we find 95% confidence interval (CI) forthe difference in their means. As per the results givenin Tables 13 and 15 for makespan and fitness valuerespectively, we can say that,
μEEWS − μHCRO < 0
μEEWS − μMPQGA < 0 (23)
V. Singh et al.
Table 13 ANOVA & LSD analysis on makespan on Sipht workflow containing 1000 tasks
(a) ANOVA test results
Source of variation Sum of square df MS F P-Palue F-Critical
Between groups 405 2 202.5 18.3166 9.4E-06 3.35413
Within groups 298.5 27 11.055
Total 703.5 29
(b) LSD Analysis
Difference of mean t-value SE LSD Lower-bound Upper-bound
μEEWS − μHCRO –9 2.051830516 1.05145402 3.051032039 –12.05103204 –5.948967961
μEEWS − μMPQGA –4.5 2.051830516 1.05145402 3.051032039 –7.55103 –1.448967961
Table 14 ANOVA & LSD analysis on energy conserved (Ec) on Sipht workflow containing 1000 tasks
(a) ANOVA test results
Source of variation Sum of square df MS F P-Palue F-Critical
Between groups 2.7E+10 2 1.3E+10 7.36277 .00281 3.354131
Within groups 4.9E+10 27 1.8E+9
Total 7.6E+10 29
(b) LSD analysis
Difference of mean t-value SE LSD Lower-bound Upper-bound
μEEWS − μHCRO 54519.2 2.051830516 13470.81673 39088.62647 15430.57353 93607.82647
μEEWS − μMPQGA 69437.2 2.051830516 13470.81673 39088.62647 30348.57353 108525.8265
Table 15 ANOVA & LSD analysis on fitness value on Sipht workflow containing 1000 tasks
(a) ANOVA test results
Source of variation Sum of square df MS F P-Palue F-Critical
Between groups 6.02E-07 2 3.01E-07 18.55479 8.51E-06 3.354131
Within groups 4.38E-07 27 1.62E-08
Total 1.06E-06 29
(b) LSD analysis
Difference of mean t-value SE LSD Lower-bound Upper-bound
μEEWS − μHCRO -0.00029 2.051830516 4.02768E-05 0.000116872 –0.000406872 –0.000173128
μEEWS − μMPQGA -0.00031 2.051830516 4.02768E-05 0.000116872 –0.000426872 –0.000193128
An Energy Efficient Algorithm for Workflow Scheduling in IaaS Cloud
Apart from this, from the analysis of energy conserved(Ec) as per Table 14, we can conclude that,
μEEWS − μHCRO > 0
μEEWS − μMPQGA > 0 (24)
On determining the 95% CI, i.e, (lower-bound, upper-bound), for the difference in means for EEWS andHCRO (i.e., μEEWS − μHCRO ), we find that thisinterval does not contain zero. Also, this interval islesser than zero in case of makespan and fitness value,and greater than zero in case of energy conserved,which is essential to prove the better performance ofEEWS over HCRO. We find similar results in case ofMPQGA too. Thus, from (23) and (24), we claim thatthe performance of EEWS is better than both HCROand MPQGA.
7 Conclusion
In this paper, we have presented an efficient meta-heuristic approach called energy efficient workflowscheduling (EEWS) for minimizing makespan andmaximizing energy conservation while schedulingworkflows. We have successfully incorporated variousreal world scheduling constraints like the performancevariability of VMs, VM boot and shut-down time, etc.Through simulation runs, EEWS has been shown toexhibit a better overall performance than MPQGA andHCRO, in all the cases, as is evident from the compar-isons based on their fitness value. As far as makespanis concerned, it performs better than HCRO in all thecases, and also fares better than MPQGA in more than92% of the cases. If we discuss about the energy con-servation, then too EEWS overwhelms MPQGA inmore than 92% of the cases and performs better thanHCRO in all cases except one. This in turn asserts thefact that EEWS is an improvement over HCRO. Also,through the ANOVA test and its subsequent LSD anal-ysis, we have established the fact that EEWS givesbetter results than both HCRO and MPQGA in case ofmakespan, energy conserved and fitness value.
As a future work, we would like to incorporate thetransfer time required to transmit data between twoVMs, in our approach. The foundation of this thoughtis based upon the fact that the tasks of very largeworkflows can be possibly scheduled on VMs thatare provisioned on data centers which are located atdifferent geographical locations.
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