Abstract In this paper, we assume an environ-ment with multiple, heterogeneous resources,which provide services of different capabilitiesand of a different cost. Users want to make use ofthese services to execute a workflow application,within a certain deadline and budget. The problemconsidered in this paper is to find a feasible planfor the execution of the workflow which wouldallow providers to decide whether they can agreewith the specific constraints set by the user. Ifthey agree to admit the workflow, providers canallocate services for its execution in a way thatboth deadline and budget constraints are metwhile account is also taken of the existing loadin the provider’s environment (confirmed reserva-tions from other users whose requests have been
The first author is supported by the National NaturalScience Foundation of China (Grant No.61202361)and the Fundamental Research Funds for the CentralUniversities (Grant No.2011121049).
W. ZhengSchool of Information Science and Technology,Xiamen University, Xiamen, Chinae-mail: [email protected]
R. Sakellariou (B)School of Computer Science,University of Manchester, Manchester, UKe-mail: [email protected]
accepted). A novel heuristic is proposed and eval-uated using simulation with four different real-world workflow applications.
In Grid or cloud platforms where resource ownersprovide services of different capacities and/or ofdifferent prices [4, 18, 23], users may want to usethese services to execute complex applications,such as workflows [5, 16]. Typically, a user mayrequire his/her workflow application to completewithin a certain deadline and budget; such re-quirements are generally recognised as Quality ofService (QoS) requirements. In analogy to the realworld, a Service Level Agreement (SLA) [14],which can be regarded as a bilateral contract be-tween a user and a service provider, is usuallyspecified to capture the user’s QoS requirementsand act as a guarantee of the expected QoS. If theterms of the SLA are fulfilled, the user is expectedto pay some fee to the provider. Conversely, if theterms of the SLA are not fulfilled, the providermay have to pay some penalty to the user, asprescribed by the SLA.
634 W. Zheng, R. Sakellariou
Thus, to establish an SLA, the service providermust have a way of determining in advance ifit is feasible to fulfil a user’s request. From theservice provider’s point of view, this implies thatthere is a need to find a plan for the executionof every new workflow requesting admission toand execution on the provider’s resources. Sucha plan will identify feasible reservation slots onthe resources for every task of the workflow inorder to provide an assurance that both the budgetand deadline constraints requested by the usercan be met according to the current load of theservice provider’s resources. We call such a plana Budget-Deadline Constrained plan, or, in short,BDC-plan. The planning procedure to find sucha plan is called BDC-planning. BDC-planningshould be part of the admission control of a user’srequest to execute a workflow. If a BDC-plan isfound, a user’s request can be accepted and arelevant SLA can be agreed; otherwise, the user’srequest should be rejected.
BDC-planning is important for service- andmarket-oriented environments, as its outcomedrives admission control and determines whethera user’s request should be accepted. BDC-planning is also a remarkably challenging prob-lem. First, such a planning problem is NP-complete [19]. Second, the non-dedicated natureof resources imposes more difficulties as the con-tention for shared resources (some of which areassigned to or reserved by other, already agreedworkloads) needs to be considered during plan-ning. This suggests that the planner may have tosomehow query resources for their runtime infor-mation (e.g., the existing load) to make informeddecisions. Moreover, at the same time, BDC-planning should be performed in short time, be-cause: (i) users may require a real-time response,and (ii) the (runtime) information, on which aplanning decision has been made, varies over timeand, thus, a planning decision made using out-of-date information may not be valid.
The general form of the BDC-planning prob-lem boils down to bi-criteria DAG planning, aswe assume that every workflow application is rep-resented by a Directed Acyclic Graph (DAG).This problem involves the planning process tooptimize two metrics at the same time to meet thespecified constraints (budget and deadline). There
have been quite a few bi-criteria DAG planningheuristics in the literature [7, 19, 24, 29, 31, 37, 38].However, some of them do not take the existingload of resources into account (or modifying themto do so could be too costly). Moreover, most ofthese heuristics have sophisticated designs, suchas guided random research or local search, whichusually require considerably high planning costs.Such features do not make existing heuristicsparticularly suitable for the BDC-planning prob-lem discussed above (as opposed to the problemof scheduling a workflow already admitted, inwhich case high-cost approaches could be easilyjustified). The need for fast and efficient heuris-tics, suitable for the specific problem of BDC-planning, which also takes into account existingload of the resources, motivates the work pre-sented in this paper.
In the paper, a new BDC-planning heuristicis proposed with the objective to simultaneouslyprovide effective BDC-planning and fast planningtime. The proposed heuristic is based on the Het-erogeneous Earliest Finish Time (HEFT) algo-rithm [32], which is a well-known list schedulingheuristic aiming at minimizing the overall exe-cution time of a DAG application in a hetero-geneous environment. While being effective atoptimizing makespan, the HEFT algorithm doesnot consider the monetary cost and budget con-straint when making scheduling decisions. In thispaper, the HEFT algorithm is extended in order toresolve the BDC-planning problem and the newalgorithm is called the Budget-constrained Hetero-geneous Earliest Finish Time (BHEFT). In the ex-perimental section of the paper, it is demonstratedthat, for the BDC-planning problem, the pro-posed heuristic addresses well the aforementionedchallenges. In addition, it performs well com-pared to sophisticated heuristics, but costs muchless in terms of computation and communicationoverheads.
This paper is an extended version of a paperthat first appeared in [40]. The main changes madein this paper include: (1) a detailed descriptionof the BDC-planning model with a sequence dia-gram to depict the BDC-planning procedure hasbeen added; (2) a more sophisticated exampleto illustrate the proposed heuristic has been in-cluded; (3) a more flexible model to calculate
Budget-Deadline Constrained Workflow Planning for Admission Control 635
execution time and cost without the restriction ofthe notion of power (Section 3 in [40]); (4) two ofthe four DAGs used in the evaluation in [40], werereplaced by DAGs with a larger number of nodesto allow the investigation of a wider spectrum ofdifferent workflow types.
In the rest of this paper, related work is re-viewed in Section 2. The model assumed and aproblem definition are presented in Section 3.A novel BDC-planning heuristic (BHEFT), aswell as an illustrative example, is described inSection 4. Experimental details and simulationresults are discussed in Section 5. The paper isconcluded in Section 6.
2 Related Work
Admission control problems have been studiedin various computing platforms where QoS isconsidered. Yeo and Buyya [35] investigated theadvance impact of inaccurate runtime estimatesfor deadline constrained job admission controlin clusters. Yin et al. [36] proposed a predictiveadmission control algorithm to support advancereservation in equipment Grids. Admission con-trol issues were also studied as a subproblemof resource management in Grids which supportSLAs [1, 13]. Nevertheless, none of these pa-pers takes budget requirements from users intoaccount; moreover, the applications they targetare not workflows. Cost and deadline constrainedadmission control for workflows in IaaS cloudswas studied in [17], where algorithms for bothtask scheduling and resource provisioning wereproposed and assessed. However, the resourcemodel considered in these algorithms consists ofhomogeneous virtual machines.
Admission control for workflows in market-oriented Grids requires bi-criteria DAG planningtechniques. A Grid capacity planning approachis presented in [27], which aims at producing aplan for a workflow without reservation conflictsto optimize resource utilization and multiple QoSconstraints. However, this paper mainly focusedon a 3-layer negotiation mechanism rather thana planning heuristic itself. The studies in [21, 22]proposed mapping heuristics to meet deadlineconstraints, at the same time minimizing the reser-
vation cost of workflows, but they assumed thatworkflow tasks can be multiprogramming, some-thing not commonly encountered in workflowscheduling studies [33]. Based on the model ofUtility Grids, the time-cost constrained optimiza-tion has been studied for meta-scheduling [9–11]in which planning is considered at application-level, but applications are assumed to be inde-pendent rather than task-based and bounded bydependencies as is the case in workflow DAGs.Therefore, although they consider both time andcost constraints in planning, these techniques arenot really applicable for admission control forworkflows.
To resolve the multi-objective (time and cost,commonly) DAG planning problem, evolutionarytechniques (e.g., genetic algorithms) have beenwidely used. Examples can be found in [29, 31,37, 38]. Although algorithms based on evolu-tionary techniques normally perform well on op-timization, they also require significantly highplanning costs and, thus, are naturally too time-consuming for BDC-planning. Even though anaccelerated genetic algorithm has been proposedfor multi-criteria job scheduling in Grid environ-ments [12], the application model and constraintsare different to our work. Another multi-objectivescheduling effort for heterogeneous environmentsis presented in [8], where a multi-objective listscheduling (MOLS) algorithm is proposed to finda solution which dominates or converges to a con-straint vector (a set of constraint values specifiedby the user for several objectives). MOLS differsfrom our work on the aim the algorithm wants toachieve. More specifically, the aim of MOLS is tofind a dominant solution by using Pareto relations.In contrast, our proposed heuristic focuses onmaximizing the likelihood that a BDC-plan can befound in the presence of varying user constraintsand existing loads.
There are also bi-criteria scheduling heuris-tics for workflow applications derived from localsearch and list scheduling techniques. Wieczoreket al. [19] propose a two-phase algorithm (DCA)to address the optimization problem with two in-dependent generic criteria for workflows in Gridenvironments. The algorithm optimizes the pri-mary criterion in the first phase, then optimizesthe secondary criterion while keeping the primary
636 W. Zheng, R. Sakellariou
one within the defined sliding constraint. In [24],two scheduling heuristics based on guided localoptimization, LOSS and GAIN, were proposed toadjust a schedule; these may be based on a time-optimized heuristic or a cost-optimized heuristic,to meet users’ budget constraints. As an exten-sion to the DLS algorithm [28], BDLS, presentedin [7], focuses on developing bi-criteria schedulingalgorithms to achieve a trade-off between execu-tion time and reliability. Based on local search,DCA and LOSS require a considerable numberof repetitions to obtain a final result. As a listscheduling heuristic, BDLS may have low com-plexity. The main planning costs of BDLS arisefrom the computation of dynamic priorities whenmaking scheduling decisions.
However, the key issue with these heuristicsis that they do not consider the existing loadof resources in their assumptions, and thus tendto produce plans which may lead to reservationconflicts, i.e., given that one resource can onlyexecute one task at a time, the planned task mayoverlap with the tasks of other workflows whichhave already been reserved. With an added com-munication phase between the planner and serviceprovider (as will be described in Section 4.3) anda slight change in algorithm design, these heuris-tics may be modified in order to produce BDC-plans without reservation conflicts. In Section 5,such modified heuristics will be compared withour proposed heuristic, BHEFT, in terms of bothplanning performance and overhead.
To the best of our knowledge, there is no pre-vious study which attempts to address equally allfour key elements of the BDC-planning problemat the same time, that is: (i) workflow planningfor (ii) admission control of (iii) market-orientedenvironments while (iv) considering dynamicallyexisting loads in non-dedicated resources. Unlikethe aforementioned works which exhibit draw-backs with respect to the BDC-planning chal-lenges mentioned in Section 1, BHEFT is a novelbi-criteria DAG planning heuristic proposed toaddress these challenges. By applying BHEFT,the planner of a market-oriented environmentis enabled to effectively determine whether aworkflow request should be accepted or not in areal-time manner so that the establishment of anSLA can be facilitated.
3 Problem Description
Given a workflow request with budget B anddeadline D, the BDC-planning problem is to mapevery workflow task onto a suitable service in-stance (i.e., a resource) and specify an appropriatestart time for each mapped task so that the overallcost and execution time of the workflow are withinB and D, respectively. Of course, such a producedplan cannot overlap with existing reservations. Wenote that finding an appropriate start time forevery task results in a reservation for every task ona specific resource; then, the whole plan consistsof a set of reservation slots for all the tasks. Suchan approach for task execution is commonly usedin practice [20, 26, 29, 30, 34, 37, 39]. As explicitlyshown in [39], such reservations may also includesome slack to provide ample time for the success-ful execution of each task.
From the service provider’s perspective, thereis an incentive to maximize the number ofworkflow requests that are serviced. Thus, as longas a BDC-plan can be found to satisfy the con-straints of a new request to execute a workflow, itis expected that the provider’s admission controlwill give consent to the admission of a request.Therefore, a key objective of a BDC-planningheuristic is to maximize the likelihood that aBDC-plan can be successfully found for a givenworkflow request, which, in turn, can maximizethe acceptance ratio of admission control for theprovider.
3.1 Notation and Assumptions
The notation used and the assumptions made tosolve the BDC-planning problem are summarizedbelow:
– A Directed Acyclic Graph (DAG) G is usedto represent the submitted workflow applica-tion. A DAG consists of a set of nodes V, eachof which denotes a workflow task, and a set ofedges E, each of which denotes a dependencybetween two dependent tasks.
– A set of resources, which are assumed to beheterogeneous (that is, of different capaci-ties), is given. It is also assumed that each
Budget-Deadline Constrained Workflow Planning for Admission Control 637
resource provides a set of service types andeach task is associated with a particular servicetype. For simplicity, it is assumed that eachresource can provide every type of service,hence it can serve any task of the DAG. Thus,when task ti runs on resource r j, it meansthat task ti uses the service si, j provided byresource r j.
– For each task of the DAG, ti, on each re-source, r j, an estimated execution time, de-noted by eti, j, is known. For each resource,the price of running on the resource, denotedby pj, is also known. Then, the cost of run-ning ti on r j, denoted by costi, j, can be cal-culated by costi, j = eti, j × pj. In addition, theamount of data that needs to be transmittedbetween tasks is known, as well as the trans-mission time per data unit between resources.So the data transmission time, denoted bydt, between any two allocated tasks can bedetermined.
– A user specifies a deadline (that is, the time bywhich the whole DAG/workflow must finish),denoted by D, and budget (that is, the maxi-mum cost that the user is willing to pay), de-noted by B. In real practice, users may specifyan earliest start time as well as a latest finishtime. In our setting, without loss of generality,we can assume that the execution of the appli-cation starts at time zero.
– In every resource, confirmed reservationsmay exist. This is regarded as existingload denoted by the set of pairs L ={(st0, f t0), · · · (stk, f tk), · · · }, where st denotesthe start time of a reservation and f t denotesthe finish time of this reservation. Here, itis assumed that only one service can run ata time on a resource. Thus, each reservationreserves the whole resource for a certain pe-riod of time to execute a task which makesuse of a service instance provided by theresource.
– The planner has to communicate withresource owners to produce a plan withoutreservation conflicts. We assume that theplanner has to send a Time Slot Query(TSQ), i.e., ask for a certain length of timeslot on a specific resource, and then theresource owner responds with the earliest
availability. Here, the alternative of allowingthe planner to retrieve all free time slots of allresources is not considered, since individualresource owners may not want their workload,which may be commercially sensitive, to beexposed. Let Lp be the existing load ofresource rp, we define TSQ in the formof fQ(ti, rp, dati,p, dur) = min{(a, b)|(a, b)∩Lp = ∅, a ≥ dati,p, b = a + dur}, where dati,p
means the time all required data is availablefor task ti on resource rp, and dur denotes therequired duration which is considered to beequal to the estimated execution time eti,p.For instance, let L1 = {(0, 6), (8, 12), (30, 50)}and for task 0, dat0,1 = 0 and et0,1 = 3, then itholds that fQ(0, 1, 0, 3) = (12, 15).
3.2 Planning Model
As indicated above, three different entities areconsidered in our model of the BDC-planningproblem: user, planner, and local resource man-ager(LRM).
A local resource manager (LRM) owns re-sources and provides particular services availablefrom its resources. The information related tothese services is registered in a service reposi-tory to be retrieved by the planner or publishedto users. Moreover, the local resource managerresponds to enquiries from the planner aboutthe availability of a requested time slot on itsresources, information which is needed to makeplanning decisions.
A user is the consumer of the provided ser-vices. To run an application on the resources, theuser needs to submit first a request specifyingthe workflow he/she wants to run, as well as thebudget and deadline constraints.
A planner comes up with a plan of how thesubmitted workflow can run on the resourcesowned by LRMs, taking into account their exist-ing reservations. The planner does not own anyresource, so it is not supposed to directly schedulethe workflow tasks to the resources. Instead, itplans based on the retrieved information aboutresources from LRMs.
Figure 1 shows how the user, the plannerand the LRMs interact during a BDC-planning
638 W. Zheng, R. Sakellariou
Fig. 1 Sequence diagramfor BDC-planning
procedure. The protocol can be summarized asfollows:
1. A user submits a workflow request with bud-get and deadline to the planner.
2. Upon receiving the workflow and associatedconstraints, the planner begins planning in or-der to find possible allocations for all tasks ofthe workflow. To do this, the planner needsto find the earliest finish time of a task on aparticular resource (assuming an earliest starttime). To get this information, the plannerneeds to send an enquiry (TSQ) to the LRMwhich controls the resource.
3. Once planning completes, the planner checkswhether the constraints can be satisfied andresponds to the user. If any of the constraintsis not met, the workflow request will be re-jected; otherwise, the workflow tasks will bereserved according to the planning result andthe user will be notified with acceptance.
It is also assumed that the user will accept thereservation as long as constraints are met. It iseasy to modify the protocol to cover the case thateven though user constraints are met, the usermay still not proceed with a reservation.
4 Solution of the BDC-Planning Problem
4.1 The Proposed Heuristic
The proposed heuristic, BHEFT, is an exten-sion of the well-known DAG scheduling heuristicHEFT by taking a budget constraint into accountwhen planning tasks. Similar to the original HEFTalgorithm, BHEFT also has two major phases:task prioritizing and service selection. BHEFT isshown in Fig. 2.
In the task prioritizing phase, the prioritiesof all tasks are computed using upward rankingwhich is the same as defined in the original versionof HEFT [32]. The rank of a task i is recursivelydefined by
ranki = eti + maxj∈Succ(i)
{dti, j + rank j
}(1)
where Succ(i) is the set of the child tasks of task i,eti is the average execution time of task ti, dti, j isthe average data transfer time of edge ti → t j. Inthe case of childless nodes, the rank equals to theaverage execution time.
In the service selection phase, the tasks areselected in order of priority. Each selected task isallocated to its “best possible” service, of whichthe metric may change according to an assess-
Budget-Deadline Constrained Workflow Planning for Admission Control 639
Fig. 2 The BHEFT heuristic
ment of the spare budget which varies as plan-ning proceeds. For this assessment, three variablesare used: Spare Application Budget (SAB), Cur-rent Task Budget (CT B), and Adjustment Factor(AF). Suppose that the kth task is being allocated,SABk and CT Bk are respectively computed by
SABk = B −∑k−1
i=0ci −
∑n−1
j=kc j (2)
CT Bk = ck + SABk × AFk (3)
where B is the given budget, ci is the reserva-tion cost of the allocated task i, c j is the averagereservation cost of the unallocated task j overdifferent resource mappings, n is the number oftasks. It is not difficult to see that SABk is a valueintended to depict the expected spared budgetwhen planning task tk, CT Bk is a value intendedto quantify the budget allocated to tk, and AFk isa value intended to act as a weight that tunes theimpact of SABk on CT Bk. We note that differentvalues for AFk may lead to different variants ofBHEFT with different results. Apparently, givencertain values of ck and SABk, CT Bk grows asAFk increases. For a task k, the larger CT Bk is,the more likely it is that k will be allocated toa more expensive but more powerful resource.This is because AFk is used to adjust the amountof spare budget for the whole workflow (SABk)given to the current task. A reasonable approach
is to make AFk equal to the ratio between theaverage cost of the current task to the sum of theaverage costs of the remaining tasks as follows:
AFk ={
ck/∑n−1
i=k ci : SABk ≥ 00 : SABk < 0
(4)
Based on the allocated budget to task tk, aset S∗
k is constructed consisting of an af fordableservice for task k, i.e.,
S∗k = {sx,p|∃sx,p, ck,p ≤ CT Bk} (5)
Then the “best possible” service is selected by theselection rules as follows:
1. If S∗k = ∅, the affordable service with the ear-
liest finish time is selected;2. If S∗
k = ∅ and SBA ≥ 0, the service with theearliest finish time selected;
3. If S∗k = ∅ and SBA < 0, the cheapest service
is selected;
The algorithm terminates when all tasks, asranked in the task prioritizing phase, areconsidered.
4.2 An Example
An example workflow with 10 tasks is used hereto illustrate the BHEFT heuristic. The example isshown in Fig. 3. More specifically: Fig. 3a showsthe structure of the DAG and the amount ofdata transferred as a result of each dependence;
640 W. Zheng, R. Sakellariou
Fig. 3 An exampleof BDC-planning
Fig. 3b gives the estimated execution time of eachtask on three different resources; Fig. 3c givesthe data transmission cost between different re-sources; Fig. 3d gives the price for running taskson each resource; and Fig. 3e depicts the exist-ing load (that is, existing reservations, which aredenoted by the shaded part and annotated withspecific start and finish times next to each part)of each resource.
We note that the arrows in Fig. 3a, denot-ing a dependence, may cause a delay to transferdata between two dependent tasks if the tasksare executed on different resources. This delayis computed by the product of the amount ofdata transferred and the transmission cost. Forexample, task 8 needs to transmit 35 units ofdata to task 9 and the transmission cost betweenresource 0 and resource 2 is 1.40. This means thatif task 8 is executed on resource 0 and task 9 isexecuted on resource 2, there will be a delay equalto 35 × 1.40 = 49 until all the data generated bytask 8 and needed by task 9 is transferred acrossresources. We assume that this delay is zero if two
tasks, connected by a dependence, are executedon the same resource.
Assume a deadline of 250 and a budget of 150.Then, the steps taken by BHEFT to find a possi-ble allocation for each task (and, hence, a BDC-plan) can be summarized as shown in Table 1;workflow tasks are sorted in the order that theyget planned (as ranked). The values computed foreach planned task clearly suggest how BHEFTguides the planning to be within budget and dead-line constraints. For instance, when the first task isplanned, the expected spare budget for the wholeapplication (represented by SAB0) is less thanzero. Then there is only one affordable service fortask 0, which is provided by the cheapest resource.When task 8 is planned, there is an abundance ofspare budget, so all three services are affordable.In this case, for task 8, the service with the mini-mum execution time can be chosen.
Figure 4 shows the outcome of BDC-planningusing BHEFT on the example DAG. In orderto satisfy the budget constraint in this example,BHEFT allocates most of the workflow tasks to
Budget-Deadline Constrained Workflow Planning for Admission Control 641
Table 1 An example to illustrate the steps of BHEFT using the workflow in Fig. 3
the cheapest resource R2, while only one task isallocated to the more expensive resource R0. Itcan also be seen that the start time of task 7 andtask 9 relies not only on task dependencies, butthe existing load as well.
Fig. 4 The possible schedule plan generated by BHEFTusing the workflow in Fig. 3
4.3 Extensions to Existing Bi-Criteria PlanningHeuristics
As already mentioned in Section 2, thereare several bi-criteria scheduling heuristics forworkflows, which, however, were not designedspecifically for the BDC-planning problem andneed to be modified to produce BDC-plans. Thismeans that they need to incorporate a mecha-nism for obtaining existing reservations from re-sources, by means of Time Slot Queries (TSQs),as specified in Section 3.1.
There are two ways for a scheduling heuristicto produce a plan that avoids reservation conflicts.One way is to produce an initial plan without con-sidering the existing reservations and then, usingTSQs, to reallocate the time slot for each mappedtask in the order that tasks are initially scheduled(essentially, time slots will be shifted towards alater time, which can fully accommodate the slotsonto a resource). In this case, the communicationcosts may be small but the overall performance ofthe heuristic may degrade, as a result of longermakespans. The second way is to modify algo-rithms to take into account existing reservations,but this requires more fine-grain changes to thealgorithms. The first approach is less costly andwe used it to extend DCA [19], which alreadyhas a high execution time cost, whereas we usedthe second approach to modify LOSS [24] andBDLS [7] as will be described next.
The basic idea of the LOSS approach [24] isas follows. The approach uses the schedule pro-duced by any DAG scheduling heuristic (e.g.,HEFT [32], HBMCT [25], etc.) as an initial
642 W. Zheng, R. Sakellariou
assignment. If the cost of this assignment exceedsthe budget, the LOSS routine is invoked. Theapproach computes the LOSS weight for each taskto each resource, and recursively re-assigns tasksuntil the budget constraint is met or all possiblereassignments have been tried. Here, the LOSSweight is defined as follows:
LossWeighti, j = Tnew − Told
Cold − Cnew(6)
where Told and Cold (Tnew and Cnew, respectively)stand for some time property and cost propertyassociated with the current assignment (or theassignment after re-assigning task i to resourcej, respectively). For example, T and C can referto the execution time and cost for an individualtask; or they can refer to the makespan and theoverall cost for the whole application. Based onour experience, using the latter leads to betterperformance for LOSS.
Within this setting, in order to ensure the planproduced by LOSS will not conflict with existingreservations, we make a simple extension. Wetake into account the existing load every time theLOSS weight is computed. That is to say, given anassignment of tasks to resources, for each task, theplanner has to communicate with a local resourcemanager to get an idea about the earliest finishtime of the task on a particular resource. Thiscan be realized by using TSQ as introduced inSection 3.1. Using such an extension, LOSS willno longer produce a plan conflicting with existingreservations. However, as LOSS needs to com-pute the LOSS weight for each task on each re-source, the computation and communication costwill be considerably higher with this extension.
The extension of BDLS is similar to that ofLOSS. We change BDLS in such a way that everytime there is a need to compute the earliest finishtime of a task on a resource, TSQ is used.
5 Performance Evaluation
5.1 Experimental Setting
To run the experiments, a job planner and aset of resources were simulated by Java pro-
grams distributed on computing nodes with IntelI3 CPU with 3.1 GHz, 2 GB memory and con-nected through Gigabit Ethernet. The communi-cation between the job planner and the serviceproviders was implemented by socket program-ming. The existing load of resources was also ran-domly generated for simulation. Given a specificperiod between time a and b , the existing loadof each resource p (i.e., Lp) is parameterized bytwo pre-specified values: Utilization Rate (UR)and Average Task Load (ATL). The former isthe ratio of the total reserved time to the wholeperiod, and the latter is the ratio of the numberof tasks appearing during a certain period to thelength of this period. Then, the average durationof a reservation slot is RD = UR/ATL; for theaverage duration of an idle slot we can use theformula I D = (1 − UR)/ATL.
The following procedure describes how the ex-isting load of resource p (Lp) was constructed fora given period of time, specified by the interval[a, b ].1. Set Lp = ∅ and current time CT = a.2. Randomly determine current state among re-
served and idle with equal probability.3. If reserved: (a) randomly generate reserved
duration RD by normal distribution withmean RD and standard deviation RD/2 usingonly positive values for RD (RD > 0); (b)set Lp = Lp ∪ (CT, CT + RD); (c) set CT =CT + RD; (d) switch current state to idle.
4. If idle: (a) randomly generate idle durationI D by normal distribution with mean I D andstandard deviation I D/2 using only positivevalues for I D (I D > 0); (b) set CT = CT +I D; (c) switch current state to reserved.
5. Repeat Steps 3 and 4 until CT reaches b .
There were two service providers in the eval-uation, each of which managed three resources,hence, there were 6 resources in total. Note thatthe model of task execution time and cost in thispaper is different to the model of our earlier workpresented in [40]. Instead of assuming task execu-tion times and costs are consistent with resourcepower as in [40], we assume there is arbitraryheterogeneity with respect to task execution time.For each task on each resource, the estimatedtask execution times are randomly chosen from
Budget-Deadline Constrained Workflow Planning for Admission Control 643
the interval [10, 100]. For each resource, the pricefor running a task on it is randomly chosen fromthe interval [0.1, 1]. The period considered formodelling existing reservations was [0, 5000].
Four types of DAGs, corresponding to real-world workflow applications, were considered inthe experiments. These are:
– AIRSN [15] with 53 nodes– LIGO [6] with 77 nodes– Montage [3] with 98 nodes– SDSS [2] with 124 nodes
The communication computation ratio (CCR)was randomly selected from the interval [0.1, 1.0]and the data amount transmitted between tasks israndomly generated according to the CCR.
Given a DAG, constraints for reasonable val-ues for deadline and budget were generated asfollows. For simplicity, a job was always assumedto start at time 0. The makespan MHEFT wascomputed by applying the HEFT algorithm [32]to the DAG without considering the existing loadof resources. The deadline constraint DC wasconsidered to be located between the lower boundLBdc = MHEFT and the upper bound UBdc = 3 ×MHEFT. A deadline ratio φd was used to depict theposition of DC by DC = LBdc + φd × (UBdc −LBdc), where 0 ≤ φd ≤ 1.0. For budget constraint,LBbc was the lowest total cost obtained bymapping each task to the cheapest service, andU Pbc, the highest total cost obtained conversely.Similarly, a budget ratio φb was used to spec-ify the possible budget constraint BC = LBbc +φb × (UBbc − LBbc), where 0 ≤ φb ≤ 1.0.
BHEFT was compared with DCA [19],LOSS [24] and BDLS [7] in the experiments.As mentioned in Section 3, some modificationis needed to use these heuristics, which donot consider the existing load of resources, to
produce a contention-free BDC-plan. Accordingto the evaluation in [19], where existing loads onresources (and hence TSQ) are not considered,DCA, which is based on extensive local search,has the best optimization performance but thehighest time overhead, as opposed to BDLSwhich is a static list scheduling heuristic using adynamic priority. Therefore, TSQ was introducedinto LOSS and BDLS only, while DCA wasmodified as mentioned in Section 3 (that is, a planis first generated without considering existingloads and, then, TSQ is used to reallocate the timeslot allocated to each task to resolve reservationconflicts).
When showing the experimental results infigures, the suffix _TSQ was added to the namesof the algorithms which used TSQ, to distin-guish them from DCA which does not considerTSQ. The original names, without the suffix, areused for short in the discussion. In terms of theconfiguration of DCA and BDLS, the same set-tings as used in [19] are adopted, i.e., a memo-rization table consisting of 100 cells with up to10 intermediate solutions stored in each cell wasused by DCA, and the parameter δ for BDLS wasdetermined by a binary search with a maximumof 15 loop iterations. Furthermore, LOSS3 in [24]is assumed to represent LOSS. Finally, all heuris-tics terminate immediately when a BDC-plan isfound.
For each experiment, all of the parametersexcept for those which were given and fixed,were re-initialized at random with the abovespecifications. After a heuristic was run, if a BDC-plan was found, the planning succeeded, oth-erwise, a failure was reported. To analyze theperformance of each heuristic, the experiment wasrepeated multiple times and the metric PlanningSuccess Rate (PSR) was used, as defined below:
PSR = 100 × number of times for which a BDC-plan was found
number of total repeated times of experiment(7)
Four sets of experiments were carried out. Inthe first one, φd and φb were fixed to be 0.5,while UR was varied for each resource from 0to 0.5 in the step of 0.1 with the corresponding
ATL = 0.05 × UR. The experiment was repeated500 times to observe how the existing load ofresources affected the PSR of each heuristic. Inthe second set of experiments, UR was randomly
644 W. Zheng, R. Sakellariou
generated in the interval [0.1, 0.4], and the ATLwas computed correspondingly. φd and φb wereselected from the set {0.25, 0.5, 0.75} to form 9combinations which covered a wide spectrum ofdiverse user requests; the experiment was thenrepeated 500 times for each combination. Thus,the value of PSR was investigated under variousconstraints (from tight to relaxed). In the thirdset of experiments, we studied the same 9 com-binations for user requests but for three specificvalues of UR. Finally, in the fourth experiment,the average running time of each heuristic to doplanning was measured. This experiment was re-peated 100 times for each workflow with variouscombinations of constraints.
5.2 Experimental Results
First set of experiments Figure 5 shows the resultsof the first set of experiments where the impactof the existing load of resources is investigatedby considering six values for the Utilization Rate,UR, from 0 to 0.5. Here, φd and φb are bothfixed to be 0.5 to avoid unnecessary disturbancecaused by setting the user constraints to be tootight or too relaxed. It can be seen from Fig. 5that the behaviour of the compared heuristicsin terms of their PSR follows the same patternregardless of the type of DAG. BHEFT showsthe best performance in most cases where theutilization rate is lower than 0.3. When the uti-lization rate is equal to 0.3, LOSS outperformsBHEFT. LOSS’s superiority is more profound aswe move from the smallest DAG (AIRSN with53 nodes) to the largest DAG (SDSS with 124nodes). Only in the case where SDSS is used andutilization rate equals 0.3, BDLS performs thebest and clearly better than BHEFT. As expected,all heuristics perform worse as UR increases. Witha fixed setting of user constraints, it looks like theperformance of LOSS and BDLS is more stablethan BHEFT. In the third experiment, we will seehow, with different constraints, the performanceof these heuristics changes as the utilization rategrows.
Second set of experiments In the second set ofexperiments, the performance of each heuristicwas investigated under various circumstances of
user constraints, from tight to relaxed. As alreadymentioned we considered nine combinations ofdifferent types of constraints. Figure 6 shows thevalue of PSR for different types of DAG anddifferent budget-deadline constraints. Again, itcan be seen from Fig. 6 that the behaviour ofthe compared heuristics in terms of their PSRfollows the same pattern regardless of the type ofDAG. One interesting observation is that whenboth the deadline constraint and the budget con-straint are tight, for example, φd = 0.25 and φb =0.25, all four heuristics obtain low PSRs; amongthem, BHEFT achieves the best PSR which is be-tween 40 to 60 %, and LOSS achieves the secondbest PSR which is between 30 to 50 %. In addi-tion, although BHEFT performs worse than eitherLOSS or BDLS in some cases, it never performsclearly worse than both LOSS and BDLS at thesame time. This suggests that BHEFT may be lesssensitive to the tightness of budget and deadlineconstraints, compared to LOSS and BDLS. Infact, when the deadline constraint is tight, BDLSperforms particularly bad; while when the bud-get constraint becomes tight, LOSS’s performancedegrades significantly. In contrast, BHEFT dealswith the impact of the constraints in a more gra-cious way.
Third set of experiments In order to consider theimpact of the Utilization Rate in more detail, westudied the PSR for the nine different combina-tions of user constraints and three different valuesof utilization rate. The results, for two types ofDAG, Montage and LIGO, are shown in Figs. 7and 8. Once again, BHEFT performed the bestamong the competitive heuristics when both dead-line and budget constraints are tight. The perfor-mance of DCA, which is the only heuristic thatdoes not consider the existing load during plan-ning, degrades dramatically as the utilization rategrows. This highlights the impact that the existingload of resources may have on BDC-planning.With different values of utilization rate, we canagain observe that BHEFT is less sensitive to thevariance of constraints than LOSS and BDLS. Asexpected, when the Utilization Rate is low, thatis when there is little existing load on resources,and the constraints for budget and deadline are
Budget-Deadline Constrained Workflow Planning for Admission Control 645
Fig. 5 First set ofexperiments: PSR withdifferent utilization rateof resources
(a) AIRSN, 53 nodes
(b) LIGO, 77 nodes
(c) Montage, 98 nodes
(d) SDSS, 124 nodes
646 W. Zheng, R. Sakellariou
Fig. 6 Second set ofexperiments: PSR withdifferent types ofconstraints
(a) AIRSN, 53 nodes
(b) LIGO, 77 nodes
(c) Montage, 98 nodes
(d) SDSS, 124 nodes
Budget-Deadline Constrained Workflow Planning for Admission Control 647
Fig. 7 Third set ofexperiments: PSR withdifferent utilization ratesand constraints forMontage
(a) Montage, Utilization Rate = 0.2
(b) Montage, Utilization Rate = 0.3
(c) Montage, Utilization Rate = 0.4
relaxed (e.g., φd = 0.75 and φb = 0.75), all heuris-tics perform equally well.
In the first, second, and third set of expriments,we compared the four competing heuristics in atotal of 114 different cases. We also counted howeach of the four heuristics ranked in comparisonto the others. To do this, first we excluded thosecases where none of the heuristics obtained aPSR over 10 %. Such cases exist when: (i) the
Utilization Rate is 0.4 or 0.5 in Fig. 5; and (ii) φd =0.25 in Figs. 7c and 8c. Then, a total of 100 casesremained. In these 100 cases, for each heuristic,we count how many times the heuristic ranksfirst, second, third or fourth. The relevant countis denoted by R1, R2, R3 and R4, respectively, inTable 2. Note that two or more heuristics canshare the same rank if there is a tie. Finally, anaverage ranked value, AR, is obtained by comput-
648 W. Zheng, R. Sakellariou
Fig. 8 Third set ofexperiments: PSR withdifferent utilization ratesand constraints for LIGO
(a) LIGO, Utilization Rate = 0.2
(b) LIGO, Utilization Rate = 0.3
(c) LIGO, Utilization Rate = 0.4
ing AR = (R1 + 2R2 + 3R3 + 4R4)/100.0 for eachheuristic. As shown in Table 2, the results clearlyindicate that BHEFT outperforms other competi-tors on average.
Fourth set of experiments In the fourth experi-ment, the execution time needed by each algo-rithm to obtain a planning result was studied.Figure 9 shows how the running time of each
heuristic varies over diverse types of DAG andconstraint settings. It is not surprising that, in mostof the cases, LOSS has the highest time costs dueto the overhead caused by numerous TSQs. Itcan be easily imagined that some other sophisti-cated algorithms, such as DCA or genetic algo-rithms, if using TSQ when scheduling, may needeven more time compared to LOSS. Our resultssuggest that even LOSS may not be scalable to
Budget-Deadline Constrained Workflow Planning for Admission Control 649
Table 2 Ranking count results for the first, second andthird set of experiments
large applications and too time-consuming for on-line workflow planning. Although not using TSQ,the DCA heuristic considered in the experimentstill has an execution time comparable to BDLS,and this is significantly higher than BHEFT. Thelatter two algorithms, BDLS and BHEFT, areboth based on list scheduling, but BHEFT needsevidently less running time than BDLS due tosimpler computation and the fact that less commu-nication is needed when making scheduling deci-sions. Furthermore, BHEFT is the most scalablein terms of the growth of DAG size (and poten-tially the number of resources which is consideredconstant in this experiment). As can be seen inthe graph, when planning SDSS with 124 nodeson 6 resources, BHEFT only needs around 0.08 son average. This suggests that BHEFT copeswell with the real-time requirements of workflowplanning.
5.3 Summary of Observations
The experimental results lead to the followingobservations:
– The existing load of resources may have sig-nificant impact on BDC-planning. Directly ap-plying a heuristic that does not consier theexisting load of resources in job planning (e.g.,DCA) may result in a significant degradationof PSR. In contrast, BHEFT, which takesthe existing load of resources into account, isable to achieve a significant improvement onthe success rate of finding a BDC-plan whichsimultaneously satisfies deadline and budgetconstraints.
– Some guided local search heuristics (for exam-ple, LOSS) may sometimes perform slightlybetter than BHEFT, but at a higher executiontime cost and, thus, they are naturally non-scalable as the size of DAG increases. Suchheuristics are not suitable for BDC-planningwith real-time requirements.
– Compared to the results in our previouswork [40], where task execution times andcosts were assumed to be consistent with theresource power, the performance of BHEFTand DCA is similar in the evaluation of thispaper too, where task execution times andcosts are assumed to be arbitrary. The notable
Fig. 9 Fourth set ofexperiments: executiontime for each heuristicwith different DAGs anduser constraints
650 W. Zheng, R. Sakellariou
exception is LOSS, which performs much bet-ter when task execution times and costs are as-sumed to be arbitrary. This is possibly becauseof its use of the weight (6), which can easilytake into account differences of cost and exe-cution. This implies that LOSS may be betterused in computing environments where thereis inconsistent heterogeneity even though fur-ther investigation is required to support this.
– In the context of BDC-planning, simple listscheduling bi-criteria heuristics (for example,BHEFT and BDLS) may be as effective asmore sophisticated heuristics based on exten-sive local search, such as DCA.
– With low running cost, BHEFT seems to bea good choice satisfying the requirements ofBDC-planning.
6 Conclusion and Future Work
BDC-planning is required before an SLA is es-tablished in order to guarantee that a serviceprovider can meet the SLA without risking itsfailure. This paper proposed BHEFT, a novellow-cost bi-criteria heuristic based on the well-known DAG scheduling heuristic HEFT, to fulfillthe specific requirements of BDC-planning. Theexperimental results suggest that BHEFT appearsto be at least as effective, or even more so thanother existing sophisticated bi-criteria workflowscheduling heuristics, and has a lowest executiontime cost and good scalability. It also appearsthat BHEFT can effectively and efficiently finda BDC-plan under various circumstances of con-straints, from tight to more relaxed. Thus, the useof BHEFT can enable a quick admission controldecision (i.e., a judgement of whether or not asubmitted user request is acceptable), and makeit possible to automate the creation of an SLA(from the provider’s point of view) over diverseuser constraints.
Based on the work in this paper, further workcould try to examine the performance of BHEFTusing different DAGs, settings of resources, andpossibly a different core DAG scheduling heuris-tic (that is, not HEFT). Further experimentscould also investigate how BHEFT can cope with
significant overestimations or underestimationsof task execution time and assess its robustnessagainst such uncertainties.
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