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USC Computer Science Technical Reports, no. 650 (1997)
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USC Computer Science Technical Reports, no. 650 (1997)
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Content
On Disk Sc heduling and Data Placemen t for Video Serv ers
Shahram Ghandeharizadeh Seon Ho Kim Cyrus Shahabi
Departmen t of Computer Science
Univ ersit y of Southern California
Los Angeles California Abstract
Magnetic disks ha v e established themselv es as the mass storage device of c hoice for data in ten
siv e applications including video serv ers These devices are mec hanical in nature They p erform
useful w ork when transfering data and w asteful w ork when preparing to transfer data F or video
serv ers a disk can supp ort a higher n um ber of sim ultaneous displa ys when its p ercen tage of
w asteful w ork is minimized The fo cus of this study is on t w o recen tly in tro duced tec hniques
that minimize the w asteful w ork p erformed b y adisk The rst con trols the placemen t of data
across the surface of a disk while the second emplo ys the disk sc heduling p olicy In addition to
quan tifying the tradeos asso ciated with these t w o tec hniques w e observ e that one is orthogonal
to the other and com bine them in to one displa y strategy Wealso quan tify the memory require
mentof these t wotec hniques with b oth a coarsegrain and a negrain memory sharing tec hnique
Keyw ords con tin uous displa y disk sc heduling constrained data placemen t throughput startup
latency In tro duction
Video in v ariet y of formats has b een a v ailable since late s Enc and has enjo y ed more than a
cen tury of researc h and dev elopmen t During the s digital video started to b ecome viable due to
adv ances in information tec hnology Systems that supp ort storage and retriev al of video and audio
ob jects are exp ected to pla y a ma jor role in library information systems educational applications
en tertainmen t tec hnology etc Video ob jects exhibit the follo wing c haracteristics
They m ust be retriev ed at a presp ecied bandwidth to ensure their con tin uous displa y If
a video ob ject is retriev ed at a rate lo w er than its presp ecied bandwidth with no sp ecial
precautions eg prefetc hing then its displa yma y suer from frequen t disruptions and dela ys
termed hic cups T o illustrate the bandwidth required b y NTSC for net w orkqualit y video is
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
ab out Megabits p er second Mbs Has Recommendation of the In ternational Radio
Consultativ e Committee CCIR calls for a Mbs bandwidth for video ob jects F o x A
video ob ject based on HDTV requires appro ximately Mbs for its con tin uous displa y Video ob jects are large in size F or example a min ute uncompressed video clip based on
NTSC is gigab ytes in size
One ma y emplo y a lossy compression tec hniques eg MPEG in order to reduce b oth the size
and the bandwidth requiremen t of a video clip Ho w ev er their size con tin ues to be signican t b y
most curren t standards F or example a t w o hour MPEG compressed video clip with a Mbs
bandwidth requiremen t requires Gigab yte of storage Magnetic disks ha v e b ecome the storage
device of c hoice for storing video ob jects b ecause of their lowcost and lo w access time L V Other
c heap er storage devices eg tap e ha v e a longer access time and t ypically serv e as a tertiary storage
device to store the infrequen tly displa y ed video clips GC GDS DT FR The fo cus of
this study is on systems that emplo y magnetic disks and tec hniques to maximize their n um ber of
sim ultaneous displa ys These tec hniques are applicable to other mec hanical devices with ph ysical
c haracteristics similar to a magnetic disk driv e
A magnetic disk is a mec hanical device and incurs a dela y when required to retriev e a referenced
data item This dela y consists of the time to rep osition the head termed seek time and for the
data to app ear under the disk head termed rotational dela y Next the disk transfers the referenced
data The disk p erforms useful w ork when transfering data and w asteful w ork when incurring either
seek times or rotational dela ys By minimizing the amountof w asteful w ork the disk subsystem can
supp ort a higher n um ber of sim ultaneous displa ys One approac h to eliminate seek time is to read
the referenced data item in its en tiret y Ho w ev er this is not a practical approac h for video ob jects
for sev eral reasons First video ob jects are v ery large in size and can readily exhaust the a v ailable
memory Second this w ould b e w asteful of memory b ecause staging a t w o hour video clip in memory
implies that the tail end of the video is displa y ed after t w o hours and hence no other displa y can
use this o ccupied memory for t w o hours Third during the time required to read this clip the disk
cannot service other requests
A displa y tec hnique that minimizes the amountofw asted memory w ould partition a video ob ject
in to blo c ks and sc hedule their retriev al suc h that a blo c k is rendered memory residen t prior to its
displa y GHBC YCK P ol CL R V GVK
This blo ckis sw app ed out of memory as
so on as its displa y completes minimizing the amoun t of memory required bya displa y The remaining
memory can b e used to supp ort the displa y of other ob jects A limitation of this tec hnique is that it
m ultiplexes the disk bandwidth among the blo c k retriev als of dieren t ob jects This results in seek
op erations b et w een blo c k retriev als w asting the bandwidth of the disk One approac h to render the
percen tage of w asteful w ork insignican t is to increase the amoun t of data read during eac h disk
transfer ie the blo cksize In the extreme case the blo c k size is equiv alen t to the size of a video
clip A limitation of this approachis that itis w asteful of memory see the discussion of the previous
paragraph and increases the total amoun t of memory required from the system
An alternativ e approac h to minimize the p ercen tage of w asted disk bandwidth is to minimize the
seek time The seek time is a function of the distance tra v eled b y the disk head Minimizing this
distance reduces the seek time This can be ac hiev ed b y either con trolling the placemen t of data
across the disk surface eg REgion BasEd bloCk Allo cation termed REBECA GKS BMC and an optimized v ersion of REBECA termed OREO or emplo ying the disk sc heduling algorithms
eg Group ed Sw eeping Sc heme GSS YCK Eac h tec hnique requires a dieren t amoun t of
memory dep ending on its emplo y ed memory managemen t tec hnique W e describ e t w o memory
managemen t tec hniques based on coarsegrain and negrain sharing In general GSS requires more
memory undesirable and results in a lo w er latency desirable when compared with either OREO or
REBECA Disk sc heduling and data placemen t are orthogonal to eac h other and can b e com bined in to
one This com bination is a p o w erful generalization of these t w o tec hniques While these tec hniques
enhance the n um b er of sim ultaneous displa ys throughput supp orted b y a single disk system they
increase the startup latency observ ed b y eac h displa y Startup latency is dened as the amoun t of
time elapsed from when a request arriv es referencing an ob ject un til the system initiates its displa y The in v estigated tec hniques assume that requests arriv e randomly and are indep enden t of one
another Generally sp eaking b oth REBECA and OREO are appropriate for en vironmen ts where a
video clip consists of man y blo c ks that are displa y ed from the b eginning to the end videoondemand
is an example en vironmen t These t w o tec hniques are inappropriate for en vironmen ts where blo c ks
are arbitrarily c hosen for displa y eg authoring en vironmen ts with dieren t users constructing
presen tations dynamically due to their high startup latency p er blo c k retriev al GSS is appropriate
for b oth en vironmen ts b ecause it separates the displa y of an ob ject from its ph ysical data placemen t
GSS w as originally in tro duced in YCK REBECA w as describ ed in GKS BMC Eac h
study describ ed a conguration planner for a system that emplo ys its prop osed tec hnique This study
is a con tribution for sev eral reasons First it quan ties the tradeos asso ciated with data placemen t
REBECA and OREO and disk sc heduling GSS tec hniques that minimize seek time Second
it in tro duces an optimized v ersion of REBECA termed OREO Third it observ es that the t w o
alternativ e approac hes are orthogonal and com bines them in to one displa y strategy OREOGSS
F ourth it in tro duces a negrain memory sharing tec hnique to reduce the memory requiremen ts of
the system with GSS REBECA OREO and OREOGSS Our exp erimen tal results demonstrate
a signican t reduction in the amoun t of required memory using negrain sharing a factor of t w o
Blo c k Unit of transfer from disk to main memory laid out con tiguously on the disk surface
P age The smallest unit of memory allo cation A blo c k consists of m pages
CoarseGrain Memory Sharing CGS The gran ularit y of memory sharing is in blo c ks
System main tains a shared p o ol of blo c ks
FineGrain Memory Sharing F GS The gran ularit y of memory sharing is in pages System
main tains a shared p o ol of pages The size of a blo ckis a m ultiple of the page size
Time P erio d Time required to displaya bloc k
Startup Latency Amoun t of time elapsed from the arriv al time of a request to the onset of the
displa y of its referenced ob ject
T able Dening terms
reduction as compared to coarsegrain sharing in almost all exp erimen ts And nally it describ es
these approac hes for a m ultidisk arc hitecture
T o simplify discussion this study describ es the alternativ e tec hniques assuming a system cong
ured with a single disk Its extension to a m ultidisk arc hitecture is straigh tforw ard and describ ed
in Section The rest of this pap er is organized as follo ws Section describ es a simple tec hnique
to displa y a video ob ject assuming a system congured with a single disk Using this tec hnique it
describ es the role of disk sc heduling data placemen t and a com bination of these t w o tec hniques
Section quan ties the memory requiremen ts of these tec hniques with b oth a coarsegrain and a
negrain memory sharing tec hnique Section pro vides an o v erview of a conguration planner that
consumes the p erformance ob jectiv es of a target application its desired throughput and startup
latency to determine a v alue for system parameters Section con tains an ev aluation of the alter
nativ e strategies using the planner Section extends this discussion to a m ultidisk arc hitecture
Our conclusions and future researc h directions are con tained in Section Con tin uous Displa y
This study assumes that a disk driv e pro vides a constan t bandwidth R
D
Moreo v er all ob jects
ha v e the same displayrate R
C
T o supp ort con tin uous displa y of an ob ject X it is partitioned in to
n equisized blo c ks X
X
X
n where n is a function of the blo cksize B and the size of X W e assume a blo c k is laid out con tiguously on the disk and is the unit of transfer from disk to main
memory T able denes the terms used rep eatedly in this pap er The time required to displaya
blo c k is dened as a time p erio d T
p
T
p
B
R
C
This section describ es four alternativ e tec hniques to supp ort the con tin uous displayof m ultiple
Display W Display W
W W
Disk
Activity
System
Activity
W
i i+1 i+2
i i+1
X X
j j+1
Display X
j
T
W_Seek
Time Period (Tp)
Z
k
Z
k+1
Figure Time P erio d
ob jects The size of a blo c k and hence the memory requiremen t is dieren t with eac h tec hnique
Moreo v er the maxim um observ ed startup latency v aries p er tec hnique
A Simple T ec hnique
With this tec hnique when an ob ject X is referenced the system stages X
in memory and initiates
its displa y Prior to completion of a time period it initiates the retriev al of X
in to memory in
order to ensure a con tin uous displa y This pro cess is rep eated un til all blo c ks of an ob ject ha vebeen
displa y ed
T o supp ort sim ultaneous displa ys of sev eral ob jects a time p erio d is partitioned in to xedsize
slots with eac h slot corresp onding to the retriev al time of a blo c k from the disk driv e The n um ber
of slots in a time p erio d denes the n um ber of sim ultaneous displa ys that can b e supp orted b y the
system N F or example a blo c k size of MB corresp onding to a MPEG compressed mo vie
R
C
Mbs has a second displa y time T
p
Assuming a t ypical magnetic disk with
a transfer rate of Mbs R
D
Mbs and maxim um seek time of milliseconds suc h
blo c ks can b e retriev ed in seconds Hence a single disk supp orts sim ultaneous displa ys Figure demonstrates the concept of a time p erio d and a time slot Eachbo x represen ts a time slot Assuming
that eac h blo c k is stored con tiguously on the surface of the disk the disk incurs a seek ev ery time
it switc hes from one blo c k of an ob ject to another W e denote this as T
W Seek
and assume that it
includes the a v erage rotational latency time of the disk driv e W e will not discuss rotational latency
further b ecause it is a constan t added to ev ery seek time
The seek time is a function of the distance tra v eled b y the disk arm BG GHW R W Sev eral studies ha vein tro duced analytical mo dels to estimate seek time as a function of this distance
T o be indep enden t from an y sp ecic equation this study assumes a general seek function Th us
let S eek d denote the time required for the disk arm to tra v el d cylinders to rep osition itself from
cylinder i to cylinder i d or i d Hence Seek denotes the time required to rep osition the disk
arm bet w een t w o adjacen t cylinders while Seek cy l denotes a complete strok e from the rst to
the last cylinder of a disk with cy l cylinders T ypically seek is a linear function of distance except
for small v alues of d BG R W F or example GKS emplo y ed the follo wing seek function
Seek d
p
d if d d otherwise
Since the blo c ks of dieren t ob jects are scattered across the disk surface the simple tec hnique
should assume the maxim um seek time ie Seek cy l when m ultiplexing the bandwidth of the
disk among m ultiple displa ys Otherwise a con tin uous displayof eac h ob ject cannot b e guaran teed
Seek is a w asteful op eration that minimizes the n um ber of sim ultaneous displa ys supp orted b y
the disk In the w orst case disk p erforms N seeks during a time p erio d Hence the p ercen tage of
time that disk p erforms w asteful w ork can b e quan tied as
N Seek d T p
where d is the maxim um
distance b et w een t w o blo c ks retriev ed consecutiv ely d cy l with simple By substituting T
p
from
Eq w e obtain the p ercen tage of w asted disk bandwidth
w astef ul N Seek d R
C
B
By reducing this p ercen tage the system can supp ort a higher n um b er of sim ultaneous displa ys W e
can manipulate t w o factors to reduce this p ercen tage decrease the distance tra v ersed b y a seek
d andor increase the blo c ksize B A limitation of increasing the blo c k size is that it results in
a higher memory requiremen t In this pap er w ein v estigate displa y tec hniques that reduce the rst
factor An alternativ e asp ect is that b y manipulating d and xing the throughput one can decrease
the blo c k size and b enet from a system with a lo w er memory requiremen t for staging the blo c ks
The follo wing paragraphs elab orate more on this asp ect
Supp ose N blo c ks are retriev ed during a time p erio d then T
p
NB
R
D
N Seek cy l By
substituting T
p
from Eq w esolv e for B to obtain
B
simpl e
R
C
R
D
R
D
N R
C
N Seek cy l F rom Eq for a giv en N the size of a blo c k is prop ortional to Seek cy l Hence if one
can decrease the duration of the seek time then the same n um ber of sim ultaneous displa ys can be
supp orted with smaller blo c k sizes This will sa v e some memory Briey for a xed n um ber of
sim ultaneous displa ys as the duration of the w orst seek time decreases increases the size of the
blo c ks shrinks gro ws prop ortionally with no impact on throughput This impacts the amoun t of
memory required to supp ort N displa ys F or example assume Seek cy l msec R
D
Mbs R
C
Mbs and N F rom Eq w e compute a blo c k size of MB that w astes
of the disk bandwidth If a displaytec hnique reduces the w orst seek time b y a factor of t w o
then the same throughput can b e main tained with a blo c k size of MB reducing the amoun tof
required memory b y a factor of t w o and main taining the p ercen tage of w asted disk bandwidth at
This observ ation will b e used rep eatedly in this pap er
The maxim um startup latency observ ed b y a request with this tec hnique is
simpl e
T
p
This is b ecause a request migh t arriv e a little to o late to emplo y the empt y slot in the curren t time
period Note that is the maxim um startup latency the a v erage latency is
when the n um ber of
activeusers is N If the n um b er of activ e displa ys exceeds N then Eq should b e extended with
appropriate queuing mo dels This discussion holds true for the maxim um startup latencies computed
for other tec hniques in this pap er
In the follo wing sections wein v estigate t w o general tec hniques to reduce the duration of the w orst
seek time While the rst tec hnique sc hedules the order of blo c k retriev al from the disk the second
con trols the placemen t of the blo c ks across the disk surface These t w o tec hniques are orthogonal
and wein v estigate a tec hnique that incorp orates b oth approac hes
Disk Sc heduling
One approachto reducethe w orst seek time is Gr oup edSwe eping Scheme YCK GSS GSS groups
N activ e requests of a time p erio d in to g groups This divides a time p erio d in to g sub cycles eac h
corresp onding to the retriev al of d
N
g
e blo c ks The mo v emen t of the disk head to retriev e the blo c ks
within a group abides b y the SCAN algorithm in order to reduce the incurred seek time in a group
Across the groups there is no constrain t on the disk head mo v emen t T o supp ort the SCAN p olicy
within a group GSS sh ues the order that the blo c ks are retriev ed F or example assuming X Y and Z b elong to a single group the sequence of the blo c k retriev al migh t be X
follo w ed b y Y
and Z
denoted as X
Y
Z
during one time period while during the next time period it
migh t c hange to Z
X
Y
In this case the displa y of sa y X migh t suer from hiccups
b ecause the time elapsed bet w een the retriev als of X
and X
is greater than one time p erio d T o
Time Period (Tp)
Subcycle 1
Subcycle 2
X1 X2 Y1 Z1 W1 Y2 Z2 W2
X3 Y3 Z3 W3
X4 Y4 Z4 W4
Display X1 and Y1
...
Display X2 and Y2
Figure Con tin uous displa y with GSS
eliminate this p ossibilit y YCK suggests the follo wing displaymec hanism the displa ys of all the
blo c ks retriev ed during sub cycle i start at the b eginning of sub cycle i T o illustrate consider
Figure where g and N The blo c ks X
and Y
are retriev ed during the rst sub cycle
The displa ys are initiated at the b eginning of sub cycle and last for t w o sub cycles Therefore while
it is imp ortantto preserv e the order of groups across the time p erio ds it is no longer necessary to
main tain the order of blo c k retriev als in a group
The maxim um startup latency observ ed with this tec hnique is the summation of one time p erio d
if the request arriv es when the empt y slot is missed and the duration of a sub cycle T p
g
gss
T
p
T
p
g
By comparing Eq with Eq it ma y app ear that GSS results in a higher latency than simple
Ho w ev er this is not necessarily true b ecause the duration of the time p erio d is dieren t with these
t w o tec hniques due to a c hoice of dieren t blo c k size This can be observ ed from Eq where the
duration of a time p erio d is a function of the blo c k size
T o compute the blo c k size with GSS w e rst compute the total duration of time con tributed to
seek times during a time period Assuming d
N
g
e blo c ks retriev ed during a sub cycle are distributed
uniformly across the disk surface the disk incurs a seek time of Seek cy l
N
g
bet w een ev ery t w o
consecutiv e blo c k retriev als This assumption maximizes the seek time according to the square ro ot
mo del pro viding the w orst case scenario Since N blo c ks are retriev ed during a time p erio d the
system incurs N seek times in addition to N blo c k retriev als during a p erio d ie T
p
NB
R
D
N Seek cy l g
N
By substituting T
p
from Eq and solving for Bw eobtain B
gss
R
C
R
D
R
D
N R
C
N Seek cy l g
N
By comparing Eq with Eq observ e that the b ound on the distance b et w een t w o blo c ks retriev ed
consecutiv ely is reduced b y a factor of
g
N
noting that g N Observethat g N sim ulates the simple tec hnique of Section By substituting g with N in
One Block
One
Region
X
X
X
X
XX
1
2
3
4
56
X 12 X
X
X
X
X
11
10
9
8
7
X 13
X 0
Figure REBECA
Eq it reduces to Eq Constrained Data Placemen t
An alternativ e approac h to reduce the w orst seek time is to con trol the placementofthe bloc ks across
the disk surface REBECA BMC GKS reduces the w orst seek time b y b ounding the distance
bet w een anyt w o blo c ks that are retriev ed consecutiv ely REBECA ac hiev es this b y partitioning the
disk space in to R regions Next successiv e blo c ks of an ob ject X are assigned to the regions in a
zigzag manner as sho wn in Figure The zigzag assignmen t follo ws the e cien t mo v emen t of disk
head as in the elev ator algorithm T eo T o displa y an ob ject the disk head mo v es inw ar d see
Figure un til it reac hes the innermost region and then it mo v es outw ar d This pro cedure rep eats
itself once the head reac hes the outmost region on the disk This minimizes the mo v emen t of the
disk head required to sim ultaneously retriev e N ob jects b ecause the displa y of eac h ob ject abides b y
the follo wing rules
The disk head mo v es in one direction either inw ar d or outw ar datatime F or a giv en time p erio d the disk services those displa ys that corresp ond to a single region
termed active r e gion R
activ e
Inward Movement
Outward Movement
5
Inward Movement
Outward Movement
R
R
R
R
R
R
0
1
2
3
4
Figure Disk head mo v emen t
In the next time p erio d the disk services requests corresp onding to either R
activ e
inw ar d
direction or R
activ e
outw ar d direction The only exception is when R
activ e
is either the
rst or the last region In these t w o cases R
activ e
is either incremen ted or decremen ted after
t w o time periods b ecause the consecutiv e blo c ks of an ob ject reside in the same region F or
example in Figure X
and X
are both allo cated to the last region and R
activ e
c hanges
its v alue after t w o time p erio ds This sc heduling paradigm do es not w aste disk space an
alternativ e assignmen tsc hedule that enables R
activ e
to c hange its v alue after ev ery time p erio d
w ould w aste of the space managed b y the rst and the last region Note that for t w o
regions ie R the ab o vesc heduling paradigm is not necessary and the blo c ks should b e
assigned in a roundrobin manner to the regions
Up on the arriv al of a request referencing ob ject X it is assigned to the region con taining X
sa y R
X
The displa y of X do es not start un til the activ e region reac hes X
R
activ e
R
X
and its
direction corresp onds to that required b y X F or example X requires an inw ar d direction if
X
is assigned to R
X
and outw ar d if R
X
con tains X
assuming that the organization
of regions on the disk is p er Figure T o compute the w orst seek time with REBECA note that the distance bet w een t w o blo c ks
retriev ed consecutiv ely is b ounded b y the length of a region
ie
cy l
R
Th us the w orst incurred
seek time b et w een t w o blo c k retriev als is Seek cy l
R
and T
p
NB
R
D
N Seek cy l
R
By substituting
This distance is b ounded by cy l
R
when the blo c ks b elong to t w o dieren t regions This only o ccurs for the last
blo c k retriev ed during time p erio d i and the rst blo c kretriev ed during time p erio d i T o simplify the discussions
w e eliminated this factor from the equations see GKS for precise equations Ho w ev er the precise equations w ere
emplo y ed b y the exp erimen ts of Section
T
p
from Eq w e solv e for B to obtain
B
rebeca
R
C
R
D
R
D
N R
C
N Seek cy l
R
By comparing Eq with Eq observ e that REBECA reduces the upp er bound on the distance
bet w een t wobloc ks retriev ed consecutiv ely b y a factor of
R
In tro ducing regions to reduce the seek time increases the a v erage latency observ ed b y a request
This is b ecause during eac h time p erio d the system can initiate the displa y of only those ob jects that
corresp ond to the activ e region and whose assignmen t direction corresp onds to that of the curren t
direction of the disk head T o illustrate this consider Figure In Figure a Y is stored starting
with R
while the assignmen tofboth X and Z starts with R
Assume that the system can supp ort
three sim ultaneous displa ys N Moreo v er assume a request arriv es at time T
referencing
ob ject X This causes region R
to become activ e No w if a request arriv es during T
referencing
ob ject Y it cannot b e serviced un til the third time p erio d ev en though su cien t disk bandwidth is
a v ailable see Figure b Its displa y is dela y ed b y t w o time p erio ds un til the disk head mo v es to
the region that con tains Y
R
In the w orst case assume a request arriv es referencing ob ject Z when R
activ e
R
both
the rst and the second blo c k of ob ject Z Z
and Z
are in region R
Z
R
and the head is
mo ving inw ar d and the request arriv es when the system has already missed the empt y slot in the
time p erio d corresp onding to R
to retriev e Hence R time p erio ds are required b efore the disk
head reac hes R
in orderto start servicing the request This is computed as the summation of
R time p erio ds un til the disk head mo v es from R
to the last region and R time periods un til
the disk head mo v es from the last region backto R
in the rev erse direction Hence the maxim um
startup latency is computed as
r ebeca
R T
p
if R T
p
if R
T
p
if R
An in teresting observationisthatthe computed startup latency in Eq do es not apply for
recording of live
ob jects That is if N sessions of m ultimedia ob jects are recorded liv e the transfer
of eac h stream from memory to the disk can start immediately This is b ecause the rst blo c kofan
ob ject X can be stored starting with an y region Hence it is p ossible to start its storage from the
Recording a liv e session is similar to taping a liv e fo otball game In this case a video camera or a compression
algorithm is the pro ducer and the disk driv e is the consumer
a. REBECA
XZ Z
XZ
X
X
X
X
0 01
1 2
2
3
4
5
Z
3
Z
4
Z
5
Z
6
Y 0
Y 1
Y 2
Y
3
b. Time Period Schedule
R
R
R
R
R
R
0
1
2
3
4
5
T
1
Second Time Period
X 0 X 1 X 2 Y 0
First Time Period
Figure Latency Time
activ e region ie R
activ e
R
X
In summary partitioning the disk space in to regions using REBECA is a tradeo bet w een
throughput and latency Alternativ e Data Placemen t T ec hniques
An alternativ e placemen t of data that minimizes the incurred latency b y increasing the amoun t of
required memory is as follo ws and y et another is describ ed in CBR This tec hnique is termed
Optimized REBECA OREO for short OREO assigns the blo c ks of an ob ject to the regions in a
roundrobin manner instead of a zigzag starting with an arbitrary region Similar to REBECA the
disk head mo v es from the outermost region to w ards the innermost one Only one region is activeat
a time In con trast to REBECA once the disk head reac hes the innermost region it is rep ositioned
to the outermost region to initiate another sw eep
With this paradigm the system observ es a long seek seekcyl ev ery R regions to rep osition
the head to the outermost cylinder T o comp ensate for this the system m ust ensure that after
ev ery R blo c k retriev als enough data has b een prefetc hed on b ehalf of eac h displa y to eclipse a dela y
equiv alen t to seekcyl There are sev eral w a ys of ac hieving this eect One migh t force the rst
blo c k along with ev ery R other blo c ks to b e sligh tly larger than the other blo c ks W e describ e OREO
based on a xsized blo c k approac h that renders all blo c ks to be equisized With this approac h
ev ery blo ckis padded so that after ev ery R blo c k retriev als the system has enough data to eclipse
the seekcyl dela y Th us the duration of a time p erio d is T
p
NB
R
D
N Seek cy l
R
S eek cy l R
By substituting T
p
from Eq w e solvefor B to obtain
B
or eo
R
C
R
D
R
D
N R
C
N Seek cy l
R
Seek cy l R
With OREO the maxim um startup latency is appro ximately half that of REBECA
or eo
R T
p
if R T
p
if R
T
p
if R
Disk Sc heduling Constrained Data Placemen t
In order to co v er a wide sp ectrum of applications GSS and OREO can be com bined Recall that
with OREO the placemen t of ob jects within a region is unconstrained Hence the distance b et w een
t wobloc ks retriev ed consecutiv ely is b ounded b y the length of a region Ho w ev er one can in tro duce
the concept of grouping the retriev al of blo c ks within a region In this case assuming a uniform
distribution of blo c ks across a region surface the distance bet w een ev ery t w o blo c ks retriev ed con
secutiv ely is b ounded b y
cy l g
NR
Hence T
p
NB
R
D
N Seek cy l g
NR
Seek cy l R
By substituting
T
p
from Eq w e solv e for B to obtain
B
combined
R
C
R
D
R
D
N R
C
N Seek cy l g
NR
Seek cy l R
Observ e that with OREOGSS b oth reduction factors of GSS and OREO are applied to the upp er
b ound on the distance bet w een an y t w o consecutiv ely retriev ed blo c ks compare Eq with both
Eqs and The maxim um startup latency observ ed with OREOGSS is iden tical to OREO when R see Eq When R its startup latency is iden tical to GSS
Memory Requiremen t
The tec hnique emplo y ed to manage memory impacts the amoun t of memory required to supp ort N
sim ultaneous displa ys A simple approac h to manage memory is to assign eac h user t w o dedicated
blo c ks of memory one for retriev al of data from disk to memory and the other for deliv ery of
data from memory to the displa y station T rivially the data is retriev ed in to one blo c k while it is
consumed from the other Subsequen tly the role of these t w o blo c ks is switc hed The amoun t of
memory required with this tec hnique is
M
unshar ed
N B
Note that B is dieren t for alternativ e displa y tec hniques B
gss
with GSS B
r ebeca
with REBECA
B
or eo
with OREO and B
combined
with OREOGSS
An alternativ e approac h termed c o arsegr ain memory sharing reduces the amoun t of required
memory b y sharing blo c ks among users It main tains a shared p o ol of free blo c ks Ev ery task either
retriev al or displa y task of an activ e request allo cates blo c ks from the shared p o ol on demand Once
a task has exhausted the con ten ts of a blo c k it frees the blo c kb y returning it to a shared p o ol As
describ ed in Section when compared with the simple approac h coarsegrain sharing results in
lo w er memory requirement aslongasthe system emplo ys GSS with the n um b er of groups g smaller
than N The highest degree of sharing is pro vided b y negr ain memory sharing With this tec hnique the
gran ularit y of memory allo cation is reduced to a memory page The size of a blo ckisa m ultiple of
the page size If P denotes the memory page size then B mPwhere m is a p ositivein teger The
system main tains a pool of memory pages instead of blo c ks with coarsegrain sharing and tasks
request and free pages instead of blo c ks
In the follo wing w e describ e the memory requiremen t of eac h displa y tec hnique with b oth ne
and coarsegrain sharing The memory requiremen t of the simple displa y tec hnique is eliminated
b ecause it is a sp ecial case of GSS g N and REBECA R
X1
Y1
X1
Y1
X1
Y1
Z1
W1
Z1
W1
Z1
W1
X2
Y2
X2
Y2
X2
Y2
Z2
W2
Z2
W2
Z2
W2
X3
Y3
X3
Y3
X3
Y3
Z3
W3
Z3
W3
Z3
W3
X4
Y4
X4
Y4
Z4
W4
...
a block
subcycle 1 subcycle 2
subcycle 1 subcycle 2 subcycle 1 subcycle 2
subcycle 1 subcycle 2
Time Period 1
Time Period 2 Time Period 3
Time Period 4
Figure Memory requiremen t p er sub cycle
CoarseGrain Sharing CGS
The total amoun t of memory required b y a displaytec hnique that emplo ys b oth GSS and coarsegrain
memory sharing is
M
coar se
N d
N
g
e B
T o supp ort N sim ultaneous displa ys the system emplo ys N blo c ks for N displa ys and d
N
g
e blo c ks
for data retriev al on b ehalf of the group that reads its blo c k from disk T o illustrate consider the
example of Figure where g and N F rom Eq this requires blo c ks of memory
see YCK for deriv ation of Eq This is b ecause the displayof X
and Y
completes at the
b eginning of sub cycle in the second time p erio d These blo c ks can be sw app ed out in fa v or of Z
and W
Note that the system w ould ha v e required blo c ks without coarsegrain sharing
REBECA OREO and OREO GSS can employEq This is b ecause the memory require
men t of REBECA is a sp ecial case of GSS where g N Ho w ev er the blo cksize B computed for
eac h approac h is dieren t B
gss
with GSS B
r ebeca
with REBECA B
or eo
with OREO and B
combined
with OREOGSS see Section for the computation of the blo c k size with eac h displa y tec hnique
FineGrain Sharing F GS
W e describ e the memory requiremen t of negrain sharing with a displa y tec hnique that emplo ys
GSS This discussion is applicable to REBECA OREO and OREO GSS
When compared with coarsegrain sharing negrain sharing reduces the amoun t of required
memory b ecause during a sub cycle the disk pro duces a p ortion of some blo c ks while the activ e
displa ys consume p ortions of other blo c ks With coarsegrain sharing a partially consumed blo c k
cannot be used un til it b ecomes completely empt y Ho w ev er with negrain sharing system frees
up pages of a blo c k that has b een partially displa y ed These pages can b e used b y other tasks that
read data from disk
Mo deling the amoun t of memory required with F GS is more complex than that with CGS While
it is p ossible to compute the precise amoun t of required memory with CGS this is no longer feasible
with F GS This is b ecause CGS frees blo c ks at the end of eac h sub cycle where the duration of a
sub cycle is xed Ho w ev er F GS frees pages during a sub cycle and it is not feasible to determine
when the retriev al of a blo c k ends within a sub cycle b ecause the incurred seek times in a group are
unpredictable Therefore w e mo del the memory requiremen t within a sub cycle for the w orst case
scenario
Let t denote the time required to retriev e all the blo c ks in a group Theoretically t can be a
v alue bet w een and the duration of a sub cycle ie t T p
g
W e rst compute the memory
requiremen t as a function of t and then discuss the practical v alue of t W e in tro duce t to generate
another end poin t b eside the end of a sub cycle where the memory requiremen t can be mo deled
accurately The k ey observ ation is that bet w een t and the end of sub cycle nothing is pro duced on
b ehalf of a group while displa y of requests in a sub cycle con tin ues at a xed rate of R
C
Hence
w e mo del the memory requiremen t for the w orst case where all the blo c ks are pro duced in order to
eliminate the problem of unpredictabilit yof eachbloc k retriev al time in a sub cycle Assuming S
i
is
the end of sub cycle i the maxim um amoun t of memory required b y a group is at S
i
t b ecause the
maxim um amoun t of data is pro duced and the minim um amoun t is consumed at this p oin t Observ e
that at a p oin t x where S
i
tx S
i data is only consumed reducing the amoun t of required
memory Moreo v er at a p oin t y where S
i
y S
i
t data is still b eing pro duced
The n um b er of pages pro duced required during t is
pr oduced d
N
g
e m
The n um b er of pages consumed released during t is
consumed b
t N m
T
p
c
This is b ecause the amoun t of data consumed during a time period is N m pages and hence the
amoun t consumed during t is
t
T p
of N m pages W e use o or function for consumption and ceiling
function for the pro duction b ecause the gran ularit y of memory allo cation is in pages Hence neither
a partially consumed page o or function nor a partially pro duced page ceiling function is a v ailable
on the free list Moreo v er m is inside the o or function b ecause the unit of consumption is in n um ber
N
g
m prod =
N
g
m prod =
N
g
m prod =
cons = 0
N
g
m
g
1
cons =
2N
g
m
g
1
cons =
N
g
m prod =
3N
g
m
g
1
cons =
N
g
m prod =
N
g
m
g
1
cons =
(g-1)
consume what is produced
Time Period j
subcycle 1
subcycle g
. . .
. . .
Figure Memory requiremen t of the j th time p erio d
of pages while it is outside the ceiling function b ecause the unit of pro duction is in blo c ks
One migh t argue that the amoun t of required memory is the dierence b et w een the v olume of data
pro duced and consumed This is an optimistic view that assumes ev erything pro duced b efore S
i
has
already b een consumed Ho w ev er in the w orst case all the N displa ys migh t start sim ultaneously at
time p erio d j T
p
j Hence the amoun t of data pro duced during T
p
j is higher than the amoun t
consumed This is b ecause the pro duction starts during the rst sub cycle of T
p
j while consumption
starts at the b eginning of the second sub cycle It is su cien t to compute this remainder rem and
add it to pr oduced consumed in order to compute the total memory requiremen t b ecause all the
pro duced data is consumed after T
p
j T o compute rem Figure divides T
p
j in to g sub cycles and demonstrates the amoun t of pro
duced and consumed data during eac h sub cycle The total amoun t that is pro duced during eac h
time period is N m pages During the rst sub cycle there is nothing to consume F or the other
g sub cycles
g
of what ha v e b een pro duced can b e consumed Hence from the gure the total
consumption during T
p
jis
N m
g
g
g By substituting g with
g g
rem can b e computed as
rem N m N m g
g
The total memory requirementis pr oduced consumed remor M
f ine
N m N
g
m tN m
T
p
N m g
g
Note that Eq is an appro ximation b ecause w e eliminated the f l oor and ceil ing functions from
the equation F or large v alues of m the appro ximation is almost iden tical to the actual computation
In the ev aluation section Section our exp erimen ts emplo ys the precise equations using the floor
and ceil ing functions An in teresting observ ation is that if the size of a page is equal to the size
of a blo c k then Eq can be reduced to Eq This is because the last t w o terms in Eq corresp ond to the n um ber of pages released during t and the rst time period resp ectiv ely Since
with coarsegrain no pages is released during these t w o p erio ds the last t w o terms of Eq b ecome
zero pro ducing Eq The minim um v alue of t is computed when all the d
N
g
e blo c ks are placed con tiguously on the disk
surface The time required to retriev e them is the practical minim um v alue of t and is computed as
t
pr actical
d
N
g
e
B
R
D
The n um b er of groups g impacts the memory requiremen t with b oth coarse and negrain sharing
in t wow a ys First as one increases g the memory requiremen t of the system decreases b ecause the
n um ber of blo c ks staged in memory is d
N
g
e On the other hand this results in a larger blo c k size
in order to supp ort the desired n um ber of users resulting in higher memory requiremen t Th us
increasing g migh t result in either a higher or a lo w er memory requiremen ts YCK suggests an
exhaustiv e searc h tec hnique to determine the optimal v alue of g g N in order to minimize
the en tire memory requiremen t for a giv en N An implemen tation of F GS b ey ond the fo cus of this pap er m ust address ho w the memory is
managed This is b ecause memory migh t become fragmen ted when pages of a blo c k are allo cated
and freed incremen tally With fragmen ted memory either the disk in terface should b e able to read
ablockin to m disjoin t pages or the memory manager m ust bring m consecutiv e pages together to
pro vide the disk manage with m ph ysically con tiguous pages to read a blo ckin to The rst approac h
w ould compromise the p ortabilit y of the nal system because it en tails mo dications to the disk
in terface With the second approac h one ma y implemen t either a detectiv e or prev en tiv e memory
manager A detectiv e memory manager w aits un til memory b ecomes fragmen ted b efore reorganizing
memory to eliminate this fragmen tation A prev en tiv e memory manager a v oids the p ossibilit y of
memory fragmen tation b y con trolling ho w the pages are allo cated and freed When compared with
eac h other the detectiv e approac h requires more memory than the prev en tiv e one and w ould almost
certainly require more memory than the equations deriv ed in this section Ho w ev er the prev en tiv e
approachw ould most lik ely incur a higher CPU o v erhead b ecause it c hec ks the state of memory p er
page allo cationrelease
Conguration Planner
Alternativ e applications ha v e dieren t p erformance ob jectiv es One application migh t prefer to trade
memory for a lo w er startup latency while the other migh t tolerate a high latency as long as the cost
of the system is lo w This motiv ates the need for a conguration planner that manipulates the
system parameters R and g to satisfy the p erformance ob jectiv es of a target application The
conguration planner for REBECA and GSS w ere describ ed in GKS YCK A conguration
planner for OREOGSS can be generated b y com bining the t w o planners of OREO
and GSS In
this section w e describ e one approachtocom bine these t w o planners
The inputs to the planner include the amountof a v ailable memory M
av ail abl e
the c haracteristics
of an application eg R
C
its p erformance ob jectiv es and the ph ysical attributes of the target disk
driv e The p erformance ob jectiv es of the application include its desired startup latency desir ed
and throughput N
desir ed
The ph ysical attributes of a disk include R
D
seek c haracteristics and
rotational latency The outputs of the planner are the v alue of R and g that satisfy the p erformance
ob jectiv es while resp ecting the a v ailable memory The planner consists of t w o stages
During the rst stage it xes N at N
desir ed
and iterates o v er
R R R
max
F or eac h
v alue of Rit v aries g from to N Subsequen tly it computes B
combined
T
p
and M
coar se
M
f ine
emplo ying Eqs and resp ectiv ely F or eachv alue of R the planner migh t generate N
quadruples of RiM
i
i
where M
i
and i
are the memory requiremen t and latency computed
for a system with R regions and i groups i N The planner do es not pro duce a quadruple
for those R v alues that supp ort few er than N
desir ed
displa ys
The list of quadruples pro duced during stage one supp orts the n um b er of sim ultaneous displa ys
designed b y the target application During the second stage the planner exhaustiv ely searc hes this
list with a maxim um of N R
max
elemen ts to nd a quadruple Q RgM satisfying the
follo wing conditions
desir ed
M
av ail abl e
M
If more than one quadruple satisfy the ab o v e conditions then the one with the minim um M is
selected If no quadruple satises the ab o v e condition the user should mo dify the input parameters
and rein v ok e the planner to obtain the desired p erformance ob jectiv e Alternativ e strategies can
be dev elop ed for the second step F or example the user can only pro vide desir ed
or M
av ail abl e
and
the planner output the quadruple with the lo w est v alue of M or that satises desir ed
or
It is trivial to mo dify the conguration planner of REBECA in supp ort of OREO
The upp er b ound of R is when the length of a region b ecomes so small that the time to scan a region b e iden tical
to the minim um disk seek time see GKS
Minim um T ransfer Rate R
D
Mbs
Minim um Seek Time trac ktotrac k msec
Maxim um Seek Time msec
Rotation Time msec
Av erage Rotational Latency msec
T able Disk parameters used in the exp erimen ts Seagate STW
M
av ail abl e
M
P erformance Ev aluation
T o conrm our analytical mo dels w e p erformed some exp erimen ts with a single disk driv e The
disk parameters used in these exp erimen ts are summarized in T able Sea T o simplify the
exp erimen ts a linear seek mo del based on the minim um and maxim um seek times w as used
The
a v erage rotational latency time msec w as added to ev ery seek time W e assumed the database
consists of MPEG video ob jects with a consumption rate of Mbs R
C
Mbs Hence the
theoretical upp erb ound for N is
R
D
R
C
In computing the memory requiremen t of the system
w e assume that a blo ckis a m ultiple of disk sectors b yte disk sector
Wev eried our exp erimen tal mo del of GSS b y p erforming exp erimen ts using the disk c haracter
istics and consumption rate rep orted in YCK The obtained results w ere iden tical with those
rep orted in YCK v erifying the accuracy of our mo del The exp erimen tal results presen ted for
GSS are based on an optimal v alue for g the n um b er of groups that maximizes the p erformance of
a system for a giv en page size and desired throughput
First w e compared the memory requiremen t and the maxim um startup latency of REBECA
with those of OREO b y emplo ying coarsegrain memory sharing T able While OREO increases
the memory requirementofdispla ys b y less than when compared with REBECA it reduces the
observ ed startup latency b y almost one half Next w e compared the memory requiremen t and the
maxim um startup latency of GSS with those of OREO b y emplo ying coarsegrain memory sharing
T able GSS is sup erior to OREO when R As the n um b er of regions R increases OREO
results in a lo w er memory requiremen t and a higher startup latency when compared with GSS
Similar trends w ere observ ed when w e emplo y ed negrain memory sharing
W e also compared the memory requiremen t and the maxim um startup latency of GSS with those
of OREOGSS using coarsegrain memory sharing T able OREOGSS sim ulates GSS when
Nonlinear seek mo del suc h as the mo dels prop osed in R W could b e applied for the real implemen tation
Num ber Memory RequirementMB Startup Latency Time sec
of REBECA OREO REBECA OREO
Users R R R R R R R R R R R R
T able REBECA vs OREO with coarsegrain sharing
Num ber Memory RequirementMB Startup Latency Time sec
of GSS OREO GSS OREO
Users R R R R R R
T able GSS vs OREO with coarsegrain sharing
Num ber Memory RequirementMB Startup Latency Time sec
of GSS OREOGSS GSS OREOGSS
Users R R R R R R
T able GSS vs OREOGSS with coarsegrain sharing
Num ber Memory Requiremen t MB Startup Latency Time sec
of Coarse Fine Coarse Fine
Users R R R R R R R R R R R R
T able Coarsegrain vs negrain with OREOGSS
congured with a single region R As w e increase the n um ber of regions with OREOGSS
its memory requiremen t decreases and the maxim um startup latency increases F or example when
R OREOGSS reduces the total memory requirementof sim ultaneous displa ys from to MB for N a sa ving in memory as compared to GSS Ho w ev er the maxim um
startup latency is increased from to seconds a factor of increase V arying the n um ber
of regions with OREOGSS is a tradeo b et w een memory requiremen t and startup latency Th us
OREOGSS pro vides a wider range of conguration c hoices including those of GSS
The sa vings in memory also impact the throughput of the system If the amoun t of a v ailable
memory is xed OREOGSS ma y result in a higher throughput than GSS In T able when the
a v ailable memory for an application is xed at MB the maxim um throughput with OREOGSS
with R is while GSS supp orts displa ys
Next w ein v estigated the memory requiremen t and the maxim um startup latency of OREOGSS
with both coarsegrain and negrain memory sharing The size of a page with negrain memory
sharing w as P b ytes T able demonstrates that negrain memory sharing results in far
less memory requiremen t and sligh tly higher startup latency as compared to those of coarsegrain
memory sharing F or example when R the memory requiremen t for sim ultaneous displa ys
decreases from to MB sa vings with negrain sharing Similar sa vings in memory
requiremen t w ere observ ed with both OREO and GSS Note that the startup latency of negrain
sharing do es not matc h that of coarsegrain sharing in some cases This is b ecause the startup
latency is a function of the duration of time p erio d and the n um b er of groups The n um b er of groups
ha ving the minim um memory requiremen t with coarsegrain sharing could b e dieren t from that of
negrain sharing due to the dierence in computing the memory requiremen ts
Toin v estigate the impact of the page size on the memory requiremen t and the maxim um startup
latency of a system using negrain sharing w e p erformed exp erimen ts with three dieren t page
Num ber Memory RequirementMB Startup Latency Time sec
of Users P KB P KB P KB P KB P KB P KB
T able Impact of the page size with negrain in OREOGSS
Num ber Memory RequirementMB Startup Latency Time sec
of GSS OREOGSS GSS OREOGSS
Users R R R R
T able GSS vs OREOGSS with coarsegrain sharing no rotational latency time sizes and KB T able presen ts the memory requiremen t and the maxim um startup latency
of OREOGSS with R for v ariet y of page sizes As the page size increases the memory
requiremen t and the maxim um startup latency increases Ho w ev er the increase is small in the high
throughput range b ecause a page is m uc h smaller than a blo c k
Some disks utilize a cac he to reduce rotational latencies using onarriv al readahead R W In
the best case the rotational latency is reduced to zero All the previous observ ations remain v alid
with these disks except that reducing the seek time has a more signican t impact on the memory
requirementofthe system T able demonstrates the memory requiremen t and the maxim um startup
latency of GSS and OREOGSS assuming a zero rotational latency When R the total memory
requiremen t to supp ort sim ultaneous displa ys is reduced from with GSS to MB with
OREOGSS sa ving Note that w e observ ed only a sa ving in memory with the a v erage
rotational latency T able
X
d
0
0.0
X
3.0
...
X
d
1
0.1
X
3.1
...
X
d
2
1.0
X
4.0
...
X
d
3
1.1
X
4.1
...
X
d
4
2.0
X
5.0
...
X
d
5
2.1
X
5.1
...
CC C
0
1
2
Figure Three clusters with one region p er cluster
Multidisk Arc hitectures
The bandwidth of a single disk is insu cien t for those applications that striv e to supp ort thousands
of sim ultaneous displa ys One ma y employa m ultidisk arc hitecture for these applications Assuming
a system with D homogeneous disks the data is strip ed BGMJ GKb GKa across the disks
in order to distribute the load of a displayev enly across the disks Striping realizes a scalable serv er
that can scale as a function of additional resources The striping tec hnique is as follo ws First w e
partition the disks in to k disk clusters eac h with d disks k d
D
d
e With eachobject X partitioned
in to n blo c ks X
X
X
n w e assign the blo c ks of X to the disk clusters in a roundrobin
manner starting with an arbitrarily c hosen disk cluster Eachbloc k of X is declustered GRA Q in to d fragmen ts with eac h fragmen t assigned to a dieren t disk in a disk cluster F or example in
Figure a system consisting of six disks is partitioned in to three disk clusters eac h consisting of
t w o disks The assignmen t of X starts with disk cluster zero C
This blo c k is declustered in to
t w o fragmen ts X
and X
When a request references ob ject X the system emplo ys an idle slot
on the disk cluster that con tains X
sa y C
i
to retriev e and displa y its rst blo c k During the next
time period the system emplo ys disk cluster C
i mod k
to retriev e and displa y X
This pro cess
is similar to the discussion of Section except that a displa y visits the clusters in a roundrobin
manner utilizing a slot p er time p erio d on eac h cluster to retriev e blo c ks of X GSS has no impact
on the placemen t of data During eac h time p erio d the disks that constitute a cluster are activ ated
to read the referenced fragmen ts Eac h disk emplo ys GSS to minimize the impact of seeks
Both REBECA and OREO in tro duce regions on the individual disks In this section w e fo cus
on the placemen t of data with OREO The extension of this discussion for REBECA is trivial
OREO treats the d disks of a cluster as a single disk with the aggregate transfer rate of d disks It
constructs R equisized regions on eac h disk cluster The rst blo c k of an ob ject X is assigned to an
arbitrarily c hosen disk cluster and region sa y region R
j
of disk cluster C
i
The remaining blo c ks
X
d
0
0.0
X
3.0
X
d
1
0.1
X
3.1
X
d
2
1.0
X
4.0
X
d
3
1.1
X
4.1
X
d
4
2.0
...
X
d
5
2.1
...
CC C
0
1
2
R
0
R
1
...
...
... ...
...
...
... ...
... ...
Figure Three clusters with t w o regions p er cluster
of X are assigned to the regions and disk clusters in a roundrobin manner Blo c k X
is assigned
to region R
j mod R
of disk cluster C
i mod k
Within a cluster the fragmen ts of a blo c k are
assigned to the same region of d disks that constitute a cluster Figure sho ws the assignmentof X
to a three cluster system where eac h cluster consists of t w o regions One region of all disks is activ e
p er time p erio d T o displayobject X the system m ust w ait un til region of disk cluster C
b ecomes
activ e If an idle time slot exists for this cluster the system emplo ys the idle slot to retriev e X
During the next time p erio d the system retriev e X
from region of disk cluster C
This pro cess
is rep eated un til all blo c ks of ob ject X ha v e b een retriev ed and displa y ed
This assignmen t and displa y paradigm striv es to distribute the load of a displayev enly across the
regions of dieren t disk clusters Ho w ev er ev en with this assignmen t strategy a single disk cluster
of a thousand disk cluster system migh t become a b ottlenec k dep ending on the n um ber of regions
R the n um ber of disk clusters k the placemen t of data and the order of arriv al for requests
This is best describ ed with an example Consider the system depicted in Figure It consists of
three disk cluster eac h congured with three regions Assume that eac h cluster can supp ort four
blo c k retriev als per time p erio d Th us the theoretical n um ber of sim ultaneous displa ys supp orted
bythe system is t w elv e If the assignmentofthe rst blo c k of eac h ob ject starts with region R
of
disk cluster C
then the en tire system can supp ort only four sim ultaneous displa ys and the storage
capacit y of the system is equiv alen t to that of a single cluster This is b ecause no blo c ks are assigned
to regions R
and R
of cluster C
regions R
and R
of cluster C
and regions R
and R
of
cluster C
F or an y giv en time p erio d only one region is activ e with a single cluster pro ducing data
It is in teresting to note that there can b e m ultiple b ottlenec k clusters In our example if the system
consists of six disk clusters then there w ould b e t w o b ottlenec k clusters at an y giv en p oin t in time
supp orting only eightsim ultaneous displa ys
In these examples the probabilit y of formation of b ottlenec ks is with more than four
X
d
0
0.0
X 3.0
d
1 d
2
d
3 d
4
...
d
5
CC C
0
1
2
R
0
R
1
X
0.1
X
3.1
X
1.0
X
4.0
X
1.1
X
4.1
X
2.0
X 5.0
X
2.1
X
5.1
R
2
...
...
...
...
...
Figure Three clusters with three regions p er cluster
Maxim um Memory RequirementMB Startup Latency Time sec
d Throughput GSS OREOGSS GSS OREOGSS
R R R R R R
T able GSS vs OREOGSS b yv arying cluster size
activ e requests b ecause the placemen t of data starts with a single region and disk cluster One ma y
minimize this probabilityb y assigning the blo c ks of eac h ob ject starting with a random cluster and
region Ho w ev er the system con tin ues to run the p ossibilityof formation of b ottlenec ks as long as
either the n um b er of clusters kis a m ultiple of regions Rwith
k
R
clusters b ecoming b ottlenec ks
or the n um b er of regions Ris a m ultiple of the n um b er of disk clusters k with a single cluster
b ecoming the b ottlenec k One approachto prev en t the formation of b ottlenec ks is to a v oid system
congurations where either k is a m ultiple of R or R is a m ultiple of k W e analyzed GSS and OREOGSS as a function of the n um b er of disks that constitute a cluster
d The obtained results are presen ted in T able This table also con tains b oth the p ercen tage
reduction in memory and the p ercen tage increase in startup latency with OREOGSS relativ e
to GSS The rst observ ation to be made from this table is that while the throughput of a cluster
increases linearly as a function of d the amoun t of required memory and the incurred startup latency
increase sup erlinearly Moreo v er it ma y not be p ossible to realize congurations with large v alues
of d in practice F or example to supp ort users with d the system requires a blo c k size
of gigab yte a total of terab yte of memory and a hour maxim um startup latency These
observ ations w ere made b y TPBG GKb and not rep eated here The primary reason for
presen ting these results is to sho w the p ercen tage sa vings in memory pro vided b y OREOGSS
relativ e to GSS diminishes as the v alue of d increases and the p ercen tage increase in startup
latency pro vided b y OREOGSS relativ e to GSS increases as a function of d Ho w ev er note that it
ma y not b e practical to supp ort a cluster consisting of man y disks
F or a xed cluster size xed v alue of d as one increases the n um ber of disk clusters k the
throughput maxim um startup latency and the amoun t of memory required b y GSS and OREOGSS
increase linearly as long as there are no b ottlenec ks
Th us b oth the p ercen tage sa vings in memory
and percen tage increase in maxim um startup latency pro vided b y OREOGSS relativ e to GSS
remains unc hanged as a function of k Conclusion and F uture Directions
This study quan ties the tradeos asso ciated with t w o alternativ e tec hniques to maximize the
throughput of video serv ers that emplo y magnetic disks for mass storage The rst con trols the
disk sc heduling tec hnique while the second con trols the placemen t of data across the disk surface
These t w o tec hniques are orthogonal to one another and are com bined in to one displa y tec hnique
W e quan tied the memory requiremen t of these tec hniques with b oth a coarsegrain and negrain
memory sharing tec hnique When compared with coarsegrain sharing the analytical mo dels for
negrain memory sharing suggest that they pro vide signican t sa ving in the amoun t of required
memory Presen tlyw e are implemen ting a serv er using a cluster of w orkstations This study is our initial
eort to understand the tradeos asso ciated with alternativetec hniques prior to their implemen ta
tion These tec hniques can b e extended in sev eral w a ys First the fo cus of these tec hniques has b een
on constan tbit rate video ob jects With v ariable bit rate video the system m ust pro duce dieren t
amoun t of data at dieren tpoin ts in time to ensure a con tin uous displa y Second the conguration
planner considers the p erformance ob jectiv es of a single application when conguring a system The
design of this planner b ecomes complicated if the system striv es to strik e a compromise b et w een the
conicting requiremen ts of sev eral applications
k is not a m ultiple of R and R is not a m ultiple of k
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Abstract (if available)
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Description
Shahram Ghandeharizadeh, Seon Ho Kim, Cyrus Shahabi. "On disk scheduling and data placement for video servers." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 650 (1997).
Asset Metadata
Creator
Ghandeharizadeh, Shahram
(author),
Kim, Seon Ho
(author),
Shahabi, Cyrus
(author)
Core Title
USC Computer Science Technical Reports, no. 650 (1997)
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On disk scheduling and data placement for video servers (
title
)
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