Bidding policies for market-based HPC workflow scheduling

0.74 MB·

by  Andrew Burkimsher

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Bidding policies for market-based HPC workflow
scheduling
Andrew Burkimsher, Leandro Soares Indrusiak
{andrew.burkimsher, leandro.indrusiak}@york.ac.uk
Department of Computer Science, University of York, Heslington, York, YO10 5GH, UK
Abstract—This paper considers the scheduling of jobs on is most valuable [23]. There are real costs to HPC providers
distributed, heterogeneous High Performance Computing (HPC) for running work, so it may sometimes be more worthwhile
6 clusters. Market-based approaches are known to be efficient for
to discard work whose value is too low than to run it.
1 allocating limited resources to those that are most prepared to
Work is run on computing clusters because it is valuable to
0 pay. This context is applicable to an HPC or cloud computing
2 scenario where the platform is overloaded. the users and organisations who submit it. This value can be
Inthispaper,jobsarecomposedofdependenttasks.Eachjob represented as a real amount of money that users are willing
n
has a non-increasing time-value curve associated with it. Jobs to pay for their results. This value is not always fixed. This is
a
aresubmittedtoandscheduledbyamarket-clearingcentralised
J becauseworkreturnedearliermayallowusersororganisations
auctioneer. This paper compares the performance of several
6 policies for generating task bids. The aim investigated here is to tobemoreproductive,whereassomeworkmayhavenovalue
2 maximise the value for the platform provider while minimising at all if it is returned too late [5].
the number of jobs that do not complete (or starve). Scheduling large-scale computing systems has traditionally
C] ItisfoundthattheProjectedValueRemainingbiddingpolicy been done through list scheduling [8], [16]. This is where all
givesthehighestlevelofvalueunderatypicaloverloadsituation,
the work in a queue is ranked by an appropriate metric, and
D andgivesthelowestnumberofstarvedtasksacrossthespaceof
allocatedtohardwareinsortedorder.Wherevalueisassigned
. utilisation examined. It does this by attempting to capture the
s urgency of tasks in the queue. At high levels of overload, some towork,market-basedprinciplescanbeappliedtoscheduling.
c
alternative algorithms produce slightly higher value, but at the The usefulness of work on list scheduling can be employed
[
cost of a hugely higher number of starved workflows. in a market-based way. The values calculated for ranking in a

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Index Terms—Market-Based, Scheduling, Value, HPC, Value, list scheduler can instead be used as bids that each piece of
v
Value-Curves,ValueRemaining,Workflows,Starvation,Respons- work submits to an auctioneer. Past research has investigated
7
4 iveness using value as bids [10]. However, the bids can be different
0 than just the values of jobs at a given moment in time. It has
7 been shown [5] that in the context of list scheduling, ordering
I. INTRODUCTION
0 tasks by total job value does not necessarily give the highest
1. Inrecentyears,computationalperformancehasincreasingly overall value under overload.
0 been achieved through increasing parallelism rather than in- This paper explores the effectiveness of different bidding
6 creased single-core performance. This is mainly due to the policies in a market-based scheduling scenario. This is to
1
exponential increase in power consumption required to run evaluatewhichprovidethehighestvalue,especiallyinperiods
:
v processorsathigherclockspeeds[9].Processorshavebecome of overload when not all work is able to run.
i multicore, and multicore processors have been grouped into
X
clusters and networks of clusters, known as grids [12]. These
r II. LITERATURESURVEY
a High Performance Computing (HPC) systems have grown to
be huge in scale, especially those that support the operations Schedulingusingmarket-basedtechniqueshasbeenstudied
of cloud computing corporations. over a long period, with pioneering early work by Sutherland
ManykindsofworkrunonHPCsystemsarenotindepend- in the 1960s [21]. Since then, a great deal of work has been
ent. Instead, workflows (or jobs) are run that are made up of doneonthestructureofmarkets,investigatingwhichstructures
several individual pieces of software (tasks), each of which bestpromoteeconomicefficiency.Auction-basedmarketshave
takes some input and produces some output. This leads to the been looked at by Waldspurger et al. [24] whereas market-
notion of dependencies between tasks, which restrict tasks to clearingtechniqueswhereresourcesareallocatedtoworkuntil
starting only once all their dependencies have completed and one or other is consumed were investigated by Miller and
their input data transmitted. Drexler [17]. Lai et al. have examined doing the allocation of
Large-scalesystemssuchasthesecanexperienceperiodsof resourcesinproportiontothevalueofbids[13].Popoviciand
high demand. This can even extend into periods of overload, Wilkes [18] investigated market-inspired admission control.
where work is arriving faster than it can be executed. HPC Dube [7] gives a good survey of the state of this research
providers need to be able to effectively prioritise work during and concludes that various different market structures all hold
these periodsto ensure the mostimportant work isrun. Cloud promise, showing the benefits of better allocation and greater
providers who sell computing capacity on the open market decentralisaion(andhencescalabilityandfault-tolerance)than
will wish to maximise their profits by running the work that traditional schedulers.
2
Anecessarypartofamarketbasedsystemisthatjobshave The critical path [11] of a job, Jk, is equivalent to the
CP
a certain value to users, and that this value is represented in largest upward rank of any of its component tasks: ∀Ti ∈
the market by their bids [10]. There has been much past work Jk : Jk = max(cid:0)Ti(cid:1) [22]. This is the length of time that
CP R
on scheduling to maximise the value of a workload [14]. The the job would take to execute if the number of cores requied
problem of maximising workload value where job value is a wasunbounded,whichisequivalenttoitsminimumexecution
function of time was extensively researched by Locke [15] time.
for systems schedulable by the Earliest Deadline First list
scheduling policy, and has subsequently been applied to more
B. Platform Model
general scheduling problems [5], [6].
It seems that there has been little research into using value The basic unit of the platform model is an execution core.
curves rather than fixed job values when scheduling in a Eachclusterismadeupofanumberofcores.Multicoretasks
market-based context. This is likely because markets need a must execute within a single cluster, and consume a number
singlepriceforeachbidsubmittedbyajob,notacurve.Yetin of cores for the duration of their execution. Cores are not
previous work [5], it has been shown that value curves can be shared between executing tasks. Within a cluster, cores are
usedtocreatesinglerankingvaluesforlistschedulingatgiven assumed to have negligible communication delays between
times in a simulation. This paper will extend this approach by them. For example, this could be due to all cores sharing a
using these values as bids in a market-based framework. single networked file system. In the HPC context considered,
executiontimesaremeasuredinhourstodays,sothehighest-
III. MODELS speed communications within cores on the same multicore
processororwithinthesameservercanreasonablybeassumed
To evaluate which bidding policies are best, the simulator
to be negligible.
previouslydevelopedbytheauthors[5]wasextendedtousea
Clusters communicate through a central router. Delays are
market-based scheduling system. This simulator implements
present for data transfers between clusters, and are adjustable
several models representing the applications, the platform,
using the Communication to Computation Ratio (CCR), sup-
the scheduling scheme and the means of representing and
plied as an input to the simulations. For a task executing for
calculatingvalue.Thesimulationtakesplaceinadiscrete-time
environment, where all events happen on time ticks τ ∈N0. Teixec,thetimetakenfordatatransferwouldbeTeixec×CCR.
Heterogoneity is present in the model to a limited degree.
Tasks and cluster cores have Kinds, which must match for a
A. Application Model task to be able to run on a cluster. A task will always run for
The application model represents the work to be run on the same amount of time on clusters of the same kind. Each
the cluster. Tasks are non-pre-emptive, running to completion cluster is made up of cores of only one kind. This means that
once they have begun. This represents the behaviour of the for jobs where tasks require different kinds, some network
LSF/GridEngine systems commonly used to manage large communications are unavoidable, as some tasks must run on
HPC systems. This lack of pre-emption is less of a problem different clusters. Where this is the case, the network delays
at scale than it might seem, because in large-scale systems, are consideredin thecalculation ofthe criticalpath as wellas
the turnover of work is sufficiently high. This means that it is just the execution times.
very unlikely that any job will ever have to wait too long for
something to finish so that it can start [4].
C. Scheduling Model
For the purposes of this paper, a single, non-preemptible
piece of work will be known as a task, denoted Ti. Each task The scheduling model is market-based and works by using
will run for a duration Ti ∈ N(cid:63) on a number of cores a central auctioneer running on the central router. All jobs are
exec
Ti ∈ N(cid:63) concurrently. A set of tasks is known as a job, submitted to the central router, which maintains the queue of
cores
denoted Jk. Tasks can only depend on other tasks within the work.Jobsareimmediatelydecomposedintotheircomponent
same job and the successors of each task will be known as tasks and, once their dependencies are satisfied, are added to
Ti . The structure of the dependencies will be that of a the single global queue. This is different to previous work by
succ
Directed Acyclic Graph (DAG), which defines a topological the authors [5], where work is load-balanced on submission
ordering over the tasks in a job: a partial order that they must and then spends time queueing on the clusters.
be run in. Schedulingtakesplaceateachschedulinginstant,whichcan
Having a dependency graph means several other useful be the arrival of a job or the completion of a task on any of
metrics about a job can be calculated. The upward rank the clusters. At each instant, the tasks and the clusters submit
[22] of tasks, Ti, is defined as the longest route from any bids to the auctioneer. The tasks bid according to a bidding
R
task to its latest-finishing successor: ∀Tj ∈ Ti : Ti = policy, and these bidding policies will be described below.
succ R
Ti +max(Tj).Sortingtasksbytheirupwardrankwillgive The clusters bid according to the number of cores they have
exec R
anorderingthatrespectsthepartialorderofthedependencies. available.Theauctioneerthenassignsthehighest-biddingtask
Theupwardrankisalsousefultoestimatethefinishtimeofa to the cluster with the most cores free until there are no tasks
jobifataskisrunimmediately.Asjobsonlyrealisetheirvalue leftortherearenoclusterswithsufficientcoresfreetorunthe
once they have finished, this estimate is useful for scheduling highest-bidding task. This is an example of a market-clearing
comparisons at runtime. architecture.
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When a task is assigned to a cluster, it is run immediately,
because there are guaranteed to be sufficient cores free on a
cluster to run due to the bidding mechanism.
Backfilling is not used where tasks other than the highest
bidder could fit onto a cluster even where the highest bidder
cannot. This is for several reasons. Most importantly, when
running large-scale clusters, there is a high turnover of work.
This means that the delay until the next running task finishes
is likely to be small [4]. This means there is less likely to
be much of a penalty without doing backfilling. Secondly,
where execution times are only estimates, backfilling cannot
be perfectly precise. This may mean that some previously
lower-bidding tasks are still running when the previously Figure1. ValueCurveTemplate
high-bidding task would have started. This can delay the
executionofthehigh-biddingtask,penalisingtheoverallvalue Algorithm 1 Value Calculation
achievable. Value(cid:0)jobJk,SLR(cid:1)=
D. Value Model JVkMax ifSLR≤Dinitial
Users submit work to HPC systems because running the 0 ifSLR≥D
final
work on their own computers is likely to take a prohibit- Jk ×factor(cid:0)Jk , SLR(cid:1) ifD <SLR<D
ively long time. Furthermore, users tend to not really care VMax Ci initial final
how busy the systems are overall, but instead care most
about the responsiveness of their jobs. Therefore, a model
of value curves is required that captures these perceptions beenreached,thevalueis0.Thealgorithmforcalculatingthis
aboutresponsiveness.Itisassumedthatuserswilldefinethese factor is given in Algorithm 2.
curves and submit them along with their jobs. This is because
the decision and allocation of appropriate time and value is
IV. BIDDINGPOLICIES
context-dependent and is fundamentally a stakeholder issue.
In a market, independent agents need to make bids for
The authors previously concluded [3] that the most appro-
the services they require. In this context of market-based
priate measure of responsiveness for jobs with dependencies
scheduling, tasks will each bid for computational resource.
was Topcuoglu’s Schedule Length Ratio or SLR [22]. This
In this market, it is necessary to have policies that calculate
is the ratio of the job’s actual response time to the length
of its critical path: SLR = (cid:0)Jk −Jk (cid:1) ÷ Jk. A the bids for the tasks. These bids can be based a number of
finish arrive CP underlying attributes of the task.
particularly useful feature of the SLR is that job SLR can
Baseline policies are explicitly intended to be simplistic or
beestimated(orprojected,henceP-SLR)fortasksinadvance
naive, to show what is achievable with little processing work.
if the submission time of the job, the current time and the
upward rank of the task is known: Ti ∈Jk : PSLR(cid:0)Ti(cid:1)= Two baseline policies are considered, Random and First In
(cid:0)(cid:0)Ti +τ (cid:1)−Jk (cid:1)÷Jk. First Out (FIFO). Random places a random bid for each task
R current arrive CP in the queue at each round of bidding. FIFO places bids that
Each job submitted will also be submitted with a value
are proportional to the arrival time of each task’s parent job
curve, JK. The curve Ci is an array of coordinates of the
Ci Ti ∈ Jk, FIFO = Jk , with the smallest numerical bid
points that define the curve. The time-axis of the value curve arrive
being the highest priority.
isdefinedusingtheSLRofthejob.Thismeansthattheinitial
Several policies are considered that do not make use of the
and final deadlines along with the time coordinates of points
value curves. These instead use the upward ranks of tasks
on the curve are defined in terms of SLR. This is so that the
Ti within the dependency graph of their parent job. Shortest
valuecurvecaneasilybescaledtojobsofdifferentsizes,total R
values or lengths of critical path. This is also designed so that
the future value of a task can be estimated using its P-SLR. Algorithm 2 Value Factor Calculation
The value curve is undefined before an SLR of 1, as no job factor(cid:0)curveCi,SLR(cid:1):
can finish before the length of its critical path. t_sort=(cid:2)p[0] forpinCi(cid:3)
Figure 1 shows the template used to define value curves. v_sort=(cid:2)p[1] forpinCi(cid:3)
EveryjobisassignedamaximumvalueV thatitcanreturn
max low_index=|[tfortint_sortift≤SLR]|
to the user. A value curve is defined as a piecewise function
t_low=t_sort[low_index]
withthreesubdomains,punctuatedbyaninitial(D )and
initial t_high=t_sort[low_index+1]
a final (D ) deadline, as defined in Algorithm 1. Before
final v_low=v_sort[low_index]
theinitialdeadline,thevaluereturnedisalwaysthemaximum
v_high=v_sort[low_index+1]
V . Between the initial and final deadlines, the value is (cid:16) (cid:17)
max F =v_low+ SLR−t_low ×(v_high−v_low)
calculated using linear interpolation between a sequence of t_high−t_low
points which reach 0 at D . Once the final deadline has returnF
final
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Algorithm 3 Projected SLR algorithm
projected_slr(taskTi, job Jk,curr_time, queueQ)=
(cid:0)Ti +curr_time+1(cid:1)−Jk (cid:22)curr_time−Jk (cid:23)2
R arrive+ arrive
Jk ∀Jn ∈Q:max(Jn)
CP CP
Remaining Time First (SRTF) and Longest Remaining Time
First (LRTF) [25], [22] bid for tasks using their upward
rank, with the smallest and largest bids being given priority, Figure2. ValueCurveshowingProjectedValueRemaining
respectively.
The Projected Schedule Length Ratio (P-SLR) policy bids Algorithm 4 Algorithm to compute Projected Value Remain-
the P-SLR value, with the highest value being highest priority ing
[3]. This is so that the tasks that are most late relative to their PVR(cid:0)Ti, τ (cid:1):
current
executiontimearegiventhehighestpriority,whichisintended
to ensure that all jobs will have a waiting time proportional
Jk = Ti
to the length of their critical path, a desirable attribute for parent_job
fairnessandresponsiveness[19].TheP-SLRasdefinedabove D = Jk
final Ci
is starvation-free as long as overloads are transient (overall (cid:0)TDif+inalτ (cid:1)−Jk
loadisbelow100%).However,toensureP-SLRisstarvation- P_SLR = R current arrive
free under extremely high load, a further term is added to ˆ JCkP
the equation. The equation as used for P-SLR bidding in the PVR = DfinalValue(cid:0)Jk,s(cid:1) ds
simulation is shown in Algorithm 3. One discrete time unit is
P_SLR
also added to the P-SLR calculation in order to preferentially
return PVR
prioritise smaller tasks that arrive at the same instant as larger
ones.
Several policies based on value are considered. Projected
Value (PV) uses the estimated P-SLR to determine the parent area under the value curve remaining between the P-SLR at
job’s value if it were to finish after the task’s upward rank. the current time and the final deadline Dfinal of the job. This
PV then uses the highest bids as the most preferable. This is illustrated graphically in Figure 2.
is similar to previous market-based policies where work has The tasks with the smallest value remaining are run first.
fixed values rather than value curves Ti ∈ Jk : PV (cid:0)Ti(cid:1) = Urgent tasks would have a steeply sloping value curve, which
Value(cid:0)Jk, PSLR(cid:0)Ti(cid:1)(cid:1). would give only a small area under the curve. Tasks about
The issue with PV is that tasks that promise a large to time out would also have only a small area remaining.
amount a value may also take a large amount of resource. Prioritising these tasks would reduce starvation and loss of
Instead, the Projected Value Density (PVD) policy [15] looks value.
at how profitable running each task may be, by comparing The value curves were designed using linear interpolation
the value gained with the resource required to achieve this between the points so that the definite integral of this curve
value. The resource required, Ti , is the sum of the would be quickly and exactly calculable using the trapezoidal
succ_sum
execution times, Ti , multiplied by the cores they require, method [2]. However, the policy method generalises to any
exec
Ti , of all the tasks that depend on the considered task valuecurveswherevaluecanonlydecreaseovertime,aslong
∀cTorjes∈ Ti : Ti = (cid:0)Ti ×Ti (cid:1)+(cid:80)Tj . as a final deadline is present. The algorithm to calculate PVR
succ succ_sum exec cores succ_sum
Having defined the resource required, we can define the value is given in Algorithm 4.
density as the value divided by the resource required Ti ∈
Jk : PVD(cid:0)Ti(cid:1) = Value(cid:0)Jk, PSLR(cid:0)Ti(cid:1)(cid:1)÷Ti .
succ_sum V. EXPERIMENTALMETHOD
Higher density is prioritised as it will be most profitable.
Aldarmi and Burns [1] suggested that squaring the value Inordertobeabletocomparedifferentschedules,appropri-
density gives a better separation between tasks that will be ate metrics are required. For this work, the pertinent metric is
profitable and those that should be starved to avoid wasting that of the proportion of maximum value achieved. The max-
resources.ThisistermedtheProjectedValueDensitySQuared imumvalueofaworkloadisthesumofthemaximumvalueof
(PVDSQ) policy, PVDSQ(cid:0)Ti(cid:1)=(cid:0)PVD(cid:0)Ti(cid:1)(cid:1)2. all possible jobs, and is the value that would be achievable if
The Projected Value Remaining (PVR) policy [5] is de- the number of processors available was unbounded, there was
signed to capture the relative urgency of a task at a given no contention between work and no network delays. Because
moment. The other policies may project tasks to be valuable different workloads may have different maximum values, it is
or not, but are unable to give an indication of whether that necessarytonormalisethesevaluesbetweenworkloads.Inthis
value is likely to decrease with waiting much longer. PVR work,thevalueachievedunderagivensetofcircumstancesis
uses the P-SLR to determine the earliest possible time a task divided by the maximum possible value to give a normalised
could finish if it were run immediately. The PVR is then the figure.
necessarytonormalisethesevaluesbetweenworkloads.Inthis

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tIvhnaIvcenloapum IvclneepunoatBs r eh elnhuidpuure osamLiedereudovknro eiemsdiidinsanonm.seti desodegt Tnsi.iofrs tehs-ch iTfviaoseeoa ate rhrosvinftrber a veiyosbeeivtrebs t vcealbr,iedoeacl slaeiotra,aulfhc vlt.adufsotiaaahemde,sa[urtrae ,4 idhse etett ]eh,hs ohntd. t hoewhethtTo ew hioferevr fohewie evvarr evlva jeevlaoavuelvratatulbh,areeilru,vuesle rrj ue,,cio eej v ceou sbjdaa ucoubarscdleumrbvrscenvgr mseroenvmeas esrmeistasn dteaiws syyctiassy pyn yosyp he agpa.rh eacatkrheca tevilcta VvifiooeVfiviemaafieemea ldvdtea svxdhevxd o e ew bre iwriyswyraysi ymil d iildl ilddalj eddliu dlie tflieefslhfjefnfenutaefoaeetaetdsridddirdrctec eie antnantnttiolotlnogot.t. FFFFiiiigggguuuurrrreeee4444.... VVVVaaaalllluuuueeeeaaaaggggaaaaiiiinnnnssssttttllolloooaaaaddddffooffoorrrrddddiiffiiffffeeffrreeeerrnneetntntbtbiibbddididddiidndnigignngpgpooplplioioccliliieicecsisiee(s(DsD(e(eDtDtaaeielit)lta)aili)l)
thLetohmgaei dmvh e achpvaaeinnva igknbs gved e vurveryair nyrdgi eidfwdfif eofrfreeokrnrein tn gttrh ehreleoa lutasirtavsimvea eenu udrgwrqgeouenirncekcytlye.o.rapde rbioyd saodvjuersntiinghgt
the LianonLtaedodraa- datcr tarhcnieav nawb le eb eteivk maevrneaidser .ideoT dfhf oifsjroo erbt nhstse,hu era secasscmatomheraed t wimnwogaor nkrytkloolc oayatdchd le eb bsymyo feaatdodhvjjoueudsrslt toiininangdg
Btuhretkh aieimnn dtsienhcrtea-etarrc -rhareiirtvnr iagavl-la u. ltp i[mt4ai]mre.es e Tpsor hefoes f ej naojrtbo,rsbiav,s am, al coarccraecotorecdrhsdi anialnglreg en t gotaoi ln stgthohe se ca edmmnjueaetrsthithoeooddfdo triionna
giBvueB rspkuceirhmkaekisdmshu sedlheruer rreit thne agtan lwa. alo.[ 4cr[ko]4.ni ]ns.T gtaTh nhehto eaua rrrarrsrii vrvaiavanllad lr raqarteuatetieoses ft eawarr reope re akralilsaosonod d saa doodjnvjuueessrtttneheiddag t httiotos
angdivg aeimvt peoteh rpaeeek rawsek pedsre uedkrsuieenrnnigntda g.wt i Tvwoehrokiorsikf neirgnne gash ulohrsuoeyrusssr t tseah mnaandst d. mq Uquasuinieineytget ecrtr yhp pcieselrermisioo edodtshfs o ooodvvv,eeelrrronnlaoiidggahhdistt
varied between 70% and 140% of saturation, the state where
anadna dcn aadtt c athth ietnh gwe- ewuepek eaekrneedn .pd Tr. ehTsihesni set ,ne sanu smrueroser ste ht hacath tam mllaeannnygy ic ncyygcc lsleecsse onofaf rooivove efrrolloora aadd
the system must operate at full capacity to service the work
scahneaddn cudal ectcra httcihnhaignn-g ua-pu cpao raenr sept rapenrsete sanertn,r ti,av aam lm oroaretree c chohaf alwlleleonngrgkini naggn sdsc ceoennnaaerr iitooh affoto rri saa
arriving. Load above 100% represents overload, where not all
msocrhsecet hhdreeeupdlwerueorl esrtekrh ntachtnaaan tniavb aeec oorcnuofsn nrt.seaWtanaltni tstah yrasrtrhitrveeiavmdla salr .ia rlUyatetsea io nnofdg fw w wthoeoiersrkk k lmy aanecntdydh c ooloednns,ee lo otfthhaladaott a iidisss,
vamriomertdeor a rbrneees priteewrpneersteeeosnnve tena7rttl0aiov%taievd eosa fnwo rdfie l rla1elba4 esl0 ysp%syrtes etsomeefmn sts.s ae.U tvUuserisnanintbgige ot lnhtoh,iw sist hm1 me0e 0ets%ththaoottddeo, ,t alwlolohalaodedar ideiss.
thvea vrsiayerdsiet edbm ebt wemtewueesnet n7o 0p7%0er% aat nead na d1t 41f0u4%0ll% co aofp fsa ascatiuttyurar attiotoi onsn,e ,r tvhthiece ess ttatahtteee wwwhhoeerrrkee
artrhievth insey gss.y teLsmtoeam dm muabsuto sVvot epIo .ep1reR0ar0tEae%tS eUa tLar etTf puSfrlueAll slNc eacDnaptDpsa acIociStviCytey Ur tlSotooS a IsdOsee,rN rvwviichceee r tethh ene o wwt ooarrlklk
thaer rawirvroiinrvkgin .c gLa. noL abodea dar buaonbv.o eWv e1i 0t1h00 %0th% er edrpeaprielrysee saennntsdt s o wovveeeerlrkolloayad dc, ,y wcwlhheeser reoe f nn loootta adall,ll
trtahnetsh iwee nowTtrh okoer vckeea xcrnlpa onbear ebdi mersu ewrnnu.itn lsW.l wWbietehi rtpe htrh seteehst eed undaptia leiyslvuy eac nanhn dbtd hew awloeteewtehk kel1ylr0ye c 0cwy%ycicl lllteeoasst l aowolff a l lyoloosaaadbdd.e,,
tratnrtasrniaesnniseti neontv toevorelvorelarodlaosda wsd swi,llis lblo eb teph rapetrsenesonetnt tea vellveenwn ob brekeloloiwsw a1 1b00l0e0%%to ttoortutaanll. lloToaahddis..
is why the proportion of maximum value is below 1.0 even
at 70% loVadI..ARsElSoUadLTiSs AinNcrDe aDseIdS,CtUheSSpIrOoNportion of value
de creases foVrVI.aI l.lRbREiSdE UdSiULnTLg ST pSAo ANliNcDiDe Ds D.ISTISChCU isUSSiSsSIIObO NoNund to hap pen
trtarTnatTsnhrbmiaseheTenieonecesh rtnaixee eeutpxo nsetepvothex reevepiorretrmeivhlermoreeleioawrmneldamontidesslatoln,ssd wr,t bs essweoe,s woerw stert hoeohetar shr aettkesath et istast nteut hnt ounp eontpuor toesp t astu a ldusicllasuo clhl wnchltw het oowht. ohrtaodThrkatkroa thk ttieht siihtsin ehcs ear eharebaareabelb lwlegl wleew eii vntil tiollegtollo ln ea ar alrulrwitulwsuinwnman.at.a y.oe y yTsT,sTsfih h bthbnbihieisedsees FFFFiiiigggguuuurrrreeee5555.... SSSSttttaaaarrrrvvvvaaaattttiiiioooonnnnaaaaggggaaaaiiniinnnssssttttlloollooaaaaddddffooffororrrddididffififfefeffrreeeerrnneettnnbtbtiibdbdididddiindndgiginnpgpgooplplioicocliliieiecscsiieess
policy, but FIFO is still a long way behind the other policies
under overload. This is natural because it does not 6consider
policy, but FIFO is still a long way behind the other policies
the size or the relative urgency of jobs.
under overload. This is natural because it does not consider
thatmaAntylsomaadllelrevoenlesswbeillloswtarovev.eTrlhoiasda,fftehcetsPthVetoptoallivcyalupeerforms
the size or the relative urgency of jobs.
achiseuvrapbrlies,inangdlyitpaolosorlyle,aedvsetno twheormseostthtaansktshsetarravnindgomacrpoosslicy. PV
At load levels below overload, the PV policy performs
thegspoeecstrufomrotfheloaladr,gwesitthaonndlymLRosTtFvsatlaurvaibnlgemtaosrkes. Afitrsvte,rymeaning
surprisingly poorly, even worse than the random policy. PV
highthlaetvemlsanoyf slomaadl,lePrVondeoseswinloltstfaarlvlea.sTfhaisst aafsfescotmsethoethtoetral value
goes for the largest and most valuable tasks first, meaning
poliacciehsi,evthaobuleg,hanitdisitsatlisllobleeaatdesntobythtehemfloasvtotausrsksosftaVravliuneg across
Dentshiatyt,mSaRnTyFsamnadllPeVr Ron.es will starve. This affects the total value
the spectrum of load, with only LRTF starving more. At very
Pa-SchLiReviasbldee,saignndedittaolseonsleuaredsthtoatththeemSoLsRt toafskjsobsstaarvcrionsgsacross
high levels of load, PV does not fall as fast as some other
thetehxeecsupteiocntrutimmeofspleocatdru,mwiitsheoqnulayl L(fRaiTrnFessstawrvitihngremspoercet.toAt very
policies, though it is still beaten by the flavours of Value
resphoingshivelenveeslss) [o3f].loUandd,ePrVhigdhoelesvenlostoffallloaads, hfaoswteavser,sothmise other
Density, SRTF and PVR.
canpmoeliacnietsh,atthmoaungyhjoibtsismasytilhlavbeeathteenirbfiynalthdeeafldlaivnoeubresfoorfe Value
P-SLR is designed to ensure that the SLR of jobs across
theDSLenRsitthya,tSiRsTcuFrraenndtlyPVbeRin.g achieved, meaning that many
the execution time spectrum is equal (fairness with respect to
will stPar-vSeLR(Fiigsurdees5i)g.nPe-dSLtoReinssuunreabtlheattothtaekeSLinRtooafccjooubnstacross
responsiveness) [3]. Under high levels of load, however, this
thetfhaectetxheactujtoibosnmtiamyehsapveecvtraurmyinigsleeqvuealslo(ffauirrngeesnscyw.ith respect to
can mean that many jobs may have their final deadline before
Trheesptownosivfleanveosus)rs[3o]f. Uvnaldueer hdiegnhsitlyeveblisddoifngloa(dP,VhDowaenvder, this
PVDcthaSenQSm)LeaRarenthtchalaetatirmslyacnubyrertejtoenrbtlsythmabaneyinshgimavapeclhytiheuevsierindfig,nmavlealdauneeai-ndbglaisntehedabtemfoarney
Figure6. Starvationagainstloadfordifferentbiddingpolicies(Detail)
biddtwhineigll.SsLLtoaRcrvkteeha[(t1F5iisg]ucsruheorrwe5ne).dtlyPth-bSaetLifnRogriauscnhuipineraovbceledes,stomorestaacnkhieendgiunlttihnoagtamccaonuynt
FFiigguurree66.. SSttaarrvvaattiioonnaaggaaininssttloloaaddfofrordidffifefreernetnbtidbdidindginpgopliocileicsie(Dse(Dtaielt)ail) of wthoerkflaocatdtshathtajtobasremaalysohasvcehevdaurlyaibnleg luesvienlgs oEfDuFr,gevnalcuye.
will starve (Figure 5). P-SLR is unable to take into account
densityThbeasetdwoschfledavuoliunrgswoafs ovpatliumeal.deNnastiutyrallbyi,dwdionrgklo(aPdVsD and
the fact that jobs may have varying levels of urgency.
thatPoVvDerSloQad) tahreeircplleaatfrolyrmbeartteernotthascnhesdiumlapblyle uussiinngg EvDalFu,e-based
The two flavours of value density bidding (PVD and
so tbhiedsdeinsgc.enLaoricoksea[r1e5]oushtsoidweedthtohsaetpfororvuedniporpotcimesaslo.rTshcihseduling
PVDSQ) are clearly better than simply using value-based
evaluation shows that in the overload scenarios considered,
of workloads that are also schedulable using EDF, value
bidding. Locke [15] showed that for uniprocessor scheduling
other policies can do better than PVD.
odfenwsiotyrkbloaasdesd tshcahtedaurelinaglswoasschoepdtiumlaabl.leNuastuinrgallyE,DwFo,rkvaloluaeds
Interestingly, PVDSQ gives higher value than PVD (Figure
dtheantsiotyvebrlaosaedd tshcehierdpullaintfgorwmasaroeptnimotals.chNeadtuulraablllye, uwsoinrkgloEaDdsF,
3). This is because PVDSQ starves many fewer tasks than
tshoatthoevseerlosacdentahreiiorspalartefoormutsaidree ntohtossechperdouvlaebdleoputsiimngal.EDTFh,is
PVD (Figure 5). By squaring the value density, jobs that are
seovaltuhaetsieonscsehnoawrisosthaarteinoutthsiedeovtehroloseadprsocveendarioopsticmoanls.idTehreisd,
not worth running are more cleanly starved, leaving the rest
to beoevthaaleburlaeptiotoolnicruisenhsotwcoasncotdhmoaptlbeietnitotenthr.etPhVoavDneSrPlQoVaDadl.ssocestnaarrvieossacofenwsidered,
moroethoIenfrtetphroeelsiltcainireggselysct,aPnjoVbdsDo,SbwQehttigechrivteghsiavnheisgPhVaeDlro.vtamluoerethsapnacPeVfDor(Figure
othe3r)j.IonbTtsehrtieossrtiuisnng.blIyen,cteaPruVessDetinSPgQVlyDg,iPSvVeQsDhSstiQagrhavenerdsvSamRluaTenFytghifavenewPaelVrmDtoass(tkFsiguthraen
indi3Pst)Vi.nDgTuhi(isFshiagibsulrebeel5ecva).eulsBseyoPfsVqvuDaalSuriQengascttrahoresvsevsathlmueealnodyaednfsesiwtpyee,crjtortubamssk.tshathtaanre
HowPneVovtDerw,(oFSriRtghTuFrruens5tna)i.rnvBgesyarmseqaumnayroirnfeegwctelhereantvalasylkussetaodrvveenerdsail,tlyl,ebaejovcbainusgstehthatearreest
SRTntFootpbrweiooarribtthilseersutonsmnriuanlngl ttaaorsekcsomwmoiprthelelctiiltoetlnae.ntlPiymVesDtarServmQeadia,nlislneoga.vsitnargvethsearefsetw
EtmDoFobraeettaoabifnlesthttehoelrasurengceotsnotd-cjhooibgmsh,pelswetthiloeivcneh.lPgoVfivDveasSluQae albolestloomwsot1arr1ev0e%sspaacefewfor
loadmot(ohFreiegrujoroefbst4h)te.oHrlauornwg.eeIvsntetrej,oriebtssst,ipnwegrhlfyoi,crmhPVagnDicveSesQfaalalsnldosttSeemRpTolyrFeagfsitpvearecaelmfoorst
thato.intThdheisirstijnoisgbsubietsochaaruubsnlee.oInlnetcveereeltsshteionefgalryvl,iaePlsuVteDdeaSacQdroliasnnsedtthhSaeRtTilsoFabgdeivinsegpaelcmtrousmt.
runiHgnedotwisstienivnteogru,thiseShRpaabTslFet,elsvetevareryvlsejosobfmstvaaarntlysuemfeiaswscirenorgsstitassthkdeseadloolvianederaaslnlpdebcetrcuamus.e
FFigiguurree77.. RReessppoonnssiivveenneessss((SSLLRR))aaccrorossssthtehespsepcetrcutmrumofojofbjoebxeecxueticountitoimnetsimeslatenessstartscascading.Above110%load,thevalueattained
aatFt1ig12u20r0%e%7ll.ooaaRddesponsiveness(SLR)acrossthespectrumofjobexecutiontimesby EHSDRoFwTFefavlpelsrr,iroaSrpiRtiidTsleyFsbssemthairanvldlestthaesmkaaslntewyrnitfahetiwvlieettrlpeotlatiiscmkieses roeevvmaelruaaailntleindb.ge.cause
SRETDFFpraiottraiitnissesthsemsaelclotnasdk-hsiwghitehstliltetlveeltiomfevraelmueaibneinlogw. 110%
at120%load
After 120% load, the number of tasks starved by EDF also
loaEdD(FFiagtutariens4)t.heHsoewcoevnedr-,hiigtshepsetrfleovrmelaonfcevaflaulelsbsetleoewpl1y1a0f%ter
thepolicythatsufferstheleastlossofvaluegiventheincrease increases rapidly (Figure 6).
is why the proportion of maximum value is below 1.0 even ltohaadt. (TFhigisuries 4b)e.cHauosweeovnecr,eittshepeerafrolrimesatndceeadfalilnlsesttheaetpliys abfetienrg
in load, with the results shown in Figure 3. Below saturation and up to 110% load, PVR attains the
aits7w0%hy ltohaedp.rAopsorlotiaodn iosf imncarxeiamseudm, tvhaeluepriospobretlioown 1o.f0veavleune trhuant.gTethsisinitsobtheecapuasset,oenvceerythjoebesatraliretsstmdiesasdinligneitsthdaetaidslibneeinangd
LRTF is a policy commonly used in static scheduling as highest value of all the policies evaluated. This is due to
daetcr7e0a%seslofoadr.aAllsbliodaddingispinoclirceiaesse.dT, hthiseipsrobpoourntidontoofhavpapluene rlautnengeestssisntatortsthceapscaastd,inevge.rAybjoobvest1a1rt0s%mliossaidn,gthitesvdaelaudeliantetaainnded
it is good at bin-packing, and hence at reducing workload its ability to take into account the urgency of tasks. Small,
bdeeccaruesaesetshefomr oarlel bwidodrkingtheproelicisiest.oTdhoisinisaboguivnedntotimhea,pptehne lbayteEneDsFssftaalrltssrcaapsicdaldyinbge.hAinbdotvhee1a1l0te%rnlaotiavde,tphoelivcaieluseeavtatlauinateedd.
makespan[22].However,itisclearthatitisapoorchoicefor urgent tasks are able to run, which ensures their value is
maboedrcyeanutahsmeeircethsewchimelldoubrleeintgwhoasctrekinsathrnieoor,tebdeioscnateuo.seTdiohtewincilhlaatellgneidnvgetoneriutsinmttoeh,efitnhdecaptbAuyrfetEderDb1Fe2ffo0ar%lelstlrhoaeapydid,sltytahrbeveenh.uinPmdVbRtehreaoacftlutetaralnlsyaktsihvasestaprtovhleeicdihebisgyheevEsatDluFateadls.o
thmmeoopsrtoerlietchcyeenrtethlyawtaislrulrifvbfeeedrsthjotahbtesilsfieranssot.ttTlodhosissneois.fTbveahcleuauecshgeailvtlheeenngjtoehbesisimntcoorsetfiansderespAionnfctsreievraes1ne2ess0s%ra(ploliowdaleyds,t(tFShiLegRun)rueomf6b)a.ellrtohfe tpaoslkicsiesstaervvaelduabteydEfoDrF also
inrtehcleoenapdtol,ylicwayrirtthihvaetthdeswurfieflelsruhslattsvheeshllooetawssntolfionwssoForikgfuvlreaefltu3et.ogdivoe,nanthdesioncbreeasesmailnlecBrrejeoalbsoesws(Frsaiagptuiudrrelayt7i)o(.FnIitgaudnrodees6ut)ph.istoby1o1n0l%y leltotiandg,tPheVlRargaetsttains the
pinrLiolRoriTatidFs,edwisiotavheprthotehliocrseyesuctlhotsamtsmahrooewnslnyooiunnsFteodigfiuinnreissh3t.a.tIincasnchoevdeurlloinadg asjobshihgBahveeelsottwheviasraluStueLrRaotifoinnaclrlaeantsdhee.uHppoowtloicevi1ee1sr,0%ethvealloulaaardtge,edsP.tVjToRhbissacttaiasnindsuetheto
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mtiotakfiiesnsipsghao.noIdt[s2av1ta]l.ubHeinoa-wcphaeicvekveiern,dgiit,niasthncidsledahyrenntahcmaeticaittciarsseeadiupscoeionvgrencwhwoooirrckseelofaodra joiubtsrgtaeaknbeitslimttyaoskntosthstaartkeoerauibnnlt,eoitatmoccaoryuunbn,et awthbheleicuthorgteeannkcseuyareofsfewtthamsekiorsr.evSamluaell,is
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maodTsythnreeacmFeIinFctOlsychpaeordrliiuvclyeidnigsjosabcesfnfiaairrrsioti.,mTbpherciosavueissmebeinettcwaouinlslettehthneedrjtaoonbdrsoumnmtohsetarecrlieakspeptluoyrnetsodivdebenecefroesasres(eltorhewelayetsivtsetSalyLrvRger.)adoPufVaalRllyl.athcteuaplolylichieassetvhaeluhaitgehdefsotr
pmooliscty,rebcuetnFtlIyFOarriisvestdilljoablsofingrstw.aTyhbisehisinbdetchaeusoethtehrepjoolbicsiemsost Artesvpeorynshivigenhelsesve(llsowoefsltoSadL,RP)VoRf’sallletahdeipsoelricoideesdeavnadluaitted for
recently arrived will have lots of work left to do, and so be smaller jobs (Figure 7). It does this by only letting the largest
urencdeenrtloyvearrloriavde.dTwhiisllishanvaetulroatlsboefcawusoerkitledfotestondoot,coannsdidseor befallssmbeahllienrdjoSbRsT(FFiagnudreP7V)D. IStQdoaensdthisisebqyuaolnleldy lbeyttiPnVgDtheatlargest
prioritised over those that are soon to finish. In an overload jobs have their SLR increase. However, the largest jobs can
tphreiosriizteiseodr tohveerreltahtoivseeutrhgaetnacyreosfojoonbs.to finish. In an overloadthejhoibgshehsatvleevtehleoirf SloLaRd eivnaclrueaatseed.. HWohwenevtehre,rteheisltaorogemstucjohbs can
situation, jobs will be started continuously but never be able often also be those that are most tolerant to waiting time: if
sitAuattiloona,djolebvselwsilblebloewstoavrteerdloacdo,nttihneuoPuVslypboulitcynepveerrfobremsableworokfttoenruanl,soPVbRe ttehnodssetothkaeteapremmosotsjotbtsolreurnannitngtobywastiatirnvgingtime: if
tofinish.Itsvalueachievedinthisdynamiccaseisevenworse a job takes months to run, it may be able to take a few more
stuorfiprniissinhg.lIytspvoaolurley,aecvheienvewdorinseththisandytnhaemraicndcoamsepisoleivcye.nPwVorsethealarjgoebsttaokneess.mYoenttthhsetloarrguenst,jiotbmsacyanbaelsaoblbeettohetaokneesatfheawt more
than the baseline random policy. daysanduserswillnotmind.Thismeansthatthevaluecurves
goes for the largest and most valuable tasks first, meaning supply the most value. As can be seen from Figure 7, SRTF
than the baseline random policy. daysanduserswillnotmind.Thismeansthatthevaluecurves
The FIFO policy is a fair improvement on the random are likely to decrease relatively gradually.
The FIFO policy is a fair improvement on the random are likely to decrease relatively gradually.
7
penalises the largest jobs a little less, meaning that it keeps [5] Andrew M. Burkimsher. Fair, responsive scheduling of engineering
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