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USC Computer Science Technical Reports, no. 622 (1995)
(USC DC Other)
USC Computer Science Technical Reports, no. 622 (1995)
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Content
On Sc heduling A tomic and Comp osite Multimedia
Ob jects
Cyrus Shahabi Shahram Ghandeharizadeh
Computer Science Departmen t
Univ ersit y of Southern California
Los Angeles California shahabi shahramperspolisusc edu
Sura jit Chaudh uri
HewlettP ac k ard Labs
P age Mill Road
P alo Alto CA surajithplschplhpcom
Abstract
In m ultiuser m ultimedia information systems eg vide oondemand newse diting the p ol
icy emplo y ed to activ ate queued requests has a signican t impact on the a v erage startup latency
observ ed b y the users In this pap er w e view the retriev al of an ob ject as a task and study the
problem of sc heduling suc h tasks In this sc heduling problem tasks are IOb ound and eac hma y
utilize m ultiple disks Eac h task acquires and releases disks in a regular manner based on the
la y out of its referenced ob ject on the disks In addition there migh t b e temp oral relationships
among m ultiple tasks that constitute a comp osite task While previous studies ha v e fo cused on
both sc heduling subtasks lo calized to a single disk eg GSS YCK and determining the
regular pattern of disk utilization p er task eg striping BGMJ the metho d for selecting
a task for activ ation has receiv ed little atten tion
In this studyw e formalize a class of task sc heduling problems that arise in a large class of
m ultimedia applications W e sho w that task sc heduling problems are in tractable NP hard
justifying the use of heuristics W e tailor some of the w ell kno wn sc heduling heuristics studied
in other con texts and b y means of a sim ulation study conclude that one of the heuristics
FFDECF is sup erior to the other alternativ es W e also demonstrate that the a v erage latency
time can b e decreased further b y emplo ying buers to resolv e con ten tion
This researchw as supp orted in part b y the National Science F oundation under gran ts IRI IRI
NYI a w ard and CD A and a HewlettP ac k ard unrestricted cashequipmen t gift
In tro duction
Multimedia information systems that pro vide service to m ultiple sim ultaneous requests are starting
to become common place In these systems the p olicy emplo y ed to service requests impacts the
a v erage startup dela y incurred b y the users This impact becomes signican t in a hea vily loaded
system where servicing the tasks in their order of arriv al migh t result in a high a v erage startup
dela y as will be sho wn in our exp erimen ts This pap er in v estigates three classes of m ultimedia
applications and alternativ e p olicies for sc heduling their requests The application classes include
Ondemand A tomic Obje ct R etrieval With this class of applications a system striv es to
displa y an ob ject audio or video as so on as a user request arriv es referencing the ob ject The
en visioned videoondemand and newsondemand systems are examples of this application
class W e formalize the sc heduling problem that represen ts this class as A tomic R etrieval
Sche duling ARS problem
R eservationb ase d A tomic Obje ct R etrieval This class is similar to ondemand atomic ob ject
retriev al except that a user requests the displa y of an ob ject at some poin t in the future
An example migh t be a videoondemand system where the customers call to request the
displa y of a sp ecic mo vie at a sp ecic time eg Bob calls in the morning to request a
mo vie at pm Reserv ationbased retriev al is exp ected to be c heap er than ondemand
retriev al b ecause it enables the system to minimize the amoun t of resources required to service
requests using planning optimization tec hniques The sc heduling problem that represen ts
this application class is termed A ugmente d ARS AR S
Ondemand Comp osite Obje ct R etrieval As compared to atomic ob jects a comp osite ob ject
describ es when t w o or more atomic ob jects should be displa y ed in a temp orarily related
manner All T o illustrate the application of comp osite ob jects consider the follo wing
en vironmen t During the p ostpro duction of a mo vie a sound editor accesses an arc hiv e of
digitized audio clips to extend the mo vie with appropriate soundeects The editor migh t
c ho ose t w o clips from the arc hiv e a gunshot and a screaming sound eect Subsequen tly she authors a comp osite ob ject byo v erlapping these t w o sound clips and sync hronizing them
with the dieren t scenes of a presen tation During this pro cess she migh t try alternativ e gun
shot or screaming clips from the rep ository to ev aluate whichcom bination is appropriate T o
enable her to ev aluate her c hoices immediately the system should be able to displa y the
comp osition as so on as it is authored ondemand The sc heduling problem that represen ts
this application class is termed Comp osite R etrieval Sche duling CRS
In this study w e analyze the ab o v e three sc heduling problems in the con text of an oline
clairv o y an t sc heduler where the system has a complete kno wledge ab out all the tasks released
in future Since these sc heduling problems are no v el w e sho w that they are NP hard justifying
the use of heuristics W e revisit the heuristics prop osed for the con v en tional sc heduling problems
and adopt them for ARS AR S
and CRS The adopted heuristics are ecien t and ne tuned to
serv e as p olicies for activ ating requests in an online system An online system services requests
as they arriv e and has no kno wledge of requests that migh t arriv e in the future
A con tribution of this pap er is that it relates the three sc heduling problems W e argue that
AR S
is the core sc heduling problem b ecause it is a generalization of AR S and a sp ecialization
of CRS Therefore the online p olicies are examined for AR S
using a sim ulation study W e
conclude that one of the p olicies FFDECF is sup erior to others The role of buers to reduce
the a v erage startup dela y is also in v estigated and w e showthatforalo w system load it can reduce
the a v erage startup dela y signican tly T o put our w ork in p ersp ectiv e w e denote the retriev al of an ob ject as a task Subsequen tlyw e
consider sc heduling of tasks ha ving three lev els of abstractions where lev el one and t w o ha v e b een
in v estigated in detail and the last lev el is the main topic co v ered b y this study and has not b een
studied b efore to the b est of our kno wledge Lev el one in v estigates ho w a single con tin uous displa y
should utilize m ultiple disk driv es TPBG BGMJ GK P artitioning eac h ob ject to a n um ber
of sub ob jects this dep ends on the placemen t of the sub ob jects of an ob ject across the disks In this
pap er w e assume a roundrobin assignmen t of the sub ob jects of an ob ject to the disks starting with
an arbitrary disk BGMJ GK see Section Lev el t w o determines the order that dieren t
subtasks eac h subtask corresp onds to the retriev al of a sub ob ject should be in v ok ed on a single
disk This ordering dep ends on the placemen t of the sub ob jects on the disk and is done to minimize
the impact of the seek time In this studyw e emplo y the cycleb ase d TPBG YCK BGM
approac h and extend it to supp ort the con tin uous displa y of a mix of media t yp es see Section Lev el three determines the order that a queue of p ending tasks should b e activ ated This sc heduling
dep ends on ho w the tasks utilize the disks It in tro duces dieren t c hallenges as compared to
those addressed in other m ultimedia studies TPBG DSS V GG see Section Moreo v er
sc heduling problem in the presence of temp oral relationships among tasks is no v el and has not b een
addressed b efore
T o summarize the distinctiv e c haracteristics of the sc heduling problems ARS AR S
CRS
are tasks are IOb ound and not CPUb ound eac h task utilizes m ultiple disks during its life
timeeac h task acquires and releases disks in a regular manner the pattern that a task utilizes
the disks dep ends on the placemen t of its referenced ob ject on the disks and there migh t be
temp oral relationships among m ultiple tasks constituting a comp osite task
F ramew ork
In this section w e start b y extending the cyclebased approachto supp ort the con tin uous displa y
of atomic ob jects b elonging to a mix of media t yp e assuming a single disk hardw are platform
Subsequen tly w e extend the hardw are arc hitecture to a m ultidisk platform Most imp ortan tly weiden tify t w o desirable criteria that should b e main tained for ecien tsc heduling on a m ultidisk
platform Finallyw e describ e the con tin uous displa y of comp osite ob jects on a m ultidisk hardw are
platform
Con tin uous Displa y of a Mix of Media T yp es Single Disk
When displa ying an ob ject it m ust b e rendered to the screen at a presp ecied bandwidth This
implies that the ob ject m ust be staged from disk to memory at a presp ecied rate If retriev ed
at a lo w er rate with no precautions eg prefetc hing then the displa y will suer from frequen t
disruptions and dela ys termed hiccups Dieren t media t yp es ma y require dieren t bandwidth
F or a discussion on ho w the collection of the ab o vec haracteristics distinguish this problem from the previous
sc heduling problems see Section
Display W
W
Disk
Activity
System
Activity
W
i i+2
i-1
X X
j j+1
Z
k
c(X) < (W) < (Z) cc
j-1 k-1
, Z , X
Display W
i
j k
, Z , X
W
i+1
Z
k+1
Figure Con tin uous displa y of a mix of media t yp es
requiremen ts F or example a MPEG compressed video ob ject requires a megabit p er second
Mbs bandwidth A MPEG compressed video ob ject ma y require a bandwidth ranging from to Mbs dep ending on the resolution used to compress data A stereo CD qualit y audio ob ject
has a Mbs bandwidth requiremen tA OG Assume m media t yp es eac h with a bandwidth requiremen t of c
i
T o displa y an ob ject X it is partitioned in to f sub ob jects X
X
X
f
The size of a sub ob ject is a function of its
consumption rate and a predened sub ob ject size for media t yp e i This size is c hosen suc h that the
displa y time of all sub ob jects are iden tical indep enden t of their media t yp e The time to displaya
sub ob ject is termed a time interval Once ob ject X is referenced its displa y emplo ys a cyclebased
approac h the system stages the rst sub ob ject of X in to memory during time in terv al and initiates
its displa y at the b eginning of the second time in terv al During the second time in terv al the system
stages X
in to memory and initiate its displa y at the b eginning of the third time in terv al This
pro cess is rep eated un til all sub ob jects of X ha v e been retriev ed and displa y ed During the time
in terv al that sub ob ject X
f
is displa y ed no sub ob jects are retriev ed on b ehalf of X Giv en a database with a mix of media t yp es the displa ytimeofeac h sub ob ject of the dieren t
ob jects m ust b e iden tical in order to xedsize time in terv als and a con tin uous displa y for a mix
of displa ys referencing dieren t ob jects This is ac hiev ed as follo ws First ob jects are group ed
based on their media t yp es Next the system c ho oses media t yp e i with sub ob ject size Sub
i
and
bandwidth requiremen t c
i
to determine the duration of a time in terv al The sub ob ject size of a
media t yp e j is c hosen to satisfy the follo wing constrain t inter v al Sub
j
c
j
Sub
i
c
i
F or no w assume the bandwidth required to displa y an ob ject is lo w er than the bandwidth of
a single disk
Hence the time to retriev e sub ob ject X
i
from a disk is shorter than the duration
W e will relax this assumption in Section
of a time in terv al ie the time to displa y sub ob ject X
i
This enables the system to retriev e and
displaysev eral ob jects sim ultaneously F or example Fig sho ws the retriev al and displaysc hedule
for ob jects X Y and Z During the rst cycle of this gure the system reads sub ob jects W
i
X
j
and Z
k
from disk to memory while displa ying W
i X
j and Z
k During the next cycle the
system reads sub ob jects W
i X
j
and Z
k and displa ys sub ob jects W
i
X
j
and Z
k
Within an
in terv al the dieren t sub ob jects can be retriev ed based on an elev ator sc heduling p olicy in order
to maximize the utilization of disk bandwidth YCK
MultiDisk Hardw are Platform
Assume a m ultidisk platform consisting of N disks W e partition the disks in to D clusters eac h
with k ph ysical disks D d
N
k
e TPBG GDS BGM GK Next w e assign the sub ob jects
of X to the clusters in a roundrobin manner starting with an arbitrarily c hosen cluster
Eac h
sub ob ject of X is declustered GRA Q in to k fragmen ts with eac h fragmen t assigned to a dieren t
disk in the cluster F or example in Fig a system consisting of six disks is partitioned in to three
clusters eac h consisting of t w o disk driv es The assignmen t of the sub ob jects of X starts with
cluster This sub ob ject is declustered in to t w o fragmen ts X
and X
The bandwidth of a
cluster should alw a ys exceed the bandwidth requiremen ts of an ob ject in order to minimize the
amoun t of required memory W e conceptualize the k disks in a cluster as a single lo gic al disk
b ecause a read request activ ates all k disks in a cluster Henceforth the term disk is used
synon ymously with the term cluster W e n um ber the disks or clusters from to D d
d
D
T o displa y ob ject X the system lo cates the disk con taining its rst sub ob ject sa y disk
d
i
Assuming that disk d
i
has sucien t bandwidth a v ailable to retriev e X
during the curren t
time in terv al the system initiates its retriev al from d
i
A t the b eginning of next time in terv al the
system initiates the displa y of X This is due to the cyclebased approac h where the displa y is
alw a ys one in terv al b ehind the retriev al F or the rest of this pap er w e will ignore this extra dela y
when computing the startup dela ys observ ed b y the requests
Once all the ob jects are laid out on the same set of disks the new problem of r etrieval c ontention
The roundrobin assignmen t helps to sp eed up the sc heduling see Section
X 1.0
X
4.0
...
X 1.1
X
4.1
...
X
2.0
X 5.0
...
X 2.1
X
5.1
...
X
3.0
X
6.0
...
X
3.1
X 6.1
...
Cluster 1 Cluster 2 Cluster 3
Figure Multidisk platform
arises That is t w o sub ob jects of t w o dieren t ob jects migh t comp ete for the bandwidth of the
same disk at a sp ecic time in terv al The reason is that b oth sub ob jects are assigned to the same
disk Due to the retriev al con ten tion the system migh t not b e able to retriev e b oth sub ob jects T o
a v oid the p ossibilit y of hiccups a sc heduler that sc hedules the tasks on b ehalf of ob ject retriev als
should guaran tee that once a task is initiated it will not col l ide with other tasks In other w ords
their corresp onding ob jects will not face retriev al con ten tion The retriev al con ten tion is the main
c haracteristic of our sc heduling problems that distinguishes them from con v en tional CPU sc heduling
problems see Section for a detailed comparison
Desirable F eatures of Sc heduling for F ast Con ten tion Prediction
A ma jor c haracteristic of sc heduling algorithms is to nd the tasks that should be initiated
at eac h time in terv al rapidly while ensuring that the sc heduling will not result in a retriev al
con ten tion with the activ e tasks The duration of a time in terv al is in the order of seconds and the
sc heduler should b e in v ok ed at the b eginning of ev ery time in terv al to predict retriev al con ten tion
Although this prediction is CPUb ound its duration should o ccup yav ery small p ortion of a time
in terv al b ecause the remainder of the time in terv al should b e utilized b y the tasks to retriev e the
corresp onding sub ob jects Assuming that con ten tion prediction p er task requires ms and tasks are examined per time in terv al of a second time in terv al will be o ccupied b y the
sc heduler W e discuss t w o criteria that enable a sc heduler to predict con ten tions ecien tly First the sub ob jects should be assigned to disks using a regular pattern eg roundrobin
assignmen t This helps to sp eed up the prediction b ecause to initiate a retriev al task it is sucien t
to examine only the currentin terv al for con ten tion T o observ e consider Fig In this gure w e
made the simplifying assumptions that all ob jects b elong to a single media t yp e with bandwidth
requiremen t c and a single disk can supp ort the retriev al of a single sub ob ject p er time in terv al
ie R
D
c Eachboxin ro w u and column d demonstrates the status of disk d at time in terv al
u An empt y bo x means that the cluster is idle while a bo x with letter X
k
sho ws that the disk
is busy retrieving the k th sub ob ject of atomic ob ject X In Figs a and b a request referencing
ob ject Y arriv es at time in terv al i With random assignmen t of the sub ob jects Fig a in order to
start Y at ithe sc heduler needs to examine the future in terv als to guaran tee that there w ould b e
no con ten tion for the en tire retriev al duration of Y Assuming a t w o hour mo vie and second time
in terv al elemen ts should b e examined for con ten tion p er task Giv en a MIPS CPU and
instructions p er examination con ten tion prediction p er task requires ms resulting in o ccupation of time in terv al when c hec king tasks With a regular la y out Fig b ho w ev er b y
kno wing that the rst sub ob ject of Y will not result in con ten tion at ithe sc heduler can guaran tee
that there w ould b e no con ten tion for the en tire retriev al duration of Y Second the sc heduler should not reserv e resources in adv ance F or example in Fig c where
the ob jects still follo w the roundrobin assignmen t assume a request referencing ob ject Y arriv es
at time i while disk is busy un til time i Supp ose that the sc heduler lo oks ahead and
reserv es disk at time i for Y No w at time i a new request arriv es referencing ob ject Z
and since Z
can b e sc heduled at i with no con ten tion its retriev al task is initiated at i Ho w ev er
due to the adv ance resource reserv ation for ob ject Y a collision will o ccur at i The sc heduler
needs to lo ok ahead when sc heduling Z to prev en t suc h a collision Ho w ev er similar to the case of
random assignmen t this requires the examination of sev eral time in terv als for the en tire retriev al
duration of Z The prop osed sc heduling algorithms for atomic ob jects resp ect these t w o criteria Ho w ev er w e
sho w that these criteria cannot b e guaran teed when sc heduling the retriev al of comp osite ob jects
Comp osite Ob jects
W e conceptualize a system that supp orts comp osite ob jects as consisting of three comp onen ts
a collection of user in terfaces logical abstraction and a storage manager see Figure User
in terfaces pla y an imp ortan t role in pro viding a friendly in terface to access existing data to
author comp osite ob jects and displa y ob jects The logical abstraction tailors the user in terface
Disks
Time
Intervals
123
i
i+1
i+2
i+3
i+4
X5
X6
X7
X8, Y4
X9
Y1
Y2
Y3
Y5
Disks
Time
Intervals
123
X5
X6
X7
X9
Y1
Y2
Y3
Y5
X8 Y4
Disks
Time
Intervals
123
Z1
Z2
Z3, Y1
Z5, Y3
Z4, Y2
X5
X9
Y2 X7 Y1
Y5
X6 Y3
X8 Y4
X5
X8
Y2 X6 Y3
Y5
X7 Y1
X9 Y4
1 2 3 1
2 3
a. Random Assignment
b. Round-robin Assignment
i
i+1
i+2
i+3
i+4
i
i+1
i+2
i+3
i+4
Z1
Z4
Y2 Z2 Y3
Y5
Z3 Y1
Z5 Y4
1
2 3
c. Round-robin (with look-ahead)
Figure F ast con ten tion prediction
User Interface
Logical Abstraction
Storage Manager Retrieval Schedule
Display Schedule
Focus
Figure Three lev els of abstraction
to the storage manager and is describ ed further in Section The fo cus of this study is on the
storage manager Giv en a displaysc hedule this study in v estigates tec hniques to construct retriev al
sc hedules that satisfy the temp oral constrain ts of a displaysc hedule The retriev al sc hedule dictates
when dieren t p ortions of an ob ject should be staged from disk in to memory to be a v ailable for
displa y If the retriev al sc hedule fails to satisfy the temp oral constrain ts describ ed b y the author
then the displa y of an ob ject ma y suer from either dela ys or logical errors eg the displa y
pro duces a gun shot either a few seconds to o early or to o late the lips of an actor mayno longer
b e sync hronized with his v oice etc These failures are collectiv ely termed hiccups Our ob jectiv e
is to construct retriev al sc hedules in supp ort of a hiccupfree displa y A t the logical lev el of abstraction see Figure a comp osite ob ject is represen ted as a X Y j indicating that the comp osite ob ject consists of atomic ob jects X and Y The parameter j is the
lag p ar ameter It indicates that the displa y of ob ject Y should start j time in terv al after the
displayof X has started F or example to designate a complex ob ject where the displayof X and
Y m ust start at the same time w e will use the notation X Y Lik ewise the comp osite ob ject
sp ecication X Y indicates that the displa yof Y is initiated t woin terv als after the displayof X
has started This denition of a comp osite ob ject supp orts the alternativ e temp oral relationships
describ ed in All see CGS for more details This notation extends naturally to sp ecication
of comp osite ob jects that con tain more than one atomic ob jects A comp osite ob ject con taining n
atomic ob jects can b e c haracterized by n lag factor eg X
X
n
j
j
n
where j
i
denotes
the lag factor of ob ject X
i
with resp ect to the b eginning of the displayof object X
T o simplify the discussion w e assume in teger v alues for the lag parameter ie the temp oral
relationships are in the gran ularit y of time in terv al F or more accurate sync hronization suc h as
lipsync hing bet w een a sp ok en v oice with the mo v emen t of the sp eak ers lips real v alues of the
lag parameter should b e considered This extension is straigh tforw ard T o illustrate supp ose time
dep endency b et w een ob jects X and Y is dened suc h that the displayof Y should start seconds
after the displa y of X starts Assuming the duration of a time in terv al is one second this time
dep endency at the task sc heduling lev el can b e mapp ed to X Y Hence the system can retriev e
Y after seconds but emplo y memory to p ostp one Y s displa yfor seconds
With comp osite ob jects the problem of retriev al con ten tion b ecomes more sev ere when it
o ccurs among the atomic ob jects constituting a comp osite ob ject This t yp e of con ten tion is termed
internal c ontention The formal denition of in ternal con ten tion and its solution is discussed in
Section The rest of this pap er is organized as follo ws Section describ es three sc heduling problems
ARS AR S
CRS and prop ose some heuristics for solving them Section ev aluates the prop osed
heuristics using a sim ulation mo del In Section w e distinguish this study from the other related
studies Our conclusions and future researc h directions are con tained in Section Class of Sc heduling Problems
T o tac kle the sc heduling problem rst w e fo cus on the task of sc heduling retriev als of atomic
ob jects that b elong to dieren t media t yp es on a m ultidiskm ultiuser en vironmen t W e term this
problem A tomic R etrieval Sche duling ARS Subsequen tly w e in tro duce an augmen ted mo del of
ARS termed AR S
Finallyw e fo cus on the task of constructing retriev al sc hedules for comp osite
ob jects This pro cess is termed Comp osite R etrieval Sche duling CRS W eshowthat the solutions
prop osed for ARS and AR S
can b e extended to supp ort CRS
A tomic Retriev al Sc heduling ARS
Tomotiv ate the ARS problem consider a vide oondemand application Eac h ob ject can b e consid
ered as a mo vie with dieren t bandwidth requiremen t One compressed b y MPEG and the other
b y MPEG or mo vies with dieren t displa y qualities eg NTSC or HDTV No w the question
is in whic h order a n um b er of requests referencing these mo vies should b e serviced so that all the
customers observ e a tolerable startup dela y By slightv ariation of ARS ob jectiv es one can answ er
an um b er of other in teresting questions suc h as How much r esour c es ar e r e quir e d so that nob o dy
observes a startup delay gr e ater than x se c onds
With ARS the retriev al of eac h ob ject is termed a retriev al task The ARS problem is to
sc hedule retriev al tasks suchthat the total bandwidth requirementof the sc heduled tasks on eac h
disk during eac h in terv al do es not exceed the bandwidth of that disk Moreo v er ARS should
satisfy an optimization ob jectiv e This ob jectiv e is application dep enden t It migh t b e either to minimize the a v erage startup dela y of the tasks or minimize the total duration of sc heduling for
a set of tasks The ma jor assumption is that the b ottlenec k resource is disk bandwidth and there is
alw a ys an idle pro cessor to sc hedule the retriev al task GGJY This is a v alid assumption b ecause
the p erformance of magnetic disk driv es are restricted b y their mec hanical comp onen ts and is not
exp ected to impro v e signican tly in the near future PGK p erformance impro v emen ts ha v e b een
rated at only to p ercen tann ually R W In this section w e presen t formal mathematical
mo del of ARS sho wthatitisa NP hard problem and in v estigate some heuristics for online
sc heduling algorithms
Dening T asks
Let T be a set of tasks where eac h t T is a r etrieval task corresp onding to the retriev al of a
video ob ject Note thatifanobject X is referenced t wice byt w o dieren t requests a dieren ttask
is assigned to eac h request The time to displa y a sub ob ject is dened as a time interval that is
emplo y ed as the time unit in this study F or eachtask t T w e dene
r t Release time of t r T N The time that ts information ie the information of
its referenced ob ject b ecomes a v ailable to the sc heduler This is iden tical to the time that a
request referencing the ob ject is submitted to the system
t Length size of the ob ject referenced b y t T N The unit is in n um ber of
sub ob jects
c t Consumption rate of the ob ject referenced b y t c t This rate is normalized
b y R
D
Th us c t means that the consumption rate of the ob ject referenced b y t is
of R
D
p t The disk that con tains the rst sub ob ject of the ob ject referenced b y t p t D F ormal Denition of ARS
Denition The problem of ARS is to nd a sc hedule where T N for a set T suc h
that it minimizes the nishing time GG w where w is the least time at whic h all tasks of
T ha v e b een completed and satises the follo wing constrain ts
t T t r t u let S u be the set of tasks whic h t u t t then i i D
P
t S u R
i
t where
R
i
t
c t if p t u t mo d D i other w ise
The rst constrain t ensures that no task is sc heduled b efore its release time The second constrain t
striv es to a v oid retriev al con ten tion It guaran tees that at eac h time in terv al u and for eac h disk i the aggregate bandwidth requiremen t of the tasks that b oth emplo y disk i and are in progress ie
ha v e b een initiated at or b efore u but ha v e not committed y et do not exceeds the bandwidth of
disk i The modfunction handles the roundrobin utilization of disks p er task
t
1
t
2
t
3
Time
0
1
2
3
4
5
6
7
t
1
t
2
t
3
0
1
2
3
4
5
6
Time
t
1
t
2
t
3
0
1
2
3
4
5
6
Time
a Example b Example c Example Figure Required displaysc hedules
Y1
Y4
1 2 3
Z1
Z4
X1
X4
V3 Y2
Y5
Z2
Z5
X2
X5 V4
Y3 Z3 X3 V1
V5
V2
Figure Roundrobin ob ject placemen t D
Example Supp ose D T ft
t
t
g Giv en the task information as
t
i
r t
i
t
i
c t
i
p t
i
then
t
t
t
The required displa y sc hedules of these tasks as a function of time is depicted in Fig a The
placemen t of ob jects X V and Z referenced resp ectiv ely b y t
t
and t
is sho wn in Fig
Consider the sc hedule t r t that results in the minim um w no task can start so oner than
its release time Ho w ev er this is not a f easibl e sc hedule T o illustrate consider the follo wing
discussion
The sc hedule is
t
t
t
t
t
t
t
t
t
Iterating o v er the time in terv als u u S ft
g Hence
R
t
R
t
R
t
u S ft
g Hence
R
t
R
t
R
t
u S ft
t
g Hence
R
t
R
t
R
t
R
t
R
t
R
t
u S ft
t
t
g Hence
R
t
R
t
R
t
R
t
R
t
R
t
R
t
R
t
R
t
Since at u the aggregate bandwidth requiremen tof t
t
and t
exceeds the bandwidth
of d
the prop osed sc hedule ie t r t is not a feasible one
Note that in this example as w ell as future examples in this pap er w e assume a high bandwidth
requiremen t for the ob jects ie large c t This is done to simplify the discussions Instead in
Sectionw e used realistic v alues for c t when executing our exp erimen ts see T able ARS is NP hard
ARS can be sho wn to be NPhard b y a reduction from Bin P ac king Problem GJ The k ey
in tuition is that deciding whichrequeststo pac k together for unit disk bandwidth can b e reduced
to the problem of pac king ob jects in a bin
Denition Bin P ac king Problem Giv en a nite set U of items and a rational size s u for eac h item u U nd a partition of U in to disjoin t subsets U
U
k
suc h that the sum of
the sizes of items in eac h U
i
is no more than and suc h that k is as small as p ossible
Theorem ARS is NP har d
Pro of W e use a reduction from bin pac king W e let the total disk bandwidth to be and
corresp onding to ev ery u U w e create a task with the bandwidth requiremen t s u W e can
showthat the problem of minimizing the nishing time for the ab o v e set of tasks is equiv alen t to
minimizing the n um ber of bins for the set of ob jects U Assume that k is the few est n um ber of
bins in whic h the ob jects ma y be pac k ed Then w e can create groups of tasks eac h requiring no
more than total bandwidth of a disk Th us w e can line them one after another and nish in k
units of time Let us assume that wecan sc hedule tasks to nish in k units of time where k is the
minim um suc h time W e can map sc hedule of ev ery timeunit in to con ten ts of one bin Th us k
bins suce
Remark Note that ARS is NPhard in the strong sense since so is bin pac king
Heuristics
Since ARS is NP hard ecien t heuristics should b e dev elop ed F urthermore since in realw orld
applications suc h as videoondemand a sc heduler do es not ha v e the complete kno wledge ab out
all the tasks in adv ance an online sc heduler is desirable
Another requirementb y the realw orld applications is that they do not care m uc h ab out the
nishing time of a set of tasks Their main ob jectiv e is for the tasks to observ e a minim um a v erage
startup dela y The startup delayof a task t is dened as
t r t Hence the ob jectiv e of ARS
can b e mo died to b e minimizing
P
tT
t r t Note that the new ob jectiv e do es not impact
the in taractibilit y of the ARS problem
Sho wing a sc heduling problem is NP hard is not sucien t to justify an in v estigation for a go o d
heuristic It is p ossible that a naiv e heuristic no matter ho w bad it p erforms alw a ys pro vides a
nearoptimal solution Tosho w that this is not the case for ARS consider the follo wing example
Example Supp ose D and n Giv en the task information as t
i
r t
i
t
i
c t
i
p t
i
then
t
t
t
t
t
t
t
The precise equation is t r t b ecause of the cyclebased approac h where the displa y is alw a ys one in terv al
b ehind the retriev al
Assuming the F CFS sc heduling p olicy t
t
and t
utilize the en tire system bandwidth from
in terv al to in terv al Atin terv al u suddenly the en tire system bandwidth b ecomes a v ailable
and three out of the remaining four tasks t
t
t
t
can b e initiated F CFS selects tasks t
t
and t
based on their release time Subsequen tly t
cannot b e initiated so oner than in terv al
resulting on an a v erage latency time of
in terv als for this set of tasks An alternativesc heduling
algorithm whic h selects tasks t
t
and t
to b e initiated at in terv al u will observ eana v erage
latency time of
in terv als Hence this algorithm p erforms appro ximately times b etter than
F CFS
The main structure for all the prop osed heuristics to solv e the ARS problem is as follo ws The
heuristics start with time in terv al u and incremen t u un til all t T are sc heduled F or eac h
v alue of u the follo wing steps are tak en resp ectiv ely
The required resources are assigned to the tasks that ha v e already b een started
A set T
x
of unsc heduled tasks T
x
T is constructed of tasks that can start at u without
violating an y constrain t ie t
x
T
x
r t
x
u and i i D P
t S u f t x g R
i
t
where S u and R
i
t are as dened in Def In particular T
x
is the set of the released
tasks that do not result in retriev al con ten tion if sc heduled at u The set T
x
is sorted in a nondecreasing order based on the v alue of h t the function h t v aries from one heuristic to the other
The tasks are sc heduled at u consecutiv ely from the b eginning of the sorted set to its end
Before sc heduling a task it is examined that if an y constrain t will be violated assuming
the tasks is sc heduled If so then the task will not be sc heduled Later w e sho w that this
examination is fast
Note that all the tasks in T
x
usually cannot b e sim ultaneously initiated at u without violating
an y constrain t Hence the question is whic h subset of T
x
should b e selected to b e initiated at u This is the phase that alternativ e heuristics p erform dieren tly b y emplo ying v arious h t functions
to sort and select from T
x
The reason that the prop osed structure results in online sc heduling
algorithms is that at eac h time in terv al u T
x
is constructed from the tasks that has already b een
arriv ed ie t
x
T
x
r t
x
u Therefore the heuristic functions h t ha v e all the required
information ab out the tasks of T
x
in order to sort them There are some famous heuristics discussed
in the literature emplo y ed b y alternativ e sc heduling problems The follo wing is a list of some of
those heuristics that are adopted b y ARS with their corresp onding hfunction
First Come First Serve F CFS h t r t First Fit De cr e asing FFD h t
c t Earliest Completion time First ECF h t t Earliest De ad line First EDF h t r t t FFDECF h
t
c t h
t t
With the rst four heuristics F CFS FFD ECF EDF in case of a tie an arbitrary c hoice is
made With FFDECF rst h
is emplo y ed and in case of a tie h
is emplo y ed as a tie break er
F CFS is the simplest heuristic whic h is describ ed mostly for m ultimedia task sc heduling TPBG BGMJ DSS Its rationale is that the so oner a task arriv es the so oner it should b e sc heduled
The FFD heuristic is based on a pap er b y Garey et al GGJY FFD w as originally devised
for the binpac king GJ problem In the binpac king problem a nite n um ber of v ariablesize
items should b e placed in a single unitcapacit y bin with the ob jectiv e b eing to pac k all the items
in as few suc h bins as p ossible T o adopt it to ARS eac hin terv al can b e assumed as a bin and eac h
task as an item Subsequen tly the ob jectiv e is to sc hedule all the tasks in order to minimize the
nishing time
as few time in terv als as p ossible The FFD heuristic lls a bin starting from the
larger items that can t in the bin and hence its adopted v ersion for ARS should start sc heduling
the tasks with a higher bandwidth requiremen t The justication is that if there is some a v ailable
bandwidth then it should b e dedicated to a task that can utilize it more b ecause those requiring
less bandwidth ha v e a higher c hance to b e sc heduled in the future
T o justify the ECF heuristic consider the follo wing discussion Supp ose that at time in terv al
i there are only enough resources a v ailable to start the retriev al of either t
or t
but not b oth
If w e start t
and p ostp one t
assuming no new resources become a v ailable t
will observ e a
startup dela y of del ay t
i t
r t
while del ay t
i r t
On the other hand if
t
is sc heduled rst then del ay t
i t
r t
and del ay t
i r t
If w e compute
del ay t
del ay t
for eac h case and compare them with eachotherw e observ e that the minim um
Note that although binpac king and ARS ha v e some similarities they also ha v e some ma jor dierences F or
example in ARS sc heduling a task t will o ccup y t future bins F urthermore while a bin has enough space for an
item task it migh t not b e feasible to t the task in the bin time in terv al b ecause of the constrained placemen t
among the t w o dep ends on the length of eachtask In other w ords if t
t
then it is b etter
to sc hedule t
and then t
EDF is the most p opular heuristic for realtime sc heduling problems and is originally describ ed
in Der It is ne tuned for m ultipro cessor task sc heduling b y assigning deadlines to tasks suc h
that the execution of eac h task should be completed prior to its deadline In the case of ARS
supp ose ev ery tasks in T can tolerate a maxim um startup delayof M axD el Hence the deadline
for a task t can b e computed as r t t M axD el Therefore among a set of tasks the one
with the minim um r t t has also the earliest deadline
Finally FFDECF is a com bined heuristic that attempts to impro v e the p erformance of FFD in
the ev entof a tie It com bines t w o heuristics that emplo y dieren t parameters in their hfunctions
Sim ulations ha v e sho wn see Section that FFDECF is sup erior to the others Ho w ev er when
w e eliminate the constrain t placementb y assuming a single disk whose bandwidth is iden tical to the
aggregate bandwidth of m ultiple disks ECF outp erformed the rest This implies that FFDECF
captures the constrain t placementc haracteristic of ARS and supp orts the fact that ARS is a new
sc heduling problem that requires new atten tion In particular when D with a hea vy system
load the probabilit y that a task t nds the disk p t with sucien t bandwidth is lo w er than for
when D With D as so on as a task t
commits and free c t
of disk bandwidth another
task t
where c t
c t
can start Ho w ev er with D another restriction should also be
satised and that is the disk that b ecomes free should b e the same as the disk con taining the rst
sub ob ject of t
ie p t
F or a hea vy load system there is a high c hance that the freed bandwidth
b ecome utilized b y another task resulting in a higher startup delayfor t
Since a task with a higher
bandwidth requiremen t has a less c hance to nd sucien t disk bandwidth it should b e utilized as
so on as the t w o restrictions are satised This explains wh y FFDECF p erforms b etter than ECF
when D while the rev erse b ecomes true with D Since the sub ob ject assignmen t follo ws a regular pattern roundrobin and the sc heduling
algorithms do not lo ok ahead and reserv e resources in adv ance the prop osed system is fast see
Section T o implemen t the ab o v e heuristics a sc heduler should main tain a queue of the
W e also in v estigated other com binations suc h as ECFFFD and EDFFFD Ho w ev er w e eliminated them from
the pap er b ecause they did not result in an y new observ ations b esides those that are rep orted for other heuristics
retriev al tasks As so on as a request arriv es a retriev al task is generated and added to the queue in
the correct lo cation The correct lo cation of the task in the queue is determined b y the h function of
the c hosen heuristic ie the queue should remain sorted based on h t after insertion Note that
no resorting is required instead an insertion will b e sucien t O log nvs O n log n where n is
the maxim um length of the queue The sc heduler main tains a data structure that determines the
bandwidth consumption of eac h disk p er in terv al Assume the data structure is a matrix busy where
eachro w corresp onds to a time in terv al and eac h column to a disk
F or example busy u d determines that of the bandwidth of disk d is busy at time in terv al u A t the b eginning of
eac h time in terv al the sc heduler starts from the head of the queue and decides if a task can be
sc heduled or not Note that this decision making is fast b ecause only the currentin terv al and the
required disk driv e is examined for retriev al con ten tion In other w ords to examine if task t can
be sc heduled at uit is sucien ttoc hec k the condition busy u p t c t If the task can
b e initiated it is remo v ed from the queue and started A t this p oin t it is only required to up date
busy u p t This pro cedure con tin ues un til the tail of the queue is reac hed No w that the tasks
are initiated and the sc heduler has nothing else to do for the rest of the curren t time in terv al it
can up date busy for the maxim um length of the tasks that are sc heduled The rst p ortion of the
sc heduler whic h should b e in v ok ed at the b eginning of eac h time in terv al is fast and ideally can b e
implemen ted b y the hardw are The p ortion whic h is in c harge of adding tasks to the queue can
also be implemen ted b y the hardw are Ho w ev er it is not a critical p ortion b ecause in the w orst
case a task will observ e a small extra startup dela y b ecause of its late insertion to the queue
Augmen ted ARS A RS
W e use the augmen ted ARS problem termed AR S
asatransien t phase b et w een ARS and CRS
AR S
is iden tical to ARS except that eac h task t has a lag parameter x t that determines the
start time of the task That is the displa y of a task that is released at r t should not start so oner
than r t x t T o motiv ate AR S
consider a videoondemand application where the customers
reserv e mo vies in adv ance F or example at pm Alice reserv es Go d F ather to be displa y ed at
In real implemen tation it can b e a link list where as the sc heduling pro ceeds the no des prior to the curren t time
in terv al are released
pm Hence assuming t b e the task corresp onding to Alice retrieving GodF ather r t and x t
Supp ose t is started at time in terv al u there are three p ossible scenarios r t u r t x t u r t x t or ur t x t T rivially with the second and third scenarios t
will observ e a startup delayofzeroand r t x t u in terv als resp ectiv ely These t w o scenarios
are similar to ARS where a task is started at or after its release time The in teresting case is the
rst scenario In this case although the retriev al of the corresp onding ob ject is started so oner
than r t x t the displa y can still b e initiated at r t x t This can b e ac hiev ed b y buering
the data retriev ed prior to r t x t termed upsliding describ ed
in CGS Upsliding starts a
retriev al task so oner than the displa y of its corresp onding ob ject Memory buers are emplo y ed
to store those sub ob jects that are retriev ed so oner and ha v e not been displa y ed as y et As the
dela y bet w een retriev al and displa y increases the amoun t of required memory also increases T o
illustrate the concept of upsliding and its memory requiremen t consider the follo wing example
Example Supp ose D T ft
t
t
g Giv en the task information as
t
i
r t
i
x t
i
t
i
c t
i
p t
i
then
t
t
t
The required displa y sc hedules of these tasks as a function of time is depicted in Fig b The
placemen t of ob jects X Y and Z referenced resp ectiv ely b y t
t
and t
is sho wn in Fig
Note that to simplify the example all the tasks ha v e equal start time ie r t x t length
displa y bandwidth and their rst sub ob jects reside on the same disk Hence if a sc heduler starts
all the tasks at their start time there w ould be a retriev al con ten tion for disk One solution
is to p ostp one the retriev al of t
and t
for one and t w o in terv als resp ectiv ely observing a total
startup dela y of in terv als for this collection of tasks Ho w ev er since the information ab out t
t
is released one t w o in terv als so oner than its start time its retriev al can start earlier b y
emplo ying upsliding In this case no startup dela y will be observ ed T able demonstrates the
status of retriev al memory and displa y p er time in terv al
The dierence is that in CGS w ein tro duced upsliding for binary singlemedia comp osite ob jects
Time Retriev e Memory Displa y
In terv al Sliding Cyclebased
X X X Y X X Y X Y Z X X Y X Y Z X Y Z X X Y X Y Z X Y Z X Y Z X X Y X Y Z X Y Z Y Z X Y X Y Z X Y Z Z X Y Z X Y Z X Y Z T able System status with upsliding for Example F rom the ab o v e example the memory requirementfor an upslided task has a gro wing phase
steady phase and a shrinking phase The detailed computation of memory requiremen t for eac h
phase can be found
in SG The imp ortan t phase is the steady phase whic h determines the
maxim um memory requiremen t The maxim um memory requiremen t for eac h upslided task is
prop ortional to b oth the n um b er of upslided in terv als and its displa y bandwidth requiremen ts
M axM em t
c t r t x t t if r t x t t other w ise
Note that the amoun t of required memory in megabit can be computed as M axM em t R
D
inter v al where inter v al is the duration of a time in terv al in seconds This is b ecause the bandwidth
requiremen t of t is c t R
D
and the displa y time of one sub ob ject of the ob ject referenced b y
t is inter v al seconds Since Equation has already incorp orated c t it is sucien t to m ultiply
M axM em tb y R
D
inter v al to compute the memory requiremen t in megabits
Theorem AR S
is NP har d
Pro of AR S
can b e restricted to ARS b y assuming t T x t T o describ e the heuristics for AR S
assume the maxim um amoun t of sliding for a task t is
denoted b y B t The main structure of the heuristics for AR S
is v ery similar to that of ARS see
Section The dierence is that at eac hin terv al u the set T
x
is constructed from the tasks t
x
suchthat t
x
T
x
In SG w e assumed a single media t yp e The extension of equations to a mix of media t yp e can b e done
similar to Eq whic h computes the memory requiremen t for the steady phase
u r t
x
r t
x
x t
x
u B t
x
t
x
can b e sc heduled at u with no retriev al con ten tion ie i i D P
t S u f t x g R
i
t where S uand R
i
t are as dened in Def t
x
can b e sc heduled at u without exhausting the system memory SYSMEM ie assuming
t
x
u then
P
t S u f t x g M axM em t SY SM EM Previously with ARS as so on as a task w as released item and it resulted in no retriev al
con ten tion item it w as added to T
x
Here ho w ev er a task can start b efore its start time
item if it is allo w ed to based on B t and it will b e added to T
x
if b esides all the men tioned
constrain ts the system memory do es not o v ero w item Once T
x
is constructed alternativ e
metho ds to sort T
x
and the pro cedure of selecting tasks will be exactly iden tical to those of ARS
heuristics Indeed the same heuristics and h functions can b e emplo y ed
The v alues of B t pla ys an imp ortan t role in all the heuristics It determines ho w so on the
sc heduler can start a task t although due to retriev al or memory con ten tion it migh t not b e able to
initiate t Indeed B t determines the share of task t from the system memory If t T B t then no sliding is allo w ed In this case the ARS and AR S
heuristics are iden tical b ecause among
the ab o v e four restrictions to add a task to T
x
item is redundan t as it is iden tical to item assuming r t r t x t and item is alw a ys true t T MaxM em t In Section
the optimal v alue of B is b oth computed analytically and v eried using a sim ulation study Since the main structure of the AR S
sc heduling algorithm is iden tical to that of the AR S the same implemen tation tec hniques describ ed for ARS see Section can be applied here
The sole reason that the main structure of the AR S
heuristics are constructed similar to that
of the AR S is to main tain the sp eed of the sc heduling algorithms Otherwise a sc heduler that
attempts to sc hedule a task t at r t x t and in case of failure slides t up w ard migh t be more
successful Ho w ev er the problem with this algorithm is that it needs to lo ok ahead and reserv e
resources in adv ance resulting in slo wsc heduling see the discussion of Section T o observ e
assume r t and x t ie t should start at in terv al If at time in terv al u where u
the sc heduler decides to sc hedule t at it should reserv e resources for t in adv ance Hence the
only time that the sc heduler can initiate t at time without adv ance resource reserv ation is at
u Ho w ev er time in terv al u is to o late to decide for upsliding a task b ecause the system
has already missed the previous in terv als This explains wh y to sc hedule a task t our prop osed
algorithm starts from r t x t B t and pro ceeds do wn the time in terv als instead of starting
from r t x t and analyzing the previous time in terv als
Comp osite Retriev al Sc heduling CRS
With CRS eac h composite task consists of a n um ber of atomic tasks W e use t to represen t an
atomic task and for a comp osite task Similarly T represen t a set of atomic tasks while is a
set of comp osite tasks A comp osite task itself is a set of atomic tasks eg ft
t
t
n
g Eac h atomic task has the same parameters as dened in Section except for the release time
r t Instead eac h atomic task has a lag time denoted b y x t Without loss of generalit y w e
assume for a comp osite task x t
x t
x t
n
Subsequen tlyw e denote the rst atomic
task in the set as f ie f t
Lag time of a task is iden tical to the lag parameter see
Section of its corresp onding ob ject and determines the start time of the task with resp ect to
x f T rivially x f Eac h comp osite task on the other hand has only a release time
r whic h is the time that a request for the corresp onding comp osite ob ject is submitted
Denition An atomic task t is sc hedulable at u i t can be started at u and completes at
u t without violating an y resource constrain t as dened in Def Denition A comp osite task ft
t
t
n
g is said to b e sc hedulable at u ie u i t t is sc hedulable at u x t ie t u x t
Based on the ab o v e denition the CRS problem can b e dened similar to the ARS problem The
denition of CRS along with its pro of of NP hardness is pro vided in App endix A
Approac hes to Solv e CRS
There are t w o general approac hes to solv e the CRS problem One is to view a comp osite task as
a set of indep enden t atomic tasks The other is to view a comp osite task as a single atomic task
As is explained b elo w either of these approac hes increases complexityinsc heduling
The rst approac h constructs a set T as T S
The release time for an atomic task t can b e computed as r t r ie an atomic task is released once its corresp onding comp osite
task is released No w the CRS problem can b e view ed as the AR S
problem that should sc hedule
the set T The main dierence is that for those t that are not the rst task of an y comp osite task
ie st t f they should either be sc heduled immediately at their start time ie
r t x t or the displa y of their corresp onding comp osite ob ject will suer from hiccups In other
w ords they cannot tolerate an y startup dela y once the displa y of their comp osite task has started
The only case that t can tolerate a startup delayof ! is when f observ es the startup dela y
of ! Adding this constrainttothe AR S
problem increases the complexityofsc heduler b ecause it
is no w forced to sc hedule tasks indep enden tly while they dep end on eac h other due to the structure
of the comp osition
An alternativ e approachis tosc hedule comp osite tasks as if they are atomic tasks emplo ying
ARS heuristics Toac hievethis w e should assign a length and a bandwidth requiremen t c t
to eac h comp osite task so that the heuristics b e able to prefer one task to the other T o w ards that
end for eac h comp osite task with n atomic tasks w e dene
c
X
t c t n
Max
t x t t If more than one comp osite task is sc hedulable at u then one of the ARS heuristics is emplo y ed to
select one or more tasks The denition of a comp osite task b eing sc hedulable at u is as dened
in Def Ho w ev er w e should emphasize that the use of c and is to only enable ARS
heuristics to compute h As in the previous approac h the k ey problem with this approac h is
also to v erify sc hedulabilit y ie it is more complex to infer retriev al con ten tion
T o pro vide an analogy on ho w the rst and second approac hes are dieren t consider Fig
In Fig a eac h shaded b o x is an atomic task and the problem of ARS is to t them all in the big
rectangle on the righ t with the ob jectiv e to minimize the amoun t of required time b y consuming as
m uc h of the a v ailable disk bandwidth as p ossible With CRS the problem of lling the rectangle is
iden tical to ARS ho w ev er eac h task is no w a p olygon instead of a rectangle The rst approac h
b. CRS Problem a. ARS Problem
Time
Bandwidth
Time
Bandwidth
Figure ARS vs CRS analogy
striv es to partition a p olygon in to bo xes so that it can use the AR S
solutions to solv e CRS
The problem is that the AR S
solutions migh t destro y the shap e of the p olygons in the pro cess
of sc heduling Hence more constrain ts should be added to AR S
The second approac h on the
other hand main tains the shap e of the p olygons while sc heduling them Instead it emplo ys ARS
solutions to select a p olygon among all the p olygons that can t from a certain p oin t In this pap er
w e fo cus on the second approac h and do not consider the rst further
W e no w return to the problem of determining retriev al con ten tion with the second approac h
The k ey poin t is that the structure of a comp osite task do es not follo w a regular pattern th us
violating the rst criteria for fast sc heduling see Section Hence to sc hedule a comp osite
task at uthe en tire duration from u to u should b e examined for retriev al con ten tion In
other w ords adv ance resource reserv ation via lo okahead b ecomes essen tial Implemen tation of this
tec hnique demands c ho osing longer time in terv al in order to comp ensate for the extended duration
of computation of the sc heduler This results in less n um ber of sim ultaneous displa ys p er in terv al
compared to a system with the same system load whic h do es not supp ort comp osite ob jects
The Critical Role of Memory
As weha v e sho wn in Section sc heduling of AR S
can b enet form memory Ho w ev er in case
of CRS memory ma ybe ne c essary to ac hiev e sc hedulabilit y as discussed b elo w
A comp osite ob ject mayha v e internal c ontention ie atomic tasks that constitute a comp osite
task ma y comp ete with one another for the a v ailable disk bandwidth Hence it is p ossible that
due to internal c ontention a comp osite task cannot b e initiated at an y time in terv al indep enden t
of the system load T o observ e consider a comp osite task that consists of the atomic tasks of
Example Note that the release time of the tasks of this example should b e considered as their
lag time Indep enden t of the time in terv al that is initiated there is an in ternal con ten tion b et w een
t
and t
after in terv als from the start time of In other w ords it is not p ossible to start all the
atomic tasks of at their start time
Denition In ternal con ten tion Consider a comp osite task ft
t
t
n
g and u let S u be the set of atomic tasks whic h x t u x t t The comp osite task has
in ternal con ten tion i u i i D suc h that
P
t S u R
i
t where
R
i
t
c t if p t u x t mo d D i other w ise
The ab o v e denition in tuitiv ely means that the retriev al of all the atomic tasks of cannot be
sc heduled at their start time without violating the bandwidth constrain t In other w ords u suc h
that be sc hedulable at u see Def Using our graphical analogy the width of the p olygon
that represen ts a comp osite task with in ternal con ten tion is larger than the width of the rectangle
see Fig T o resolvein ternal con ten tion one should mo v e atomic tasks of so that the deformed p olygon
can t in the rectangle This can be ac hiev ed b y buer e d sliding describ ed in CGS Resolving
the in ternal con ten tion for a comp osite task is to mo dify the start time of its consisting atomic
tasks suc h that Def do es not hold true for Suc h a mo dication requires use of buers
Ideallyw e should minimize the amoun t of required buer There are t wot yp es of buered sliding
for comp osite tasks upsliding and downsliding Consider eac h case in turn
Upsliding is similar to the discussion of Section Its resolving of in ternal con ten tion for a
comp osite task is the same as solving AR S
for a set of atomic tasks where t r t r
Once this problem is solv ed the start time of atomic tasks can b e up dated to their sc heduled time
W e use the terms buer and memory in terc hangeably in this section
ie x t t r t and the mo died comp osite task will ha v e no in ternal con ten tion Since
resolving in ternal con ten tion is equiv alen t to solving AR S
Theorem R esolving internal c ontention for a c omp osite task by upsliding is NP har d
Emplo ying AR S
it is p ossible that a task starts after its start time This can also b e comp ensated
for b y memory as describ ed later as part of a dow nsl iding approac h Note that the ob jectiv e of
AR S
should be mo died to minimize the amoun t of required memory instead of minimizing
the a v erage startup dela y This is ac hiev ed b y minimizing
P
tT
j t r t x t j b ecause the
dierence b et w een the sc heduled time of a task and its start time determines the amoun t of required
memory An alternativ e approac h to resolving in ternal con ten tion is dow nsl iding With this approac h
the start time of constituting atomic tasks of a comp osite task is p ostp oned mo v ed do wn w ard
T o comp ensate for this dela y the displa y of the en tire comp osite ob ject is dela y ed T o illustrate
consider the follo wing example
Example Supp ose D ft
t
t
g and r Giv en the task information as
t
i
x t
i
t
i
c t
i
p t
i
then
t
t
t
The required displa y sc hedules of these tasks as a function of time is depicted in Fig c The
placemen t of ob jects V Y and Z referenced resp ectiv ely b y t
t
and t
is sho wn in Fig If all
the tasks is initiated at their start time ie r x t there will be a retriev al con ten tion for
disk at u Ho w ev er the system can do wnslide the retriev al of t
t
b yone t w o in terv als
while the retriev al of still starts at In this case the displa yof will observ es a startup delayof
t woin terv als T able demonstrates the status of retriev al memory and displa y p er time in terv al
The amountofstartup dela y in tro duced bydo wnsliding for comp osite task is
del ay Max
t t r t x t
Time Retriev e Memory Displa y
In terv al Sliding Cyclebased
V V V V V V V V V V Y V V Y V V V Y Z V V Y V Y Z V Y Z V Y V Y Z V Y Z Y Z Y V Y Z V Y Z Y Z Y Y Z V Y Z Z Y Z Y Z Y Z T able System status with do wnsliding for Example The memory requiremen t of a comp osite task con tributed bydo wnsliding for eac h time in terv al u
is
Mem u Mem u Ret u D isp u where Ret uand D isp u are the amoun t of data retriev ed and displa y ed at u resp ectiv ely That
is whatev er remains should be accum ulated in memory Subsequen tly Ret u and D isp u are
computed as follo ws
Disp u
P
t Disp t u Disp t u
c t if r t x t del ay ur t x t del ay t other w ise
Ret u
P
t Ret t u Ret t u
c t if t u t t other w ise
Assuming only dow nsl iding resolving in ternal con ten tion b ecomes v ery similar to solving the
ARS problem A comp osite task can be considered as T in ARS and the start time of the tasks
as their release time Subsequen tly minimizing the startup dela y can be translated directly to
minimizing the memory requiremen t Hence
Theorem R esolving internal c ontention by dow nsl iding is NP har d
Due to the ab o v e argumen t heuristics for solving ARS problem can be emplo y ed to resolv e the
in ternal con ten tion as w ell That is as a prepro cessing stage one can apply the heuristics on
those comp osite tasks that con tain in ternal con ten tion in order to mo dify the start time of their
corresp onding atomic tasks The resulting set of comp osite tasks can be sc heduled as describ ed
b efore
P erformance Ev aluation
In this section w e rep ort the results of our exp erimen ts on AR S
W e fo cused on AR S
for t w o
reasons First ARS is a sp ecial case of AR S
Second CRS can be solv ed b y extending the
solutions of ARS and AR S
as describ ed in Section Hence the observ ations with AR S
hold true for b oth ARS and CRS
W e implemen ted a sim ulation mo del to compare the p erformance of alternativ e heuristics
and in v estigate the impact of B and system memory on their p erformances First w e describ e
the sim ulation mo del Next w e rep ort the results of our exp erimen ts
Sim ulation Mo del
F or the purp oses of this ev aluation w e assumed a hardw are platform consisting of disk clusters
ie D eac h consisting of t w o Seagate STW disks Hence the eectiv e bandwidth of
eac h cluster is Mbs The amoun t of memory a v ailable for buered sliding is
Gigab yte
GB
W e assumed a newsondemand application where ob jects b elong to either of the four dieren t
media t yp es sho wn in T able The sub ob ject sizes are computed assuming that the duration of
a time in terv al is seconds The size of the clips t is random and v aries from seconds
one sub ob ject up to min utes sub ob jects The ob jects are assigned to the disks in a
roundrobin manner starting with a random disk
W e emplo y ed an op en sim ulation mo del for our ev aluation the n um ber of tasks n released ev ery min ute is con trolled byaP oisson distribution W e manipulated the P oisson param
Note that for a system with ph ysical disk driv es this is a reasonable amoun t of memory conceptually translated
to MB of memory p er ph ysical disk
Media t yp e Consumption rate Mbs Sub ob ject size MB c t MPEG or stereo CD qualit y audio
Lo w qualit y MPEG High qualit y MPEG Compressed HDTV T able Media parameters
Heuristics D Imaginary disk
Ligh t Mo derate Hea vy Ligh t Mo derate Hea vy
F CFS
FFD
ECF
EDF
FFDECF
T able Comparison of alternativ e heuristics
eter to mo del four alternativ e system loads V ery ligh t tasks per min ute ligh t tasks per
min ute mo derate tasks per min ute and hea vy tasks per min ute system load The lag
parameter x t v aries from to in terv als seconds
Exp erimen tal Results
W e rep ort the results of t w o sets of exp erimen ts In the rst set w e compared the p erformance
of dieren t heuristics F or the sak e of comparison w e executed all the exp erimen ts not only on a
platform of clusters but also on an imag inar y disk whose bandwidth is iden tical to the aggregate
bandwidth of those clusters Note that to construct suc h an imaginary disk in real w orld more
than ph ysical Seagate disks are required
In this imaginary disk the placemen t of data and
roundrobin sc heduling of resources on b ehalf of a displa y becomes redundan t pro viding a data
indep endentev aluation of the alternativ e prop osed heuristics
T able presen ts the a v erage startup dela y in n um ber of in terv als observ ed with alternativ e
heuristics The dierence bet w een the a v erage startup dela y observ ed b y eac h of F CFS FFD
and EDF with D and the imaginary disk is not signican t This is b ecause at high system
This is b ecause this platform is not scalable see GK
Alternative Scenarios
Average Startup Delay (in number of intervals)
300
350
400
450
500
550
600
01234 56789
FCFS
FFD
EDF
ECF
FFD+ECF
a D Alternative Scenarios
Average Startup Delay (in number of intervals)
200
300
400
500
600
700
800
900
1000
1100
1200
0123456789
FCFS
FFD
EDF
ECF
FFD+ECF
b Imaginary disk
Figure Hea vy requests p er min ute
load the disks b ecome completely utilized with D due to the roundrobin assignmen t of the
sub ob jects sim ulating a single disk with an aggregate bandwidth of disks Ho w ev er for a
lo w er system load columns and disk platform results in a higher a v erage startup
dela y b ecause the placemen t of data forces some tasks to w ait un til the disk con taining their rst
sub ob ject p t b ecomes a v ailable In general the p erformance of the heuristics b ecomes closer to
eac h other as the system load decreases The reason is that for lo w system load the queue generated
at eachin terv al do es not ha v e enough elemen ts for a heuristic to mak e a dierence With a hea vily
loaded system ho w ev er b oth FFDECF and ECF outp erform other heuristics with D and
imaginary disk resp ectiv ely This sho ws that considering the bandwidth of the tasks when ordering
the queue is b enecial to resolv e con ten tion on m ultiple disks while it is not crucial when all the
tasks are comp eting for a single disk see Section T o determine whether this is a general trend
or a phenomena that occurs b y c hance due to the start times of tasks r t x t w e analyzed
alternativ e scenarios byv arying
x t F urthermore since the same trend holds from ligh t to hea vy
system load in T able w e selected the hea vy system load b ecause in this case the p erformance of
the heuristics diers signican tly larger queues are constructed The obtained results see Fig demonstrates while FFDECF is sup erior to other heuristics with D ECF is sup erior with
the imaginary disk FFDECF outp erformed with D F CFS by on a v erage
The reduction in a v erage startup dela y is not for free Sometimes one or more tasks migh t
starv e with b oth ECF and FFDECF In the real implemen tation a threshold can b e determined
for the maxim um tolerable startup dela y and once a task exceeds that threshold it should b e mo v ed
to the head of the queue
In a second set of exp erimen ts w e in v estigated the impact of sliding on the a v erage startup
dela y Wev aried the v alue of B t from up to and compared the a v erage startup dela y observ ed
byboth F CFS and FFDECF A theoretically optimal v alue for B t is the one that satises the
follo wing equation
X
t S u B t Sub t sy smem where Su denotes the set of tasks executed at u Subt is the sub ob ject size of the ob ject
W e could not v ary r t b ecause it results in a dieren t load
0 5 10 15 20
0
0.1
0.2
0.3
0.4
0.5
0.6
B (in number of intervals)
Avg. Startup Delay (in number of intervals)
FCFS, ECF+FFD
0 5 10 15 20
0.4
0.6
0.8
1
1.2
1.4
1.6
B (in number of intervals)
Avg. Startup Delay (in number of intervals)
FFD+ECF
FCFS
0 5 10 15 20
16
18
20
22
24
26
28
30
B (in number of intervals)
Avg. Startup Delay (in number of intervals)
FFD+ECF
FCFS
a V ery Ligh t b Ligh t c Mo derate
requests p er min ute requests p er min ute requests p er min ute
Figure V alue of B t referenced b y t and sy smem is the a v ailable system memory in MB Giv en a task t
big
where
c t
big
w e can compute Sub t
big
R
D
inter v al
whic h is the size of its sub ob ject in MB
Subsequen tly for an y t Sub t Sub t
big
c t c t
big
or Sub t R
D
inter v al c t Substituting
Sub t in Equation and assuming a x v alue OptB for all B t w e obtain
R
D
inter v al OptB
X
t S u c t sy smem Note that in the w orst case
P
t S u c t D and hence from Equation w e obtain
OptB sy smem R
D
inter v al D
The v alue of OptB for our exp erimen ts is In Fig a as w e increase the v alue of Bthe a v erage
startup dela y decreases un til B Assigning more than buers to eac h task for sliding results
in comp etition for the a v ailable memory resulting in a nondeterministic p erformance of the system
The reason that this phenomena did not happ en at B is b ecause the system load is v ery
lowand
P
t S u c t D With a lowsystem loadFig b w e observ e that the system b ecomes
nondeterministic when B increases b ey ond With a mo derate system load Fig c this b eha vior
o ccurs with smaller v alues of B The reduction in the a v erage startup dela y with buered sliding
ranges from to dep ending on the system load
W e also examined the v alue of B t to be a function of both x t ie B t x t B
and
sy smem ie B t
sy smem R
D
inter v al B
In eac h case wev aried the v alue of B With B t
x t B
the
observ ations w ere similar to those rep orted for a constan t B Ho w ev er the reduction in the a v erage
startup dela y w as less than when B is xed The second case where B t sy smem R
D
inter v al B
has
already been co v ered b ecause it is a subset of the rep orted cases T o illustrate note that all the
tasks are assigned an iden tical B tv alue Subsequen tlyb y xing sy smem at GB and v arying
B dieren tv alues generated for B t are a subset of the rep orted v alues
Related w ork
Sev eral studies ha vein v estigated tec hniques to supp ort the con tin uous displa y of atomic m ultimedia
ob jects P ol GS TPBG R V CL GHBC BGMJ There are others that study
the problem of sc heduling the retriev als of the sub obje cts of dieren t atomic ob jects during a time
in terv al in order to utilize more of the disk bandwidth and less memory b y eliminating the
impact of the seek time YCK BMC GHBC GKS CBR OBRS Ho w ev er w e are
only a w are of few studies DSS V GG TPBG that are related to sc heduling the retriev als of
atomic ob jects Our w ork is dieren t from all of the ab o v e in that our sc heduling tec hniques rely
on and exploit the regular pattern roundrobin in whic h a task utilizes the disks In addition w e
fo cus on a hea vily loaded system while in TPBG it is assumed that the n um b er of activ e requests
is less than the n um b er of streams supp orted b y the system ligh t system load In V GG they
fo cus on the metho ds to admit a submitted request without violating the qualit y of service for
the activ e requests Ho w ev er the p olicy used to c ho ose a task from a set of queued requests
has not been addressed in V GG The con ten tion prediction in our sc heduling algorithms see
Section is similar in principle to admission con trol p olicies Ho w ev er due to our fo cus on
roundrobin activ ation of the disks the tec hniques adopted in our w ork are dieren t Finally Dan
et al DSS prop ose a batc hing tec hnique to group the requests that reference the same video
in order to reduce the retriev al load This tec hnique can b e adopted and tuned to our sc heduling
algorithms In this case eac h task can be view ed as a represen tativ e of a collection of requests
referencing the same ob ject
When compared with the atomic ob jects the retriev al of comp osite ob jects using a m ultidisk
hardw are platform has receiv ed ev en less atten tion An um b er of studies ha v e analyzed comp osite
ob jects and temp oral relationships from a conceptual p ersp ectiv e Her VM LG HFK Their fo cus is on alternativ e abstract represen tations of comp osite ob jects Other studies Ste LG RR concen trate on the net w orking asp ects of a geographically distributed system and
prop ose tec hniques to supp ort the temp oral relationships of a comp osite ob ject when displa y ed at
a remote clien t A surv ey of these studies is presen ted in Buf RR In CGS w e prop osed
atec hnique buered sliding to a v oid retriev al con ten tion when sc heduling the retriev al of a single
binary comp osite ob ject ie consisting of t w o atomic ob jects b elonging to a single media t yp e
This study is a generalization of CGS to supp ort a mix of media t yp es and nary comp osite
ob jects consisting of a mix of media t yp es Moreo v er the approac hes describ ed in this study are
more general and subsume those of CGS
ARS migh t app ear to b e similar to the problem of realtime sc heduling of tasks on m ultipro ces
sors from MC LL to KS One migh t conceptualize a disk as a pro cessor to reduce ARS
to a m ultipro cessor task sc heduling problem Ho w ev er the constrained placemen t of data across
the disks in tro duces new c hallenges In m ultipro cessor task sc heduling a task can be sc heduled
for execution on an y pro cessor at an y time ho w ev er with ARS the retriev al of ob ject X m ust
start with the disk con taining its rst sub ob ject and emplo y other disks in a roundrobin manner
Stank o vic et al suggests that the placemen t constrain ts and the impact of this placemen t on the
run time sc heduling is an op en researc h area SSNB SSNB An alternativ e reduction of ARS is to consider eac h disk as a resource This suggests the
similarit y of ARS with the task sc heduling under resource constrain t GJ GGJY Bla ZR WL One ma jor c haracteristic of ARS dieren tiates it from these studies All these studies
assume that the resources are o ccupied b y a task during its life time Ho w ev er with ARS a displa y
acquires and releases resources p erio dically in a roundrobin manner A metho d to comp ensate for
this is to break a task in to subtasks where eac h subtask acquires resources for its en tire duration
Subsequen tly a precedence relation La w can be emplo y ed to relate the subtasks of a task
Ho w ev er the precedence relation is not restricted enough for ARS If a partial order is assumed
suchthat task t
precedes task t
then this means that t
should complete b efore t
starts Ho w ev er
with ARS assuming t
and t
corresp ond to retriev al subtasks from disks i and i on b ehalf of
a single request then t
should start immediately after t
completes Otherwise the displayma y
suer from hiccup Hence it is not sucien ttostart t
an y time after the completion of t
Conclusions and F uture Researc h Directions
W e in v estigated a class of sc heduling problems ARS AR S
CRS co v ering a large n um ber of
m ultimedia applications Due to the sp ecial requiremen ts of these applications they in tro duce
new c hallenges to the con v en tional sc heduling problems Hence w e sho w ed their uniqueness and
concluded that the solutions prop osed to the con v en tional sc heduling problems need to b e revisited
and adopted for ARS AR S
and CRS W e formalized these problems pro v ed their NP hardness
and dev elop ed some heuristics F CFS FFD ECF EDF FFDECF These heuristics are appro
priate for a hea vy system load that results in the formation of a queue of p ending tasks Using
asim ulation mo del w e concluded that FFDECF is sup erior to the other alternativ es Ho w ev er
as the n um ber of disks D decreases ECF b ecomes more eectiv e and ev en tually it outp erforms
FFD EC F when D This implies that FFDECF captures the constrain t placementc har
acteristic of ARS and supp orts the fact that ARS is a new sc heduling problem that requires new
atten tion W e also demonstrated that b y emplo ying buers the a v erage startup dela y can b e de
creased further when the system load is lo w Note that buer sliding is una v oidable indep enden t
of the system load to resolv e in ternal con ten tion for comp osite tasks The optimal share of eac h
task from memory used for buered sliding w as computed analytically and it w as v eried using a
sim ulation study This study can b e extended in t wow a ys First the role of buered sliding to resolv e con ten tion
bet w een atomic tasks of dieren t comp osite tasks should b e in v estigated This will result in a more
exible and complex sc heduling algorithms This in v estigation can be done in the con text of the
rst approac h for solving CRS where atomic tasks are sc heduled indep enden tly In this case adding
a constrain t to the atomic tasks suchthat their start time and release time b ecome a function of
the release time of the comp osite task is essen tial
Second in this study w e fo cused on the demand driv en paradigm SG That is a task
is released based on a submitted request Ho w ev er tasks migh t be released in a regular manner
based on a data driv en paradigm SG T o illustrate suchanen vironmen t supp ose that there is
a large database of digitized mo vies An um b er of Cable companies eg HBO Sho wtimes Mo vie
Channel migh t render this database to serv e their customers The sc hedules of Cable companies
are kno wn in adv ance This can b e the sc hedule of a da ya w eek or a mon th Mean while a p ayp er
view service pro vider migh t use the same database to displaymo vies for its customers on demand
It is w orth while to study the sc heduling problems in a com bined en vironmen t that incorp orates
b oth data and demand driv en paradigms
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Tasks with Time and Resource Constrain ts Journal of Systems and Softwar e A CRS is NP hard
Denition A The problem of CRS is to nd a sc hedule where N for a set suc h that
it minimizes the nishing time GG w where w is the least time at whic h all tasks of ha vebeen
completed and satises the follo wing constrain ts
r u let S u be the set of atomic tasks whic h t u t t then i i D
P
t S u R
i
t where
R
i
t
c t if p t u t mo d D i other w ise
Theorem A CRS is an NP har dpr oblem
Pro of W e restrict CRS to ARS b y assuming all the comp osite tasks are singleton sets F urthermore for
a comp osite task ftgw e consider t p p t and r r t Hence the restricted CRS
b ecomes iden tical to ARS
Abstract (if available)
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Description
Cyrus Shahabi, Shahram Ghandeharizadeh and Surajit Chaudhuri. "On scheduling atomic and composite multimedia objects." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 622 (1995).
Asset Metadata
Creator
Chaudhuri, Surajit
(author),
Ghandeharizadeh, Shahram
(author),
Shahabi, Cyrus
(author)
Core Title
USC Computer Science Technical Reports, no. 622 (1995)
Alternative Title
On scheduling atomic and composite multimedia objects (
title
)
Publisher
Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA
(publisher)
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OAI-PMH Harvest
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39 pages
(extent),
technical reports
(aat)
Language
English
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UC16269507
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95-622 On Scheduling Atomic and Composite Multimedia Objects (filename)
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usc-cstr-95-622
Format
39 pages (extent),technical reports (aat)
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Department of Computer Science (University of Southern California) and the author(s).
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In copyright - Non-commercial use permitted (https://rightsstatements.org/vocab/InC-NC/1.0/
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20180426-rozan-cstechreports-shoaf
(batch),
Computer Science Technical Report Archive
(collection),
University of Southern California. Department of Computer Science. Technical Reports
(series)
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USC Viterbi School of Engineering Department of Computer Science
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Department of Computer Science. USC Viterbi School of Engineering. Los Angeles\, CA\, 90089
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csdept@usc.edu
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Title
Computer Science Technical Report Archive
Coverage Temporal
1991/2017
Repository Email
csdept@usc.edu
Repository Name
USC Viterbi School of Engineering Department of Computer Science
Repository Location
Department of Computer Science. USC Viterbi School of Engineering. Los Angeles\, CA\, 90089
Publisher
Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA
(publisher)
Copyright
In copyright - Non-commercial use permitted (https://rightsstatements.org/vocab/InC-NC/1.0/