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USC Computer Science Technical Reports, no. 623 (1995)
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USC Computer Science Technical Reports, no. 623 (1995)
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Content
An Analysis of Striping in Scalable MultiDisk Video Serv ers
Shahram Ghandeharizadeh and Seon Ho Kim
Departmen t of Computer Science
Univ ersit y of Southern California
Los Angeles California No v em ber
Abstract
With a scalable video serv er the n um ber of sim ultaneous displa ys supp orted b y the system
increases as a function of additional resources Suc h a serv er can supp ort those applications
that striv e to supp ort either h undreds eg a hotel pro viding service to its guests or thousands
eg a cable compan y pro viding service to a cit y of sim ultaneous displa ys The only dierence
bet w een the dieren t systems is the size of their hardw are platform ie n um b er of disks amoun t
of memoryetc Striping is a tec hnique that distributes the w orkload of a displayev enly across
the a v ailable resources and is the k ey to realizing a scalable serv er
While it is desirable for the n um b er of concurren t displa ys to scale as a function of additional
resources it is also desirable for the startup latency to not increase Startup latency is dened
as the amoun t of time elapsed from when a request is issued to the time that its displa y starts
In this pap er w edev elop analytical mo dels that estimate the exp ected startup latency incurred
b y a request as a function of both additional resources and the load imp osed on the system
W e describ e replication and request migration as t w o alternativeapproac hes to minimizing the
exp ected latency Wequan tify their tradeos using analytical mo dels
In tro duction
During the past decade the information tec hnology has ev olv ed to where it is economically viable to
store and retriev e video ob jects While the en tertainmen t industry en visions the use of video serv ers
as a sup erior alternativ e to curren t video stores these serv ers are exp ected to pla y a ma jor role in
educational applications library information systems health care and n umerous other applications
A serv er m ust retriev e a video ob ject at a presp ecied rate in order to ensure its con tin uous displa y Without sp ecial precautions the displa y of an ob ject ma y suer from frequen t disruptions and
dela ys termed hiccups T o supp ort a hiccupfree displa yitma y not b e practical to stage an ob ject
This researchw as supp orted in part b y the National Science F oundation under gran ts IRI IRI
NYI a w ard and CD A and a HewlettP ac k ard unrestricted cashequipmen t gift
in memory in its en tiret y b efore initiating its displa y This is b ecause video ob jects are large in
size F or example a min ute uncompressed video clip based on NTSC is gigab ytes in size
With a lossy compression tec hnique that reduces the bandwidth requiremen t of this ob ject to Mbs this ob ject is megab ytes in size Assuming the bandwidth required to displa y an ob ject
R
C
is lo w er than the bandwidth of a disk driv e R
D
a sup erior approac h to displa y an ob ject
X is as follo ws First the system partitions the ob ject in to equisized blo c ks Once an ob ject
X is referenced the system stages its rst blo c k in memory and initiates its displa y Prior to
completion of the displa y of the rst blo c k of X the system stages the next blo c k of X in memory
to supp ort a hiccupfree displa y Since R
D
R
C
the bandwidth of the disk can be m ultiplexed
to supp ort sev eral sim ultaneous displa ys V ariations of this simple tec hnique ha v e b een describ ed
in P ol CP R V TPBG R W BGMJ In addition to ensuring a con tin uous displa y a system designer m ust consider the p erformance
requiremen ts of an application In an ideal en vironmen t a system costs zero dollars serv es an
innite n um b er of displa ys with eac h displa y observing a zero startup latency time Ho w ev er suc ha
system is infeasible motiv ating one to design a system based on the n um b er of sim ultaneous displa ys
desired b y the target application and the w aiting tolerance of a displa y Dieren t applications ma y
require dieren t p erformance criteria F or example a videoondemand system designed for a cit y
ma y exp ect to ha v e thousands of sim ultaneous displa ys as its maxim um load F or suc h a system it
migh t b e reasonable to assume that a clien t at home can tolerate a latency in the order of min utes
previewing commercial clips that reduce cost Alternativ ely a system targeted for a hotel ma y exp ect
to supp ort h undreds of sim ultaneous displa ys as its maxim um load with eac h displa y tolerating a
latency in the order of seconds
The bandwidth of a single disk driv e migh t b e insucien t to supp ort the n um b er of sim ultaneous
displa ys desired b y an application One ma y assume a m ultidisk platform consisting of D disks to
resolv e this limitation With suc h a platform the w orkload of a displayshould be ev enly distributed
across the D disks in order to a v oid formation of b ottlenec ks Striping BGMJ GK is a tec hnique
to accomplish this ob jectiv e This tec hnique partitions the D disks in to C clusters of disks with eac h
cluster consisting of d disks C b
D
d
c Next it assigns the blo c ks of ob ject X to the clusters in
a roundrobin manner The rst blo c k of X is assigned to an arbitrarily c hosen disk cluster Eac h
blo c k of an ob ject is declustered GRA Q across the d disks that constitute a cluster F or example
in Figure a system consisting of six disks is partitioned in to three clusters eac h consisting of t w o
disk driv es The assignmen t of the blo c ks of X starts with cluster 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 the idle slot
This assumption is relaxed in the follo wing paragraphs
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 Simple Striping
on the cluster that con tains X
sa y C
i
to displa y its rst blo c k Before the displayof X
completes
the system emplo ys cluster C
i mod k
to displa y X
This pro cess is rep eated un til all blo c ks of an
ob ject ha v e b een retriev ed and displa y ed
Striping results in a scalable serv er b ecause it distributes the w orkload of a displayev enly across
the a v ailable disks Th us as one increases the n um b er of disks in a system the n um b er of sim ulta
neous displa ys supp orted b y the system increases as w ell This study dev elops analytical mo dels to
compute the exp ected startup latency observ ed b y a new request as a function of the n um ber
of clusters in the system and the load imp osed on the system T o the best of our kno wledge
these mo dels are no v el and ha v e not app eared in the past They dier from mo dels presen ted in
the con text of parallel le system or database managemen t systems MY WYS in that a
displa y emplo ys clusters in a roundrobin manner a displa ym ust start with the cluster con tain
ing its rst blo c k and a displa y migh t be activ e for a long time dep ending on the displa y time
of a clip p oten tially t w o hours for a t w o hour mo vie A secondary con tribution of this study is
its prop osed tec hniques to minimize the exp ected latency of a request These tec hniques replicate
an ob ject m ultiple times One of these tec hniques termed Selectiv e replication replicates the most
frequen tly accessed ob jects Our analysis demonstrates the sup eriorit y of this tec hnique to others
The rest of this pap er is organized as follo ws Section completes the paradigm that supp orts
a con tin uous displa y It separates the activ ation of clusters bandwidth of clusters from ph ysical
clusters storage space of clusters b y in tro ducing the concept of groups Using this abstraction
Section describ es analytical mo dels based on queuing theory to estimate the exp ected startup
latency observ ed b y a request Subsequen tly Section describ es t w o alternativ e approac hes that
minimize the exp ected startup latency W e quan tify these t w o alternativ es in Section Brief
conclusions are oered in Section
T erm Denition
T
W S eek
W orst seek time with maxim um rotational latency
m Maxim um n um b er of sim ultaneous displa ys in a system
R
C
Displa y bandwidth requiremen t Displa y rate
R
D
T ransfer rate of a single disk driv e
B Size of a blo c k
G
i
Group i
T
p
Time to displa y a blo c k
N Maxim um n um b er of sim ultaneous displa ys in a cluster
L Latency
D T otal n umberof diskdriv es in a system
d Num b er of disk driv es in a cluster
C Num b er of clusters in a system
k Num ber of activ e requests busy serv ers in a system
i Num b er of failures that a request migh t observ e b efore a success
Av erage arriv al rate requests p er min ute
s Av erage service time of a request min utes
T able List of terms used rep eatedly in this pap er and their resp ectiv e denitions
Con tin uous Displa y
T o supp ort con tin uous displayof anobject X it is partitioned in to n equisized blo c ks X
X
X
n where n is a function of the blo c k size B and the size of X 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
When an ob ject X is referenced the system stages X
in memory and initiates its displa y Prior
to completion of a time p erio d 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 v e b een displa y ed
T o supp ort sim ultaneous displa y of sev eral ob jects a time period is partitioned in to xsized
slots with eac h slot corresp onding to the retriev al time of a blo c k from a cluster The n um ber of
slots N in a time p erio d denes the n um ber of sim ultaneous displa ys that can b e supp orted bya
cluster Figure demonstrates the concept of a time p erio d and a time slot Eac h bo x represen ts a
time slot for a system consisting of a single cluster Assuming that eac h fragmen t of a blo c k is stored
con tiguously on the surface of a disk eac h disk driv e in a cluster incurs a seek ev ery time it switc hes
from one blo c k of an ob ject to another due to the sync hronized access to fragmen ts in a cluster W e
denote this as T
W Seek
and assume that it includes the maxim um rotational latency time of the disk
driv e
When a cluster with d disks supp orts N sim ultaneous displa ys it is trivial to compute the size
Display W Display W
W W
Cluster
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
of a blo c k from Figure B
T
p
N
T
W Seek
d R
D
By substituting B from Equation in to Equation w e obtain
T
p
N T
W Seek
d R
D
d R
D
N R
C
F or a system with a single cluster the duration of a time p erio d T
p
denes the maxim um startup
latency incurred when the n um b er of activ e displa ys is few er than N With a system consisting of C clusters there are C time p erio ds eac h consisting of N time slots
W e conceptualize a time p erio d as a group with eac h group ha ving a unique iden tier T o supp ort
a con tin uous displa y in a m ulticluster system a request maps on to one group and the individual
groups visit the clusters in a roundrobin manner Figure If group G
accesses cluster C
during
a time period G
w ould access C
during the next time period During a giv en time p erio d the
requests o ccup ying the slots of a cluster retriev e blo c ks that reside in the cluster that is b eing visited
b y a group
Assuming a rstcomerstserv ed p olicy up on the arriv al of a request the system assigns it to
a group that services this request un til the end of its displa y With a request referencing ob ject
X the system rst determines the group sa y G
x
whic h is curren tly accessing the cluster where
the rst blo c k of X resides If G
x
has an a v ailable time slot the system assigns this request to G
x
to initiate the retriev al on b ehalf of this request Otherwise a failure has o ccurred and the system
c hec ks whether the next coming group has an empt y time slot This is rep eated un til the system
nds an a v ailable group group un til the end of its displa y Due to the rotation of groups there is
a fair c hance for a request to be assigned to a sp ecic group regardless of the lo cation of the rst
blo c k of eac h ob ject and their access frequency
With the load balancing sc heme of Section a request can b e migrated to another group during its displa y
C CC C CC
G
G G GG G
2 1 0
0
1
2 3 4 5
3 4 5
X XX X X X
X
YY Y YY Y
Y
0 12 3 4 5
6
0 1 2
3 4 5
6
...
...
Figure Rotating groups
Therefore if there are C clusters C groups in the system and eac h cluster eac h group can
supp ort N sim ultaneous displa ys maxim um throughput of the system is m N C sim ultaneous
displa ys W orst latency is T
p
C b ecause groups are rotating ie pla ying m usical c hairs with the
C clusters using eac h for a T
p
in terv al of time and at most C failures migh t occur when activ ating
a request when the n um ber of activ e displa ys is few er than N C Hence throughput in our
prop osed tec hnique scales linearly Ho w ev er the w orst latency also scales linearly Note that system
parameters blo c ks size time period throughput etc can be computed in a cluster using an y
displa y tec hnique suc h as REBECA GKS GSS YCK This is b ecause displa y tec hniques
with a cluster p erform lo cal optimizations that are orthogonal to the global optimizations p erformed
b y our prop osed tec hnique
Throughput and Latency
Our approac h in the previous section demonstrates the scalabilit y of a system in terms of both its
throughput and w orst latency It migh t be p essimistic to consider the w orst latency as an actual
latency that a request exp eriences b efore b eing serviced This section quan ties the c haracteristics
of latency and emplo ys a probabilistic approac h to determine the exp ected latency of a request
In general a m ultidisk platform cannot be mo deled as a m serv er queueing system b ecause
not all serv ers are iden tical Up on the arriv al of a request it should be assigned to a sp ecic disk
cluster con taining its rst blo c k and not an arbitrarily c hosen cluster Ho w ev er due to a random
distribution of the rst blo c ks of ob jects across disks and a roundrobin access pattern a request
can b e assigned to a time slot of an y group W e can conceptualize our striping system as a queueing
system with m iden tical serv ers where a serv er corresp onds to a time slot and not a cluster Hence
w e can compute the probability p k that there are exactly k busy serv ers in the system at a giv en
poin t in time b y applying a queueing mo del F or example with a P oisson arriv al pattern and an
exp onen tial service time the probabilit yof k busy serv ers in an m serv er loss system is Kle p k Probfk busy serv ers in the systemg k
k P
m
k k
k where and are the arriv al rate of requests and the service rate of the serv er a v erage service
time resp ectiv ely When a request for an ob ject X arriv es at time tthe system determines the cluster con taining
the rst blo c kof X sa y C
x
and the group curren tly accessing this cluster sa y G
x
If G
x
has at
least one a v ailable slot the request is assigned to G
x
and its displa y is initiated If the time slots of
G
x
are exhausted o ccupied b y other requests the request cannot b e sev ered b y this group failure
Next the system c hec ks the a v ailabilit y of cluster G
x
mod C Note that in con trast to ho w
the clusters are n um b ered the n um b ering of the groups is descending see Figure If the time slots
of this group are also fully exhausted the system c hec ks the a v ailabilit y of cluster G
x
mo d
C This pro cedure is rep eated un til an group with an idle slot is found success Hence a request
mightha v e sev eral failures b efore b eing assigned to a sp ecic group in the system
This results in
a longer latency for the request b ecause sev eral time p erio ds migh t pass b efore the assigned group
reac hes cluster C
x
If a request exp eriences i failures b efore a success the latency for the request is
L i T
p
Let p
f
i k be the probabilit y that the request has i failures b efore a success when there are k
busy serv ers in the system Foragiv en k the probabilit y that a request exp erience i failures b efore
a success is
p
f
i k
m i N
k i N
m i N
k i N
m
k
where k m and i b
k
N
c The calculation of p
f
i k migh t best be explained using an
example
Assume that a system consists of four clusters with eac h group supp orting serv ers Hence
there are t w elv e serv ers a v ailable If a request arriv es when serv ers are busy then this request
This is a rstcomerstserv e p olicy for activ ating requests
migh t exp erience at most failures b
c b efore succeeding The n um ber of all the p ossible w a ys
to allo cate busy serv ers in to serv ers is
Note that this is iden tical to the n um ber of
w a ys to c ho ose busy serv ers from serv ers
F or a request to exp erience failures relativ e to the group con taining the rst blo c k of the
referenced ob ject the serv ers of consecutiv e groups m ust b e fully exhausted This implies that consecutiv e serv ers should be busy Therefore once consecutiv e busy serv ers are allo cated to consecutiv e groups there are
w a ys to allo cate a busy serv er to remaining serv ers Hence
the probabilityofha ving failures is
the n um ber of w a ys to allo cate busy serv ers
to serv ers with the condition of consecutiv e busy serv ers divided bythe n um b er of all p ossible
w a ys to allo cate busy serv ers in to serv ers
F or a request to exp erience failures consecutiv e groups consecutiv e serv ers m ust b e busy Once consecutiv e serv ers are allo cated to consecutiv e groups there are
w a ys to allo cate
busy serv ers to remaining serv ers Ho w ev er this also includes the previous failure cases
Therefore
is the n um ber of w a ys to ha v e exactly failures Hence the probabilit y
of ha ving failures is
Th us when m N and k failures p
f
failures p
f
failure p
f
failure p
f
Let arandom v ariable L dene the latency for a request with i failures The probabilit y that a
request has a latency of i T
p
is the summation of the probabilityof i failures conditioned b y
all k v alues Hence the exp ected latency is
E L
m X
k b
k
N
c
X
i
p k p
f
i k i T
p
C CC C CC
G G G GG G
2 1 0
0
1
2 3 4 5
3 4 5
X XX X X X
X
YY Y YY Y
Y
0 12 3 4 5
6
0 1 2
3 4 5
6
...
...
Figure Load balancing
Tw o Alternativ e T ec hniques to Minimize Exp ected Latency
Request Migration
Ev en though the w ork load of a system is relativ ely w ell distributed across clusters with a round
robin assignmen t of blo c ks a group migh t ha v e a higher w ork load as compared to other groups
F or example in Figure serving a request for an ob ject X using group G
causes all serv ers in G
to b ecome busy while sev eral other groups ha v e t w o idle serv ers This un balance migh t result in a
higher latency for other requests F or example if another request for X arriv es it w ould incur a
latency equiv alentto t w o time p erio ds b ecause it m ust b e assigned to G
By migrating one or more requests from a group with zero idle slots to a group with man y idle
slots the system can minimize the latency incurred b y a request F or example if the system migrates
a request from G
to G
then the request for X w ould incur a maxim um latency of one time p erio d
Migrating a request from one group to another increases the memory requiremen ts of a displa y
b ecause relativ e in time the retriev al of data falls ahead of its displa y Migrating a request from
G
to G
increases the memory requiremen t of this request b y three buers This is b ecause when a
request migrates from G
to G
Figure G
reads X
and sends it to the displa y During the same
time p erio d G
reads X
in to a buer sa y B
and G
reads X
in to a buer B
During the
next time p erio d G
reads X
in to a buer B
and X
is displa y ed from memory buer B
G
reads X
b ecause the groups mo v e one cluster to the rightatthe endofeac h time p erio d During
the next time period G
reads X
in to a memory buer B
while X
is displa y ed from memory
buer B
This roundrobin retriev al of data from clusters b y G
con tin ues un til all blo c ks of X ha v e
b een retriev ed and displa y ed
With this tec hnique if the distance from the original group to the destination group is B B
buers are needed for load balancing A request ma y migrate bac k to its original group once a
request in the original group terminates and relinquishes its slot ie time slot b ecomes idle This
reduces memory requiremen t of the displa y When k C N with the prob of
P
C N k
p k load balancing sc heme can b e applied
due to the a v ailabilit y of idle slots This means that Probfa group is fullg Hence p
f
k If k C N with the prob of
P
m k C N
p k no load balancing sc heme can b e applied
b ecause no empt y slot is a v ailable in some groups and load is already ev enly distributed
Hence the probabilit y of failures is
p
f
i k
C i
k
i
C i k
i C
k
where k
k C N The exp ectation of latency with load balancing is
E L
C N X
k p k T
p
m X
k C N k
X
i p k p
f
i k
i T
p
Ob ject Replication
T o reduce the startup latency of the system one ma y replicate ob jects By replicating an ob ject
once and starting its assignmen t with a cluster dieren t than the one con taining its other replica
the maxim um startup latency can be reduced b y one half ob ject X in Figure This migh t also
reduce the exp ected latency The assignmen t of the rst blo c k of the replicas of an ob ject should be separated b y a xed
n um b er of clusters in order to maximize the b enets of replication T o assign R additional copies of
an ob ject X to the disk clusters w e n um ber them from R
X to R
XR
Note that with the primary
copyof X a total of R instances of X reside in the database The primary cop y can b e assigned
starting with an arbitrary cluster sa y cluster C
i
The assignmen t of the rst blo c k of cop y R
Xj
should starts with cluster C
i
jC
R mod C F or example Figure sho ws the placemen t for three
instances of ob ject Y primary cop yand t w o copies R
Y R
Y The primary copyof Y is assigned
starting with cluster C
R
Y cop y is assigned starting with cluster C
while R
Y is assigned starting
C CC C CC
2 1 0 3 4 5
X XX X X X
X
YY Y YY Y
Y
0 12 3 4 5
6
4 5 0 1 2 3
6
...
...
X XX X X X
X
3 45 0 1 2
6 ...
YY Y Y Y Y
Y
2 3 4
5
0 1
6
...
Y Y Y YY Y
Y
0 1 2
3 4 5
6
...
Figure An example of m ultiple cop y placemen t
with cluster C
This assignmen t reduces both the maxim um and the exp ected startup latency of
the system
When there are t w o copies of an ob ject the exp ected latency can be computed as follo ws T o
nd an a v ailable serv er the system sim ultaneously c hec ks t w o groups corresp onding to the t w o
dieren t clusters that con tain the rst blo c ks of t w o copies of the ob ject A failure happ ens only
if both groups are full reducing the n um ber of failures for a request The maxim um n um ber of
failures b efore a success is reduced to b
k
N
c due to t w o sim ultaneous c hec king of groups pro ceeding
in parallel Therefore the probabilit yof i failures in a system with eac h ob ject ha ving t w o copies is
iden tical to that of the system ha ving N serv ers in a cluster with
C
clusters
F or an arbitrary j copies of eac h ob ject in the system the probabilit y of a request observing i
failures is
p
f
j
i k
m j i N
k j i N
m j i N
k j i N
m
k
where i b
k
j N
c Hence the exp ected latency is
E L
m X
k b
k
j N
c
X
i
p k p
f
j
i k i T
p
Replicating all ob jects increases the storage requiremen t of an application One imp ortan t ob
serv ation in real applications is that ob jects ma y ha v e dieren t access frequencies F or example in
Probability
Number of failures before a success
5 10 15 20
0
0.2
0.4
0.6
0.8
1
Figure The probabilit y of failures
VideoOnDemand system more than half of the activ e requests migh t reference only a handful of
recen tly released mo vies
Selectiv e replication for frequen tly referenced ie hot ob jects could signican tly reduce the
latency without a dramatic increase in storage space requirementof an application Selectiv e repli
cation pro vides for a higher n um b er of replicas for the hot ob jects The n um b er of copies p er ob ject is
based on its access frequency and with a giv en system storage capacit y can b e computed b ysev eral
algorithms as describ ed in IK Using one of these algorithms w e classify ob jects b y the n um ber
of copies per ob ject Therefore ob jects in a class ha v e the same n um ber of copies An example of
classication is sho wn in T able Let R
i
be the n um ber of copies per ob ject in class i and F
i
the
total access frequency of ob jects in class i The exp ected latency in this system with n classes is
E L
n
X
i
F
i
E L
R
i
where E L
R
i
is the exp ected latency for ob jects ha ving R
i
copies p er ob ject This is computed using
Equation A Comparison
W e conducted sev eral exp erimen ts to analyze ho w the exp ected startup latency of a system
b eha v es as a function of the n um ber of disk clusters and system load and to compare request
migration with replication In our exp erimen ts eac h disk driv e pro vides a Mbs transfer rate
R
D
and a maxim um seek time of milliseconds including maxim um rotational latency of milliseconds W e consider a single media t yp e requiring Mbs bandwidth R
C
for its con tin uous
displa y W e assume a P oisson arriv al rate for user requests and an exp onen tial distribution for the service
time of eac h request Up on arriv al of a request it is assigned to aserv er of the m a v ailable serv ers
in the system If all the serv ers in the system are busy then this request is rejected Let be the
a v erage arriv al rate of requests and s the a v erage service time In our exp erimen ts w e xed s to
min utes
In the rst exp erimen t w e computed the probabilit y that a request exp eriences a certain n um ber
of failures b efore b eing assigned to a serv er W e assumed a serv er system consisting of clusters
groups with slots p er group and an arriv al rate of requests p er min ute This assumed
arriv al rate results in a system utilization Figure sho ws that the probabilit y of a request
observing m ultiple failures is v ery small relativ e to a single failure F or example the probabilit yofa
request exp eriences failures is only while the probabilit y of a request exp eriences zero failure is
higher than Another observ ation is that of requests exp erience less than failures Because
latency is a function of the n um b er of failures this implies that the exp ected startup latency could
b e far less than the maxim um startup latency In our assumed en vironmen t the exp ected latency is
seconds while the w orst latency is seconds Similar trends w ere observ ed when wev aried the
arriv al rate of requests and the n um b er of clusters in the system
Next w e increased b oth the n um b er of clusters and the arriv al rate of requests b y a xed factor to
analyze the scalabilityc haracteristics of the system The obtained results are presen ted in Figure W e xed the throughput of a t w odisk cluster at serv ers and at requests p er min ute as the
base conguration Next w e increased b oth the n um ber of serv ers and the arriv al rate of requests
bya xed factor The xaxis of Figure presen ts this factor of increase F or example the v alue on the xaxis captures a system consisting of clusters with an arriv al rate of requests p er
min ute The increase in b oth system resources and the arriv al rate of requests results in a constan t
utilization of system resources Figure a demonstrates a linear increase in system throughput
Figure b sho ws a linear increase in the maxim um startup latency Ho w ev er note that the exp ected
latency remains stable Moreo v er the latency incurred b y of requests is nonlinear as a function
of additional resources This v alue drops past a factor of ten increase in additional resources This is
due to a lo w er n um b er of failures p er request With a factor of increase of requests observ e
few er than nine failures With a factor of increase it reduces to six
In a third exp erimen t w e explored the relationship b et w een the n um ber of serv ers within a group
Throughput
Factor of increase
5 10 15 20
0
20
40
60
80
100
Latency
( seconds)
Factor of increase
5 10 15 20
0
2.5
5
7.5
10
maximum
98%
expected
a Throughput b Latencies
Figure System p erformance byv arying resources n
and the total n um b er of groups Giv en a desired n um ber of sim ultaneous displa ys as one increases
the n um ber of serv ers per group the total n um ber of groups decreases T o illustrate assume that
a system designer striv es to supp ort sim ultaneous displa ys If eac h group supp orts v e serv ers
then the system requires groups On the other hand if eac h group supp orts ten serv ers then only
groups are required In a system consisting of few er groups the n um ber of failures is reduced
Ho w ev er this do es not translate in to alo w er exp ected latency b ecause the duration of time p erio d
T
p
increases as a function of the n um ber of serv ers per group T o demonstrate this w e assumed
that a cluster consists of four disk driv es By v arying the blo c k size from megab ytes to megab ytes the n um ber of sim ultaneous displa ys supp orted b y this cluster v aries from to ie
the n um b er of serv ers in a group mayv ary from to serv ers Ho w ev er this increases the duration
of a time p erio d from seconds to second Assuming a system that supp orts sim ultaneous
displa ys to requests p er min ute utilization of the system Figure sho ws the n um ber
of failures as a function of the n um b er of serv ers in a cluster the duration of a time p erio d using
Equation and the exp ected latency of the system Note that while the n um ber of failures
decreases as a function of the n um ber of serv ers the duration of a time p erio d increases resulting in a
higher exp ected latency As one increases the n um ber of serv ers p er group the total n um ber of disks
required to supp ort displa ys decreases T o illustrate with v e serv ers p er group or cluster the
system requires groups clusters resulting in a system with disks recall that there are four
disks p er cluster With ten serv ers p er group or cluster the system requires groups clusters
resulting in a system with disks The c hoice of a v alue for the n um ber of serv ers in a group
2 4 6 8 10 12
0
1
2
3
4
5
6
7
Expected latency
Duration of a time period
Number of failures
Latency
(sec)
No. of servers in a cluster
Figure Latency as a function of the n um ber of serv ers in a group
dep ends on the p erformance criteria of a target application and the nal cost of the system
In a nal exp erimen t w e analyzed the impact of selectiv e replication attributed to the access
frequency of eac h ob ject T able sho ws an example of classied ob jects with their n um ber of
copies and access frequencies F or example class consists of ob jects with copies per ob ject
and the total access frequency of these ob jects is By v arying the arriv al rate from utilization of the system to w e computed the exp ected latency for three p ossible
scenarios with a database consisting of unique ob jects The rst case Case replicates none
of the ob jects With Case eac h ob ject is replicated once ob jects replicas With Case
the n um ber of copies per ob ject is determined based on its classication as sho wn in T able A
xed throughput of sim ultaneous displa ys is assumed in this exp erimen t Figure sho ws that
replication signican tly reduces the exp ected latency When w e assume that the size of eac h ob ject
is iden tical Case requires the minimal amoun t of storage Ho w ev er it incurs a higher exp ected
latency when compared with b oth Case and Case outp erforms Case while requiring a lo w er
amoun t of storage This is b ecause it replicates the frequen tly accessed video clips more than t w o
times in order to minimize the exp ected latency of requests accessing these ob jects
In the same exp erimen t w e computed exp ected latency with the load balancing sc heme of Sec
tion that migrates requests Request migration pro vides for a sligh tly b etter latency at all times
dashed lines in Figure It has a signican t impact with Case when no replication of ob jects
is allo w ed With a lo w system load it enables Case to p erform as w ell as the other
t w o cases Ho w ev er applying this sc heme should be carefully considered b ecause it migh t require
signican t amoun t of extra memory when migrating requests The memory requiremen t could not
Expected latency
(seconds)
Arrival rate (requests/min)
0.6 0.7 0.8 0.9 1
0
0.5
1
1.5
2
Case 1
Case 2
Case 3
Figure A comparison b et w een dieren t database congurations
Class of copies of T otal access T otal p er ob ject ob jects frequency F
i
of copies
T able An example of classied replication of ob jects
b e analyzed analytically Wein tend to employsim ulation based studies to quan tify this factor
Conclusions and F uture Researc h Directions
Striping enables a scalable serv er to supp ort a higher n um ber of sim ultaneous displa ys as a function of
additional disk clusters In this studyw edev elop ed analytical mo dels that quan tify ho w the exp ected
startup latency of a system b eha v es as a function of additional resources Our exp erimen tal results
indicate that the exp ected latency is dep enden t on the load of the system arriv al rate of requests
and do es not necessarily scale as a function of additional resources Replication is one approachto
minimize the exp ected latency T o minimize the storage requiremen ts of this approac h the system
should selectiv ely replicate the hot ob jects sev eral times and start the assignmen t of eac h replica
with a dieren t cluster An alternativ e approac h to replication migrates a request from one group
to another in order to balance the load more ev enly across the groups With a lo w system loads
this tec hnique p erforms as w ell as ob ject replication Ho w ev er with a high system load replication
is sup erior to this alternativ e
As part of our future researc h w ein tend to quan tify the memory requiremen ts of request migra
tion using a sim ulation study In addition w ein tend to dev elop online algorithms for replication of
ob jects across the a v ailable clusters
References
BGMJ S Berson S Ghandeharizadeh R Mun tz and X Ju Staggered Striping in Multimedia
Information Systems In Pr o c e e dings of the A CM SIGMOD International Confer enceon
Management of Data pages CP P M Chen and D P aterson A new approac h to IO p erformance ev aluation self
scaling IO b enc hmarks predicted IO p erformance In Pr o c e e dings of the A CM
SIGMETRICS Intl Conf on Me asur ement and Mo deling of Computer Systems Ma y
GK S Ghandeharizadeh and SH Kim Striping in Multidisk Video Serv ers In Pr o c e e dings
of SPIE HighDensity Data R e c or ding and R etrieval T e chnolo gies Confer enc e Octob er
GKS S Ghandeharizadeh S H Kim and C Shahabi On Conguring a Single Disk Con tin
uous Media Serv er In Pr o c e e dings of the A CM SIGMETRICSMa y
GRA Q S Ghandeharizadeh L Ramos Z Asad and W Qureshi Ob ject Placemen t in Parallel
Hyp ermedia Systems In Pr o c e e dings of the International Confer enc e on V ery L ar ge
Datab ases pages Septem ber IK T Ibark ai and N Katoh R esour c e Allo c ation Pr oblems A lgorithmic Appr o aches The
MIT Press
Kle L Kleinro c k Queueing Systems V olume I The ory page WileyIn terscience
MY A Merc hantand P S Y u Analytic Mo deling and Comparisons of Striping Strategies for
Replicated Disk Arra ys IEEE T r ansactions on Computers Marc h
P ol VG P olimenis The Design of a File System that Supp orts Multimedia T ec hnical
Rep ort 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 A L N Reddy and J C Wyllie IO Issues in a Multimedia System IEEE Computer
Magazine Marc h
TPBG FA T obagi J P ang R Baird and M Gang Streaming RAIDA Disk Arra y Manage
men t System for Video Files In First A CM Confer enc e on Multime dia August WYS JL W olf P S Y u and H Shac hnai DASD Dancing A Disk Load Balancing Sc heme
for VideoonDemand Systems In Pr o c e e dings of A CM SIGMETRICS YCK P S Y u M S Chen and D D Kandlur Design and Analysis of a Group ed Sw eep
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
Abstract (if available)
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Description
Shahram Ghandeharizadeh and Seon Ho Kim. "An analysis of striping in scalable multi-disk video servers." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 623 (1995).
Asset Metadata
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Ghandeharizadeh, Shahram
(author),
Kim, Seon Ho
(author)
Core Title
USC Computer Science Technical Reports, no. 623 (1995)
Alternative Title
An analysis of striping in scalable multi-disk video servers (
title
)
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Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA
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