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USC Computer Science Technical Reports, no. 590 (1994)

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USC Computer Science Technical Reports, no. 590 (1994)

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Content On Conguring a Single Disk Con tin uous Media Serv er
Shahram Ghandeharizadeh Seon Ho Kim and Cyrus Shahabi
Departmen t of Computer Science
Univ ersit y of Southern California
Los Angeles California No v em ber Abstract
The past decade has witnessed a proliferation of rep ositories that store and retriev e con tin uous
media data t yp es eg audio and video ob jects These rep ositories are exp ected to pla y a ma jor
role in sev eral emerging applications eg library information systems educational applications
en tertainmen t industry etc T o supp ort the displa y of a video ob ject the system partitions
eachobjectin to xed size blo c ks All blo c ks of an ob ject reside p ermanen tly on the disk driv e
When displa ying an ob ject the system stages the blo c ks of the ob ject in to memory one at a
time for immedia te displa y In the presence of m ultiple displa ys referencing dieren t ob jects the
bandwidth of the disk driveism ultiplexed among requests This in tro duces disk seeks that reduce
the useful utilization of the disk bandwidth resulting in a lo w er n um ber of sim ultaneous displa ys
throughput
This pap er c haracterizes the impact of disk seeks on the throughput of the system It de
scrib es REBECA as a mec hanism that maximi zes the throughput of the system byminim izing
the amoun t of time attributed to eac h incurred seek A limitati on of REBECA is that it increases
the latency observ ed byeac h request W e quan tify this throughput vs latency tradeo of RE
BECA and dev elop an ecien ttec hnique that computes its conguration parameters to realize
the p erformance requiremen ts desired latency and throughput of an application
In tro duction
During the past decade the information tec hnology has ev olv ed to where it is economically viable to
store and retrievecon tin uous media MWS data t yp es eg audio and video ob jects The ob jects
of this data t yp e in particular video are large in size Moreo v er they are t ypically retriev ed in a
sequen tial manner F or example a hour MPEG compressed video ob ject is appro ximately Gigab ytes in size In a videoondemand application a clien t retriev es and displa ys an ob ject in a
sequen tial manner
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

T o supp ort a con tin uous displa y of a video ob ject sa y X sev eral studies P ol TPBG CL BGMJ NY ha v e prop osed to strip e X in to n equisized blo c ks X
X
X
n
Both
the displa y time of a blo c k and its transfer time from the disk are a xed function of the displa y
requiremen ts of an ob ject and the transfer rate of the disk resp ectiv ely Using this information the
system stages a blo ckof X sa y X
from the disk in to main memory and initiates its displa yIt
sc hedules the disk driveto read X
in to memory prior to completion of the displa y time of X
This
ensures a smo oth transition b et w een the t wobloc ks in order to supp ort a con tin uous displa y This
pro cess is rep eated un til all blo c ks of X ha v e b een retriev ed and displa y ed
Note that the displa y time of a blo c k is signican tly longer than its transfer time from the
disk driv e assuming a compressed video ob ject Th us the disk driv ecan be m ultiplexed among
sev eral displa ys referencing dieren t ob jects Ho w ev er magnetic disk driv es are mec hanical devices
Multiplexing it among sev eral displa ys causes it to p erform seeks The seek time is a function of the
distance tra v eled b y the disk arm BG GHW R W Moreo v er seek is a w asteful op eration
that minimizes the n umberofsim ultaneous displa ys supp orted b y the system The disk p erforms
useful w ork when it transfers data
This study in tro duces REBECA as a mec hanism that reduces the time attributed to a seek
op eration b y minimizing the distance that the disk head tra v els when m ultiplexed among sev eral
requests This results in a higher utilization of the disk bandwidth pro viding for a higher n um ber
of sim ultaneous displa ys ie throughput Ho w ev er REBECA increases the latency time incurred
b y a request ie time elapsed from when the request arriv es un til the onset of its displa y The
conguration parameters of REBECA can b e ne tuned to strik e a compromise b et w een a desired
throughput and a tolerable latency time
T rading latency time for a higher throughput is dep enden t on the requiremen ts of the target
application As illustrated b y the rst column of T able the throughput of a single disk serv er
with four megab ytes of memory ma yv ary from to sim ultaneous displa ys using REBECA
This causes the maxim um latency time to increase from a fraction of a second to seconds
see the second column of T able A vide oondemand serv er ma y exp ect to ha vesim ultaneous
displa ys as its maxim um load with eac h displa y lasting t w o hours Without REBECA the disk driv e
supp orts a maxim um of sim ultaneous displa ys eac h observing a fraction of a second latency During p eak system loads activ e requests sev eral requests mayw ait in a queue un til one of the
activ e requests completes its displa y These requests observ e a latency time signican tly longer than
a fraction of second p oten tially in the range of hours dep ending on the status of the activ e displa ys
and the queue of p ending requests In this scenario it migh t b e reasonable to force eac h request to
observeaw orst case latency of seconds in order to supp ort sim ultaneous displa ys

T erm Denition
R
D
Disk bandwidth Pro duction rate in Mbps
cy l Num b er of cylinders in a disk driv e
T
w seek
W orst seek time of a disk driv e in seconds
including the maxim um rotational latency time
R Num b er of regions a disk driv e is partitioned to
B Size of a blo c k in Mbits
b Numberofbloc ks p er region
R
C
Displa y bandwidth requiremen t Consumption rate in Mbps
n Numberofbloc ks of an ob ject X d
siz e X B
e
Mem Pro vided amoun t of memory in Mbits
T
p
Time p erio d in seconds
N Maxim um n umberofsim ultaneous displa ys throughput
N
desir ed
Desired throughput
Maxim um latency time in seconds
desir ed
Maxim um desired latency time in seconds
T able List of terms used rep eatedly in this pap er and their resp ectiv e denitions
Alternativ ely with an application that pro vides a news on demand service with a t ypical news
clip lasting appro ximately four min utes a second latency time migh t not b e a reasonable tradeo
for a higher n um ber of sim ultaneous displa ys In this case the system designer migh t decide to
in tro duce more resources eg memory in to the en vironmen t to enable the system to supp ort a
higher n um ber of sim ultaneous displa ys with eac h request incurring a fraction of a second latency
time This study pro vides a mec hanism to compute a v alue for the conguration parameters of a
system in order to satisfy the p erformance ob jectiv es of an application Hence a service pro vider
can congure its serv er based on b oth its exp ected n um ber of activ e customers as w ell as the w aiting
tolerance of its customers
Ov erview
In this pap er w emak e the follo wing simplifying assumptions
The system is congured with a xed amoun t of memory and a single disk driv e The disk
driv e has a constan t bandwidth R
D
and pro vides a large storage capacit y more than one
gigab yte An example disk driv e from the commercial arena is Seagate Barracuda HP
that pro vides a Gigab yte storage capacit y and a minim um transfer rate of Megabits p er
second Mbps Sea A single media t yp e with a xed displa y bandwidth R
C
R
D
R
C

A m ultiuser en vironmen t requiring sim ultaneous displa y of ob jects to dieren t users
F or the rest of this section rst w e describ e ho w the displayof con tin uous media is supp orted in
our target platform Next a brief o v erview of REBECA is pro vided
Displayof Con tin uous Media
W e use the design prop osed b y b oth CL and P ol to ensure con tin uous displayof N m ultimedia
ob jects satisfying N sim ultaneous requests Ho w ev er there are dierences b et w een the original
design and its summary as presen ted here First CL assumes an unpredictable seek time b et w een
the retriev al of anyt w o blo c ks ranging in v alue from the minim um to the maxim um latency time
Therefore it computes an a v erage seek time and b ounds the p ossibilit y of observing a seek time
higher than the a v erage byemplo ying a probabilistic approac h Con v ersely this study guaran tees
a con tin uous displayof N m ultimedia ob jects b y imp osing an upp er b ound on the w orst seek time
T
w seek
F or no w assume T
wseek
is the maxim um p ossible seek time for a disk
Moreo v er a
maxim um r otational latency time is added to this v alue to compute the total disk access time Since
this is a constan t added to ev ery seek time w e will not discuss it an y further Hence whenev er
w e talk ab out seek time w e assume that it incorp orates a xed maxim um rotational latency time
Second w e assume that the consumption rate is xed This assumption is relaxed in Section Figure demonstrates the con tin uous displayof N ob jects Eac hm ultimedia ob ject is strip ed
in to n equisized blo c ks X
X
X
n
where n is a function of the blo c k size and the size of X
see T able A time p erio d T
p
is dened as the time required to displa y a blo c k
T
p
B
R
C

where B is the blo cksizeand R
C
is the consumption rate required to supp ort a con tin uous displa y F or example a blo c k size of Kb ytes corresp onding to a MPEG compressed mo vie R
C
Mbps has a second displa y time T
p
Assuming a t ypical magnetic disk with a transfer rate
of Mbps R
D
Mbps and maxim um seek time of milliseconds suc h blo c ks can b e
retriev ed in seconds The system o v erlaps the sequen tial retriev al of these blo c ks of dieren t
ob jects with the parallel displa y of their previously retriev ed blo c ks Hence a single disk supp orts
sim ultaneous displa ys
In Figure eac hbo x represen ts the retriev al of a blo c k of an ob ject The disk incurs a seek ev ery
time it switc hes from one blo c k to the other T o displa y N sim ultaneous blo c ks p er time p erio d the
Later w e demonstrate ho w T wseek is reduced using REBECA
Note that w e are not ignoring this dela y instead it is not emphasized Its impact is c haracterized in Section
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
wseek
Time Period (Tp)
Z
k
Z
k
Figure Time P erio d
system should pro vide sucien t memory for staging the blo c ks In the w orst case N sim ultaneous
displa ys requires N B memory in bits
Hence if Mem denotes the amoun t of congured memory
for a system then the follo wing constraintm ust b e satised
N B Mem
T o compute the size of a blo c k from Figure it is trivial that
B
T
p
N
T
w seek
R
D

By substituting B from Equation in to Equation w e obtain
T
p
N T
w seek
R
D
R
D
N R
C

Ov erview of REBECA
This study in tro duces a REgion BasEd bloCk Allo cation REBECA mec hanism that reduces T
w seek
b y partitioning the disk space in to R regions and forcing the system to retriev e the blo c k
of N activ e requests from a single region By reducing the w orst seek time some of the disk
bandwidth is freed to retriev e additional blo c ks per time period pro viding for a higher n um ber of
sim ultaneous displa ys throughput Ho w ev er with a xed amoun tofmemory the latency increases
In order to simplify the discussion w e assumed no pip elini ng or ecien t metho d to minimize the memory require
men ts Ho w ev er it is imp ortan t to note that our design can b e extended with these tec hniques in order to minimize
the memory requiremen ts

as the n um b er of regions R is increased Hence this study pro vides a metho d to determine a
v alue for the conguration parameters of a single disk m ultimedia serv er to realize a presp ecied
throughput and latency time requiremen t
The inputs to the conguration planner are the ph ysical attributes of the hardw are platform
and the c haracteristics of the target application disk c haracteristic suc h as its bandwidth seek
c haracteristic and n um b er of cylinders memory size media displa y bandwidth consumption
rate R
C
and the desired throughput and latency time While throughput is dened as the
numb er of simultane ous displays p er time p erio d N the latency time is dened as the amoun t
of time a request w aits b efore the displa y of its referenced ob ject b egins elapsed time from the
arriv al of a request to the onset of displa y
The output of the conguration mec hanism is the blo c ksize B and the n um b er of regions
R for the desired latency and throughput desir ed
and N
desir ed
resp ectiv ely If there is no suc h B
and R that results in the desired latency and throughput the user has t w o p ossible c hoices either sacrice one in fa v or of the other or mo dify the ph ysical attributes of the hardw are eg a v ailable
memory and rein v ok e the conguration mec hanism
A naiv e conguration mec hanism ma y p erform an exhaustivesearc h on all the plausible v alues
of R to generate a list of N B R quadruples whic h is subsequen tly searc hed to compute the
quadruple that satises the follo wing
N
desir ed
N
desir ed

Increasing the v alue of R ma y increase the latency time signican tly without impro ving the
throughput N b ecause the v alue of N is an in teger Hence the impro v ed v ersion of the conguration
mec hanism searc hes the space b y iterating o v er N instead of RT oac hiev e this the p ossible v alues
of N should b e b ounded The lo w er b ound on N termed N
min
is computed when R The
upp er b ound for throughput is N
max
b
R
D
R
C
c The idea b ehind the conguration mec hanism can b e summarized as in Figure The y axis of
this gure is the latency time while its xaxis is RThe in teger v alue of N ranging from N
min
to
N
max
increases as the n um b er of regions increase Hence as R increases b oth the latency time
and throughput increase The in teresting v alues of R are dened as those that c hange the in teger
v alue of N In Figure thesev alues are presen ted as dark dots Based on the pro vided inputs the
conguration mec hanism searc hes for the in teresting v alues of R and outputs those that satisfy the
desired throughput and latency time
The rest of this pap er is organized as follo ws Section describ es REBECA and ho w it reduces the

Search Space
Nmin+i
Nmin
Nmax
Latency (seconds)
R Interesting values of
Nmin+j
Figure The conguration mec hanism
seek time The details of the conguration mec hanism are discussed in Section Section presen ts
the latency time and throughput graphs obtained for dieren tn um b er of regions and memory sizes
for a sp ecic commercial disk driv e In Section w e categorize related studies and compare them
with REBECA Section concludes this pap er and lists our future researc h directions
Region Based Blo c k Allo cation Mec hanism REBECA
The seek time is a function of the distance that the disk head tra v els from its curren t tracktothe
trac k that con tains the referenced blo c k Hence the w orst p ossible seek time dep ends on the longest
distance b et w een the t wobloc ks that could p oten tially b e retriev ed after eachother F or example
assume the j th blo ckof object X X
j
should b e retriev ed after the ith blo c k of ob ject W W
i
in
Figure If the blo c ks of an ob ject are assigned to the a v ailable disk space in a random manner then
the w orst seek time T
w seek
dep ends on the distance b et w een the rst and the last cylinder of the
disk l ong est d Ho w ev er if the placemen tof X
j
and W
i
are con trolled suc h that their distance is
at most dwhere d l ong est d then T
w seek
is reduced By reducing the seek time w asteful w ork
the disk can sp end more of its time transfering data useful w ork resulting in a higher throughput
REBECA uses the ab o v e observ ation to increase the throughput Its design is as follo ws Assume
that N blo c ks of N dieren t ob jects can b e retriev ed and displa y ed in one time p erio d T
p
The
disk incurs a seek time ev ery time it switc hes from one blo c k to another see Figure T o ensure
a con tin uous displayof all N ob jects the system emplo ys the l ong est d to compute the w orst seek
time T
w seek
bet w een transfering the blo c ks Ho w ever ifitcan guaran tee that the N blo c ks are
ph ysically close to eac h other then it can minimize T
w seek

XX X
XX X
XX
XX
XX
XX
112 13
211 14
310
49
58
67
One Block
One
Region
Figure REBECA
Toac hiev e this REBECA rst partitions 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 ts of blo c ks to regions follo ws the ecien tmo v emen t of disk head as in the elev ator al
gorithm T eo T oretriev e the blo c ks of an ob ject the disk head mo v es inw ar d see Figure un til it reac hes the cen ter of the disk and then it mo v es outw ar d This pro cedure rep eats itself once
the head reac hes the outmost trac k on the disk This minimizes the mo v emen t of the disk head
required to sim ultaneously retriev e N ob jects T oac hiev e this minimized mo v emen t the displa yof
the ob jects should follo w the follo wing rules
The disk head mo v es in one direction either inw ar d or outw ar data time A tan y instan t in time one time p erio d the disk services requests corresp onding to a single
region termed active r e gion R
activ e
In the next time p erio d the disk services requests corresp onding to either R
activ e
inward
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 wocases R
activ e
is either incremen ted or decremen ted after
t w o time p erio ds b ecause the consecutiv e blo c ks of an ob ject reside in the same region F or

Inward Movement
Outward Movement
R
1
R
2 R
3
R
Outward Movement
4
R
6
R
5
Inward Movement
Figure Disk head mo v emen t
example in Figure X
and X
are b oth 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
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 yof 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 XF 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 let b denote the n um b er of blo c ks p er region In
the w orst case the last sc heduled ob ject during time p erio d i eg Z
k
in Figure can b e b blo c ks apart from the rst sc heduled ob ject during time p erio d i eg W
i
in Figure This is
b ecause Z
k
and W
i
reside in t w o dieren t regions Hence the w orst seek time is the time required
for the disk head to skip b bloc ks Ho w ev er without REBECA in the w orst case the t w o
blo c ks can b e R b blo c ks apart where R bis the totaln um b er of blo c ks in the disk driv e
F or R the w orst seek time is reduced signican tly with REBECA Note that R does not
reduce the w orst seek time and is eliminated from further consideration
In tro ducing regions to reduce the seek time increases the a v erage latency time observ ed bya
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 arm 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 b ecome activ e No w if a request arriv es during

a. REBECA
X ZZ
X Z
X
X
X
X
1 12
2 3
3
4
5
6
Z
4
Z
5
Z
6
Z
7

Y 1
Y 2
Y 3
Y
4
b. Time Period Schedule
R
R
R
R
R
R
1
2
3
4
5
6
T
1
Second Time Period
X1 X2 X3 Y1
First Time Period
Figure Higher Latency Time
T
referencing ob ject Y it cannot b e serviced un til the third time p erio d see Figure b This is
b ecause it requires 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 kofobject 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
Z
Hence R time p erio ds are required
b efore the disk head reac hes R
in order to 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 p erio ds un til the disk head mo v es from the last region backto R
in the rev erse direction
Hence the maxim um latency time is computed as
R T
p
if R T
p
if R

Note that is the maxim um latency time the a v erage latency is
when the n um ber of activ e users
is less than N otherwise Equation should b e extended with appropriate queuing mo dels
An in teresting observ ation is that the computed latency time in Eq is not observ ed for
An in telligent sc heduling p olicy mightprev en t this scenario

C
Mem,
R
D
Disk char.: , #cyl
Seek-Curve
R
< N, l, B, R >
N_desired
l_desired
List of
quad.
STEP 2 STEP 1
< N, l, B, R >
Figure The conguration pro cess
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 k of an ob ject X can b e stored starting with an y region Hence it is p ossible to start its storage
from the activ e region ie R
activ e
R
X

In summary partitioning the disk space in to regions using REBECA is a tradeo b et w een
throughput and latency time
System Conguration
T o displa y N sim ultaneous blo c ks p er time p erio d the system should pro vide sucien t memory for
staging the blo c ks In the w orst case NB memory space is required for N sim ultaneous displa ys By
restricting the memory size the question is ho w to congure a system based on REBECA to ac hiev e
a desired throughput andor latency time F rom Section the basic conguration parameters whose
v alue should b e computed include R and B Figure demonstrates the inputs and outputs of the
conguration pro cess
The user pro vides STEP of the conguration pro cess with the disk parameters R
D
n um ber
of cylinders cy l and the function that denes the seek time as a function of the distance tra v eled
b y the disk head the amoun tof a v ailable memory Mem and the consumption rate R
C

The result of STEP of the conguration pro cess is a list of N B R quadruples This is
an ascending sorted list on N and R The list along with the desired throughput and latency
are inputs to STEP STEP outputs the nal quadruple The follo wing t w o paragraphs describ e
STEP Section describ es the details of STEP 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

T
P
S
E
wseek
R
C
R
D
N
Mem,
T
wseek
R
C
R
D
N R
l
d. Function P
T
wseek
R
C
R
D
T
wseek
a. Function S
Seek-Curve
#cyl
R
N
B
T
c. Function E
b. Function T
Figure The pieces of STEP The list of quadruples pro duced b y step one as w ell as desir ed
and N
desir ed
that are pro vided b y
the user are the inputs to STEP of the conguration pro cess STEP is executed in t w o passes
In the rst pass it starts from the top of the list and tries to nd the rst quadruple that satises the
conditions in Equation If it succeeds then it terminates the conguration pro cess b y outputting
the quadruple N B R R and B in this quadruple are resp ectiv ely the n um b er of regions and
blo c k size required to ac hiev e a throughput of N and a latency time of If pass one fails then the user cannot b e satised completely and a decision should b e made P ass
t w o pro vides the user with some results to simplify the decision making pro cess It also starts from
the top of the list ho w ev er it tries to nd a quadruple Q
N

B
R
that satises
N
desir ed
N
and a quadruple Q
N

B
R
that satises desir ed
If these
conditions are satised it outputs b oth quadruples T rivially Q
Q
otherwise pass one w ould
ha v e succeed The user ma y either c ho ose Q
in fa v or of Q
to sacrice the latency time in fa v or
of throughput or vice v ersa or mo dify the input parameters and rein v ok e the tec hnique to obtain
the desired p erformance ob jectiv e
STEP STEP consists of four functions S T Eand P see Figure First w e describ e the steps
tak en to deriveeac h function Next a simple algorithm is pro vided that in v ok es the four functions
to generate the list of quadruples

F unction S This function computes the w orst seek time T
w seek
based on a giv en cy l and RLet d
max
denotes the maxim um n um b er of cylinders that the disk head migh t b e required to tra v el
F or example if d
max
the maxim um n um b er of cylinders that the disk head migh t skip to
retrieveabloc k is cylinders Hence
d
max
cy l
R
if R cy l if R

In this equation
cy l
R
is m ultiplied b y b ecause in the w orst case the last blo c ksc heduled
during time slot i mightbe b blo c ks apart from the rst blo c ksc heduled during time p erio d
i Note that
cy l
R
denes the n um b er of cylinders p er regions Once d
max
is kno wn an
exp erimen t on a sp ecic disk driv e can b e p erformed to compute T
w seek
An alternativ eis to
use analytical mo dels iden tical to those deriv ed in R W F or example R W describ es the
seek time of the HP Disk Driv e mo del with cy l as
T
wseek
p
d
max
if d
max

d
max
otherwise

F unction T This function computes N based on the computed T
w seek
and the giv en Mem R
C
and R
D
By substituting B from Equation in Equation and assuming equalit y for Equation in
order to minimize the amoun t of required memory w e obtain
T
p
N
T
w seek
R
D
N Mem
By substituting T
p
from Equation in Equation N can b e computed as a function of T
wseek
Mem R
C
and R
D
Note that N is an in teger and the o or function of the computed v alue
should b e considered
F unction E T o compute the blo c k size Equation can b e used directly where T
p
is computed using
Equation F unction P Finally the latency time can b e computed using Equation T o supp ort N sim ultaneous displa ys eac h region should con tain at least N blo c ks ie b N Ho w ev er none of the functions listed for STEP examine this restriction The reason is that w e
assumed the size of memory is m uc h less than the size of the disk driv e
Mem C
R

R T
w seek
S R N T T
w seek
while N b
R
D
R
C
c do
B E T
w seek
N P T
w seek
N R output N B R N N
T
w seek
T
N if T
wseek
D isk Min Seek then return
R S
T
wseek
end while
Figure An algorithm for STEP where C is the total disk capacit yF urthermore from Equation it is kno wn that
N
Mem
B

Hence b y substituting Mem from Equation in Equation w e obtain
N
C
B R

Observ e that
C
BR
is actually equal to b Therefore b is alw a ys greater than N Figure con tains an algorithm that emplo ys the ab o v e functions to generate the list of quadruples
As sho wn in Figure R is one of the outputs of the conguration pro cess while see function S
in Figure R is also an input Therefore one migh t b e tempted to b ound the v alue of R and
do an iteration o v er R to generate a searc h space list of quadruples Ho w ev er this results in an
unnecessarily large searc h space A sup erior approac h is to iterate o v er N T o observ e consider
Figure The xaxis is R and the yaxis is the latency time As R increases b oth N and increase
Note that increasing N is desirable while increasing is undesirable Ho w ev er since N is an in teger
for some v alues of R is increasing undesirable while N is not The idea is to eliminate these
v alues of R from the searc h space Toac hiev e this although the algorithm see Figure starts
from R the v alue of R is not simply incremen ted Instead the v alue of N is incremen ted
to compute the corresp onding v alue of RIn other w ords N is b ounded b y N
min
T S and
N
max
b
R
D
R
C
c N
min
is computed based on R only in the rst iteration of the algorithm F or
the other iterations R is computed based on the v alue of N whic h is incremen ted starting from
N
min
to N
max
as R S
T
N where S
and T
are the rev erse functions of S and T resp ectiv ely
Disk Capacit y C Gigab ytes
Num b er of Cylinders cy l
Minim um T ransfer Rate R
D
Mbps
Minim um Seek Time milli seconds
Maxim um Seek Time milliseconds
Maxim um Rotational Latency Time milliseconds
Seek Characteristic Mo del T
w seek
p
d
max
d
max

T
w seek
d
max
d
max

T able Se agate Barr acuda HP disk parameters
Note that N
max
is a theoretical upp er b ound on N This is b ecause for some v alues of N T
N migh t compute a seek time that is less than the minim um seek time that the disk driv e can supp ort
The if statemen t inside the while lo op of Figure handles this situation
A Case Study
T o conrm our analytical analysis w e p erformed some exp erimen ts In these exp erimen ts w e used a
Se agate Barr acuda HP Sea disk driv ec haracteristics
The disk parameters are summarized
in T able The seek mo del last ro wofT able is an appro ximation based on the mo dels prop osed
in R W This is basically an in terp olation b et w een the minim um and the maxim um seek time
pro vided b y Seagate Note that seconds of maxim um rotational latency time is added to the
equations In this exp erimen t a consumption rate of Mbps R
C
Mbps w as assumed based
on the maxim um bandwidth requiremen t of MPEG compressed video ob ject Hence the theoretical
upp erb ound for N is ie N
max
First w ev aried the a v ailable memory Mem from MBytes up to MBytes and for eac h
conguration the maxim um latency time and throughput curv es w ere obtained see Figure In
Figure a as the size of memory increases the impact of R on throughput diminishes F or example
with MBytes of a v ailable memory the n umberofsim ultaneous displa ys increases from up to
a impro v emen t as R v aries from to Ho w ev er with Mem MBytes the rate
of impro v emen t is reduced to from N to N This is b ecause as the memory size
increases the blo c k size increases as w ell This increases the amoun t of data retriev ed from the
disk driv e p er seek op eration Hence the seek time as compared to the transfer time of eac h blo c k
b ecomes negligible Therefore the impact of increasing the n um b er of regions in order to reduce
the seek time b ecomes less signican t
W e also examined other disk driv es Ho w ev er our c hoice of a disk driv e did not impact the nal observ ations

0 50 100 150 200
20
30
40
50
60
No. of Regions
4MB
8MB
16MB
32MB
64MB
No. of Users
0 50 100 150 200
0
500
1000
1500
2000
2500
No. of Regions
4MB
8MB
16MB
32MB
64MB
Time(sec)
a Throughput b Maxim um Latency Time
Figure Throughput and maxim um latency time with REBECA
Next w e xed the amoun tofa v ailable memory to MBytes and in v estigated the tradeo b et w een
the throughput and the maxim um latency time Figure demonstrates that more regions results in
higher throughput and longer latency time Note that N
min
is computed b y rendering functions S
and T from Section for a single region ie T S Three in teresting observ ations from
Figure are as follo ws
Although the theoretical upp er b ound for N is the maxim um throughput ac hiev ed is The reason is that to supp ort more than users a disk access time of appro ximately less than
milliseconds is required Ho w ev er considering the maxim um rotational latency time of milliseconds and the minim um seek time of milliseconds this access time is infeasible
Equation is misleading b ecause it suggests that the maxim um latency time is a linear function
of RHo w ev er in Figure b there are some jumps in the maxim um latency time as the
n um b er of regions gro ws F or example when R the latency time is seconds while
with R it jumps to seconds This is b ecause the throughput N increases from sim ultaneous displa ys to at that p oin t This results in an increase in the n um b er of blo c ks
retriev ed p er time p erio d N and subsequen tly the duration of a time p erio d see Equation Therefore the latency time is a function of b oth T
p
as w ell as R see Equation and observ es
p erio dical jumps in v alue
The last observ ation is to conrm the reduced searc h space F rom Figure a N is when
R and its v alue remains as un til R b ecomes The reason is that for the v alues of
R bet w een and the throughput as a r e al v alue is increasing while N as an integ er v alue

0 50 100 150 200
20
22
24
26
28
30
32
34
No. of Regions
No. of Users
0 50 100 150 200
0
50
100
150
200
250
300
No. of Regions
Time(sec)
N=32
N=31
N=30
a Throughput b Maxim um Latency Time
Figure Throughput and maxim um latency time with REBECA Mem MBytes
N sec B Kb ytes R T p msec b
T able Searc h space
is a constan t Ho w ev er in Figure b the latency time increases as R v aries from to Therefore those v alues of R bet ween toare not in teresting and should b e ignored from
consideration The algorithm in Figure b y iterating o v er N instead of R eliminates these
v alues of R from searchspace T able demonstrates the r e duc e d searc h space of the algorithm
when Mem MBytes
Related W ork
There are t w o general approac hes for organizing the blo c ks of a con tin uous media data t yp e on the
a v ailable disk space Unc onstr aine d and Constr aine d Allo cation Unconstrained allo cation allo ws for
a random assignmen t of the blo c ks of an ob ject to the a v ailable disk space Example studies that
assume this allo cation strategy include GS GDS TPBG BGMJ T o ensure a con tin uous
displa y these studies assume the w orst seek time T
wseek
bet w een the retriev al of anyt w o blo c ks

of ob jects Here the w orst seek time is the time required for the disk head to mo v e from the rst
cylinder to the last one The adv an tages of this approac h are as follo ws First it simplies the
equations used to sc hedule the a v ailable disk bandwidth dealing with one v alue T
w seek
Second it
simplies adding deleting and editing the ob jects This can b e ac hiev ed b y represen ting an ob ject
with a link list of blo c ks Hence editing an ob ject requires no complicated disk managemen t This
is b ecause blo c ks are equisized and ev ery blo c k can b e replaced b y another without impacting the
displa y of the ob ject
The disadv an tages of this tec hnique are as follo ws First for those blo c ks that are close to
eac h other considering the w orst seek time w astes the disk bandwidth Moreo v er it reduces the
utilization of memory b ecause more data is staged in memory for a longer duration of time than
necessary ev ery time the system incurs a seek lo w er than this w orst case estimate Second large
seek time results in dening larger blo c k sizes in order to utilize the disk bandwidth Therefore the
memory requiremen t as the staging area b et w een the disk and displa y is increased
T o reduce the w orst seek time an alternativ e approac h constrained allo cation of blo c ks is
discussed W e presentt w o dieren ttec hniques for this category Con tiguous blo ckallocation The blo c ks of an ob ject are laid out con tiguously on the
disk space Example studies assuming this approac h are CL and GS The immediate
adv an tage of this approac h is that b y retrieving the disk blo c ks con tin uously the seek time is
minimized there is still some switc hing time in v olv ed This approac h is useful for readonly
applications Ho w ev er deleting and adding ob jects requires disk managemen ttec hniques eg
REBA TE GI CL main tain a double link list for blo c ks and when it is not p ossible
to nd an empt y space next to an existing blo c k it stores the blo c k in the nearest lo cation
The imp ortan t problem with this approac h is that in a m ultiuser en vironmen t where the
disk bandwidth is m ultiplexed b et w een m ultiple requests seeks con tin ue to exist T o observ e
assume that b et w een retrieving the rst and the second blo c kof an object X one blo c kof
ob jects Y and Z should b e retriev ed Note that w e assume no adv anced kno wledge that X Y and Z will b e displa y ed sim ultaneouslyGS b yin tro ducing more than one disk driv e
or cluster of disk driv es and dedicating eac h disk cluster to a single request a v oids this
problem CL kno wing that the seek times are unpredictable uses the exp ected v alue and
the v ariance of seek times and b y emplo ying Cheb yshevs form ula b ounded the probabilityof
hiccups termed star v ation in that study Although this is useful to pro vide a p olicy to
accept or reject a new session is not appropriate for conguring a system that guaran tees a
hiccupfree displa y
In terlea v ed allo cation With this approac h the blo c ks of related ob jects are laid out con
tin uously on the disk driv e Examples of w orks assuming this approac h are R V WYY YSB
In R V preassumed information ab out time dep endency of m ultimedia ob jects is
considered Although applicable for singleuser en vironmen t and some sp ecial purp ose m ulti
user en vironmen ts in a general purp ose m ultiuser en vironmen t with a wide v ariet y of users
an application dep enden t allo cation migh t not b e appropriate Moreo v er ecien t use of disk
storage where the gap bet w een t wobloc ks can b e exactly lled b y blo c ks of other ob jects
is optimistic
REBECA is a com bination of b oth constrained and unconstrained blo c k allo cation It minimizes
the impact of the seeks while enjo ying the b enets of unconstrained blo c k allo cation This is ac hiev ed
b y partitioning the disk space in to R regions The allo cation of blo c ks to the regions is constrained
while within a region the blo c k allo cation is unconstrained The blo c k allo cation to the regions is
constrained suc h that the mo v emen t of the disk head when retrieving blo c ks b ecomes almost similar
to its mo v emen t in the elev ator T eo algorithm This minimizes the exp ected w orst seek time In
essence the blo c k allo cation is constrained b y the ph ysical c haracteristics of the disk driv e instead
of the application b eha vior
An alternativ e approac h to reduce the maxim um seek time is in tro duced in YCK termed
gr oup swe eping scheme GSS GSS enforces no constrain t on blo c k allo cation unconstrained blo c k
allo cation Ho w ev er in order to reduce the seek time it groups N activ e requests of a time p erio d
in to g groups The mo v emen t of the disk head to service the streams within a group abides b y the
elev ator algorithm in the w orst case it scans the en tire disk space within a group Across the
groups there is no constrain t on the disk head mo v emen t T o supp ort the elev ator p olicy within a
group instead of constraining the placemen t of the corresp onding blo c ks GSS sh u es 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 is X
Y
Z
during one time p erio d while during the next time p erio d it
mightc hange to Z
X
Y
In this case the displa yof X suers from hiccups since the time
elapsed b et w een X
and X
is no w greater than one time p erio d T oo v ercome this problem YCK suggests a prefetc hing mec hanism The dra wbac k is that it requires more memory for prefetc hing as
g gro ws On the other hand b y increasing g the seek time is reduced whic h results in smaller blo c k
sizes and less memory requiremen t They pro vide some equations to determine the optimal v alue of
g g N in order to minimize the en tire memory requiremen t
This study diers from YCK in t w o asp ects First REBECA constrain ts the blo c k allo cation
across time p erio ds to reduce the seek time With REBECA a complete disk scan o ccurs ev ery R
time p erio ds while with GSS it mighthappen g times during eac h time p erio d Th us REBECA

results in further reduction of seek time and consequen tly smaller blo c k size Moreo v er REBECA
do es not require extra memory for prefetc hing Hence it requires less memory as compared to GSS
while it increases the maxim um latency time Second YCK concen trates on reducing the en tire
memory requiremen t of the system while w e pro vide a mec hanism to congure a system for a desired
throughput and latency time with a xed amoun tof a v ailable memory Conclusion and F uture Directions
In this study wein tro duced a regional blo c k allo cation mec hanism REBECA to congure a single
disk con tin uous media serv er REBECA partitions the a v ailable space of a disk drivein to R regions
and assigns the blo c ks of an ob ject to the regions in a zigzag manner It groups the blo c ks referenced
b y the N activ e requests in to one region in order to minimize the distance that the disk head
tra v els to retriev e the blo c ks corresp onding to the activ e requests While this grouping increases the
throughput it also results in a higher latency time W e pro vided a mec hanism that determines a
v alue for the conguration parameters n um b er of regions and blo c k size of the system based on a
presp ecied disk driv ec haracteristic a v ailable memory desired throughput and latency time
T o simplify the conguration pro cess w emade t w o simplifying assumptions First w e assumed
that all ob jects b elong to a single media t yp e and require a xed consumption rate R
C
Second
w e assumed a single zone for the disk driv e That is a xed pro duction rate R
D
w as assumed
indep enden t of the lo cation of a blo c k on the disk driv e Ho w ev er in a real disk driv e the transfer
rate increases as a function of the distance of the cylinder from the cen ter of the disk driveR W Wein tend to extend this study b y relaxing these t w o assumptions
Relaxing the rst assumption is a simple task T o observ e assume that the ob jects b elong to
m dieren t media t yp es with R
C
i as the displa y bandwidth requirementof eacht yp e i One
approac h is to rst congure the system for R
C
k using the prop osed tec hnique where R
C
k
Min R
C
i for i m Next if the computed throughput of the conguration pro cess is N
then the system can supp ort N sim ultaneous requests for ob jects of media t yp e k the one with the
minim um bandwidth requiremen t Moreo v er sa y R
C
j R
C
k then the system can supp ort
N
sim ultaneous requests for ob jects of media t yp e j The other com binations can b e considered in
a similar manner Note that in this case a nonin teger throughput is acceptable b ecause
R
C
j R
C
k can
bearealn um b er for some j Hence the complete searc h space in the algorithm of Figure should
b e considered should iterate o v er all p ossible v alues of R Extending the tec hnique to supp ort m ultiple zones on the disk driv e ho w ev er is not as straigh t

forw ard W eplan toin v estigate this in more detail as part of our future researc h direction A brief
o v erview of our initial attempt is as follo ws Let eac h zone consist of r regions where in the simplest
case r An ob ject is strip ed in to n blo c ks where blo c ks are no longer equisized Instead as the
transfer rates of zones increases the size of the blo c ks increases prop ortionally suc h that
B z R
C
z is
xed for ev ery zone z Based on this assumption t w o alternativ e approac hes can b e tak en
Assigning the rst blo c kof ev ery ob ject to the zone with the highest bandwidth
This approac h results in inecien t usage of storage space while it requires small amoun tof
memory space equal to R m ultiplied b y the size of the largest blo c k in the w orst case
Random assignmen t of blo c ks to zones
This approac h solv es the inecien t usage of storage space ho w ev er it requires a large amoun t
of memory space equal to N m ultiplied b y the size of the largest blo ckinthe w orst case
An alternativ e extension of this study is to applications that assume a prior kno wledge ab out the
time dep endencies of m ultimedia ob jects In this case the placemen t of the blo c ks of ob jects can
b e done in telligen tlyF or example if it is kno wn that ob ject X will b e referenced immediately after
Y then X
can b e allo cated to a region follo wing the last blo ckof Y In this case the minim um
latency time is observ ed when X is referenced immediately after Y Moreo v er there are some applications that while the relationship b et w een the ob jects of a
database is precisely predened eg as a directed graph a zero latency time is required p er
reference examples of these applications can b e found in SG In this case the tec hniques
describ ed in SG are directly applicable to REBECA in order to satisfy these applications
Ac kno wledgmen ts
Wew ould lik e to thank Professor Ric hard Mun tz of UCLA for his v aluable commen ts on an earlier
draft of this pap er
References
BG Dina Bitton and J Gra y Disk shado wing In Pr o c e e dings of the International Confer enc e
on V ery L ar ge Datab ases Septem ber BGMJ S Berson S Ghandeharizadeh R Mun tz and X Ju Straggered striping in m ultimedia
information systems In Pr o c e e dings of the A CM SIGMOD International Confer enceon
Management of Data
CL HJ Chen and T Little Ph ysical Storage Organizations for TimeDep enden t Multimedia
Data In Pr o c e e dings of the F oundations of Data Or ganization and A lgorithms F ODO
Confer enc e Octob er GDS S Ghandeharizadeh A Dash ti and C Shahabi A Pip elining mec hanism to minimize
the latency time in hierarc hical m ultimedia storage managers Tobeapp e ar edinJournal
of Computer Communic ation Marc h GHW J Gra y B Host and M W alk er P arit y striping of disc arra ys Lo wcost reliable storage
with acceptable throughput In Pr o c e e dings of the International Confer enceon V ery
L ar ge Datab ases August GI S Ghandeharizadeh and D Ierardi Managemen t of Disk Space with REBA TE Pr o c e e d
ings of the Thir d International Confer enc e on Information and Know le dge Management
CIKM No v em b er GS S Ghandeharizadeh and C Shahabi Managemen tof Ph ysical Replicas in P arallel Mul
timedia Information Systems In Pr o c e e dings of the F oundations of Data Or ganization
and A lgorithms F ODO Confer enc e Octob er GS S Ghandeharizadeh and C Shahabi On Multimedia Rep ositories Personal Computers
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TR ICSI R V P Rangan and H Vin Ecien t Storage Tec hniques for Digital Con tin uous Media IEEE
T r ansactions on Know le dge and Data Engine ering August R W C Ruemmler and J Wilk es An In tro duction to Disk Driv e Mo deling IEEE Computer March Sea Seagate Barracuda family The Data T e chnolo gy Comp any Pr o duct Overviewpage March SG C Shahabi and S Ghandeharizadeh Con tin uous Displa y of Nonlinear Presen tations
USC Tec hnical Rep ort USCCS Univ ersit y of Southern California T eo TJ T eory Prop erties of Disk Ssc heduling P olicies in Multiprogrammed Computer Sys
tems In Pr o c AFIPS F al l Joint Computer Conf pages ! TPBG FA T obagi J P ang R Baird and M Gang Streaming RAIDA Disk Arra y Manage
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ing Sc heme for Multimedia Storage Managemen t In Pr o c e e dings of the Thir d Interna
tional Workshop on Network and Op er ating System Supp ort for Digital A udio and Vide o No v em ber YSB
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Description

Shahram Ghandeharizadeh, Seon Ho Kim, Cyrus Shahabi. "On configuring a single disk continuous media server." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 590 (1994).

Asset Metadata

Creator Ghandeharizadeh, Shahram (author), Kim, Seon Ho (author), Shahabi, Cyrus (author)

Core Title USC Computer Science Technical Reports, no. 590 (1994)

Alternative Title On configuring a single disk continuous media server (title)

Publisher Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA (publisher)

Tag OAI-PMH Harvest

Format 22 pages (extent), technical reports (aat)

Language English

Unique identifier UC16270511

Identifier 94-590 On Configuring a Single Disk Continuous Media Server (filename)

Legacy Identifier usc-cstr-94-590

Format 22 pages (extent),technical reports (aat)

Rights Department of Computer Science (University of Southern California) and the author(s).

Internet Media Type application/pdf

Source 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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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

Repository Email csdept@usc.edu

Inherited Values

Title Computer Science Technical Report Archive

Description Archive of computer science technical reports published by the USC Department of Computer Science from 1991 - 2017.

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)