USC Computer Science Technical Reports, no. 600 (1995)

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Shahram Ghandeharizadeh and Cyrus Shahabi. "Management of virtual replicas in parallel multimedia information systems." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 600 (1995).

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Content Managemen t of Virtual Replicas in P arallel Multimedia
Information Systems
Shahram Ghandeharizadeh Cyrus Shahabi
Departmen t of Computer Science
Univ ersit y of Southern California
Los Angeles California Abstract
Multimedia information systems ha v e emerged as an essen tial comp onentofman y application
domains ranging from library information systems to en tertainmenttec hnologyHo w ev er most
implem en tations of these systems based on a w orkstation cannot supp ort a con tin uous displa y
of m ultim edia ob jects and suer from frequen t disruptions and dela ys termed hic cups This is
due to the lo w IO bandwidth of the curren t disk tec hnology the high bandwidth requiremen tof
m ultim edia ob jects and the large size of these ob jects whic h requires them to b e almost alw a ys
disk residen t One approac h to resolv e this limitatio n is to decluster a m ultimedia ob ject across
m ultiple disk driv es in order to emplo y the aggregate bandwidth of sev eral disks to supp ort
its con tin uous retriev al and displa y T o supp ort sim ultaneous displa y of sev eral m ultimedia
ob jects for dieren t users the system can replicate data across m ultiple groups of disk driv es in
a virtual manner This pap er describ es tec hniques to manage the replicas of ob jects in a parallel
m ultim edia information system These tec hniques are general and can b e customized bythe
database administrator to satisfy the constrain ts of an application W equan tify the tradeos
asso ciated with these strategies using a sim ulation study In tro duction
During the past decade information tec hnology has ev olv ed to store and retrievem ultimedia data
eg audio video Multimedia information systems utilize a v arietyof h uman senses to pro vide
an eectiv e means of con v eying information Already these systems pla y a ma jor role in educa
tional applications en tertainmenttec hnology and library information systems A c hallenging task
when implemen ting these systems is to supp ort a realtime displa yof m ultimedia ob jects By
realtime w e mean a con tin uous retriev al of an ob ject at the bandwidth required b y its media
This researchw as supp orted in part b y the NSF gran t IRI and the NYI a w ard IRI This pap er
app eared in the Pr o c e e dings of the F oundations of Data Or ganization and A lgorithms F ODO Confer enc e Octob er
t yp e This is c hallenging b ecause certain media t yp es in particular video require v ery high band
widths F or example the bandwidth required b yNTSC
for net w orkqualit y video is ab out megabits p er second m bps Has Recommendation of the In ternational Radio Consultativ e
Committee CCIR calls for a m bps bandwidth for video ob jects A video ob ject based on the
HDTV High Denition T elevision qualit y images requires appro ximately a m bps bandwidth
Compare these bandwidth requiremen ts with the t ypical m bps bandwidth of a magnetic disk
driv e
whic h is not exp ected to increase signican tly in the near future PGK Presen tly there
are sev eral w a ys to supp ort a realtime displa y of these ob jects sacrice the qualit y of the data
b y using either a lossy compression tec hnique eg predictiv e Ben frequency orien ted LB
imp ortance orien ted Gre etc or a lo w resolution device emplo y the aggregate bandwidth of
sev eral disk driv es b y declustering an ob ject across m ultiple disks GRA Q and use a com bina
tion of these t w o tec hniques Lossy compression tec hniques enco de data in to a form that consumes
a relativ ely small amoun t of space ho w ev er when the data is deco ded it yields a represen tation
similar to the original some loss of data While it is eectiv e there are applications that cannot
tolerate loss of data As an example consider the video signals collected from space This infor
mation ma y not b e compressed using a lossy compression tec hnique Doz Otherwise scien tists
who later uncompress and analyze the data run the risk of either observing phenomena that ma y
not exist due to a slightc hange in data or miss imp ortan t observ ations due to some loss of data
The fo cus of this study is on parallel m ultimedia information systems and applications that
cannot tolerate loss of data In order to simplify the discussion w e assume a sharednothing Sto arc hitecture or a m ulticomputer as our hardw are platform
Briey a sharednothing arc hitecture
consists of a n um b er of pro cessors in terconnected b y a high sp eed comm unication net w ork suchasa
h yp ercub e or a ring A pro cessor consists of a CPU a disk driv e and some random access memory Pro cessors do not share disk driv es or random access memory and can only comm unicate with one
another b y sending messages F urthermore w e assume that the stations used to displa y ob jects are
indep enden t of the bac k end pro cessors that con tain the data almost iden tical to a banking system
whic h consists of a bac k end database engine and m ultiple A TMs attac hed to it In this study w e fo cus on the IO b ottlenec k phenomena and assume that the bandwidth of b oth the net w ork
and the net w ork device driv er exceeds the bandwidth requiremen t of an ob ject This assumption
The US standard established b y the National T elevision System Committee
The concepts describ ed in this pap er are applicable to other secondary storage devices
There are also lossless compression tec hniques eg Human Lemp el Zev etc While a go o d estimate for
reduction in size with these tec hniques is an ywhere from a factor of to with lossy tec hniques it ranges from
a factor of to F o x Consequen tly it is generally accepted that lossless compression tec hniques cannot
supp ort a realtime displa y of video ob jects
Ho w ev er the tec hniques describ ed in this pap er can b e extended to a m ultidisk arc hitecture eg RAID PGK
Station
Display
Station
Tertiary
Storage
Device
K
0
K
1
K
R-1
Display
Scheduler
. . . . . .
. . . . . .
CPU CPU CPU CPU CPU
Fast Network
Figure Virtual data replication
is justied considering the curren ttec hnological trends In this pap er the term pro cessor is
used to imply a no de of the sharednothing arc hitecture consisting of a CPU some
RAM and one disk driv e
Assuming a xed bandwidth for eac hdisk B
D isk
in the system in order to supp ort a realtime
displa y of an ob ject with bandwidth requiremen t B
D isplay
an ob ject is declustered in to M pieces
termed fragmen ts where M d
B
D isplay
B
Disk
e GRA Q GR The fragmen ts of an ob ject are
constructed using a roundrobin assignmen t of its blo c ks to eac h pro cessor enabling the system
to o v erlap the displa y of an ob ject at a displa y station with its retriev al from the disk driv es
m ultiinput pip elini ng
One approac h to enable the system to supp ort sim ultaneous displayofm ultiple ob jects to
dieren tusers is virtual data r eplic ation
This tec hnique extends the sharednothing arc hitecture
with a tertiary storage device that is accessible to all the pro cessors in the system see Figure The database resides p ermanently on the tertiary storage device Assuming that all ob jects b elong
to a single media t yp e eac h ob ject has M as its degree of declustering this tec hnique organizes a
P pro cessor system in to R pro cessor partitions R b
P
M
c A partition stores ob jects transien tly
ie reads ob jects from the tertiary storage device as the need arises and deletes ob jects when its
storage capacit y is exhausted T ypically a partition con tains a fraction of the database ho w ev er
An alternativ e approachisdisk m ultitasking w e refer the in terested reader to GR for a complete description
and ev aluation of this tec hnique

it ma y con tain the en tire database if its storage capacit y exceeds the size of the database enabling
the system to supp ort R sim ultaneous displa ys This tec hnique is named virtual data replication
b ecause logically the database is replicated R times and eac h replica is virtual ie cac hed
in from the tertiary storage device on demand W e use the follo wing terminology for the rest of this
pap er All partitions con tain a virtual replica of an ob ject sa y o
x
Once a partition materializes
o
x
from the tertiary storage device it is said to con tain a physic al replica of o
x
A partition can
displa y o
x
only if it has a ph ysical replica of o
x
W e assume a pro cessor in the system is designated as the cen tralized sc heduler
This site
main tains the a v ailabilit y of eac h partition and the ob jects that are stored on eachof the R partition
All requests are rst directed to the cen tralized sc heduler When a user requests an ob ject o
x
the
sc heduler determines those idle partitions that con tain a ph ysical replica of o
x
If suc h partitions
exist it emplo ys one of them to service the request Otherwise the sc heduler determines the busy
partitions that containaph ysical replica of o
x
Either there exist at least one or none of the
partitions has a ph ysical replica of o
x
Consider eac h case in turn
If one or more partitions con tain a ph ysical replica of o
x
the sc heduler has t w o p ossible
c hoices It can either queue the request and w ait for the partition with the least w ait time
to b ecome a v ailable or utilize an idle partition that do es not con tain a ph ysical replica of o
x
sa y K
to materialize o
x
and then displa y it In the second case if the storage capacit yof K
has b een exhausted then the sc heduler should also determine whic h ob jects of this partition
should b e deleted in order to pro vide sucien t space for o
x
The decision b et w een these t w o
alternativ es has an impact on b oth the resp onse time of the system and the frequency of
access to the tertiary storage device
If none of the partitions con tains a ph ysical replica of o
x
the sc heduler c ho oses an idle
partition sa y K
to materialize a replica of o
x
and displa y o
x
once it is materialized
If the storage capacityof K
has b een exhausted then the sc heduler also determines whic h
ob jects of this partition should b e deleted in order to pro vide sucien t storage space for o
x
This pap er formalizes the problems asso ciated with managing replicas It describ es p olicies em
plo y ed b y the cen tralized sc heduler to determine the partition that should service a request in order
to maximize the p erformance of the system These p olicies are general and emplo ysev eral param
W e are a w are that the cen tralized sc heduler ma y b ecome a b ottlenec k and limit the capabilit y of the system to
scale to a large n um b er of pro cessors As discussed in Section w ein tend to replace the cen tralized sc heduler with
no v el distributed sc heduling p olicies

T erm Denition
B
D isplay
Bandwidth required to displa y an ob ject
B
D isk
Bandwidth of a single disk driv e
B
T ertiary
Bandwidth of the tertiary storage device
M Degree of declustering for an ob ject M d
B
D isplay
B
Disk
e
P Num b er of pro cessors in the system
R Num b er of partitions in the system R b
P
M
c
heat o
x
F requency of access to ob ject o
x
siz e o
x
Size of ob ject o
x
NOW The curren t time
T
D isplay
o
x
Time to displa y o
x
T
D isplay
o
x

siz e o x B
D isplay
T
M ater ializ e
o
x
Time to Materialize o
x
from tertiary storage T
M ater ializ e
o
x

siz e o x B
T er tiar y
FDT o
x
F uture Displa y Time of o
x
FDT o
x
heat o
x
T
D isplay
o
x
U sag e K
i
F uture usage time of partition K
i
AT K
i
Sp ecies when partition K
i
will b e a v ailable to service another request
T able List of terms used rep eatedly in this pap er and their resp ectiv e denitions
eters to enable the database administrator DBA to customize them to satisfy the requiremen ts
of an application
These p olicies are no v el and dieren t than those describ ed in the op erating system or database
system literature designed to manage the frames of a buer p o ol due to t wono v el features of our
system when a partition is emplo y ed to either materialize an ob ject from the tertiary storage
device or service a request the ph ysical replica of its other ob jects b ecome una v ailable and in certain cases it migh tbeadv an tageous to materialize a frequen tly accessed ob ject on sev eral
partitions in order to a v oid a partition from b ecoming the b ottlenec k for the system
Ov erview
In this studyw e assume
The size of eac h ob ject in the database is smaller than the storage capacit y of a partition A
partition maycon tain the ph ysical replica of sev eral dieren t ob jects ho w ev er it con tains at
most one ph ysical replica of an ob ject
The database consists of a single media t yp e with bandwidth requiremen t B
D isplay
ie the
degree of declustering is M for all ob jects

The bandwidth of the tertiary storage device is lo w er than the bandwidth requirementofan
ob ject B
T er tiar y
B
D isplay
hence its bandwidth is lo w er than that of a partition recall
that B
D isplay
M B
Disk

The frequency of access and the size of eac hobjectis pro vided termed he at o
x
and size o
x
resp ectiv ely CABK
Using assumption w e dene the exp ected F uture Displa y Time of an ob ject o
x
as
FDT o
x
heat o
x
T
D isplay
o
x
where T
D isplay
o
x
is the time required to displa y o
x
Assuming that a partition sa y K
i
con tains
the ph ysical replica of q ob jects its future usage time is
Usage K
i

q
X
j FDT o
j
In order to maximize the pro cessing capabilit y of the system the Usage of eac h of its partitions
should b e almost iden tical
Once a request for ob ject o
x
is issued the sc heduler can reachv e dieren t states
A One or more idle partitions con tain a ph ysical replica of o
x
B One or more busy partitions con tain a ph ysical replica of o
x
C There is one or more idle partitions with sucien t storage space to materialize o
x
these
partitions do not con tain a ph ysical replica of o
x

D There is one or more idle partitions with insucien t storage space to materialize o
x
these
partitions do not con tain a ph ysical replica of o
x

E None of the partitions is idle and no partition con tains a ph ysical replica of o
x
Both the transition from one state to another and the decisions made at eac h state dep ends on the
requiremen ts of an application In this study the p olicies dev elop ed for eac h state can b e tailored
to ac hiev e the follo wing goals
Minimize the frequency of access to the tertiary storage device in order to reduce its proba
bilit y of b ecoming a b ottlenec k for the system

Minimize the resp onse time of the system
Distribute the w orkload of the system ev enly across the partitions in order to a v oid the
formation of hot sp ots and b ottlenec k partitions GD A customized p olicy can b e further ne tuned to ac hiev e its goal for either the p ending request
termed Gpr esent
i
or the future requests termed Gf utur e
i
This c hoice is due to our
kno wledge of the exp ected frequency of access to eac h ob ject the assumption that a partition
ma y con tain the ph ysical replica of m ultiple ob jects and once a partition is emplo y ed to either
displa y an ob ject or materialize it from the tertiary storage device the ph ysical replica of other
ob jects a v ailable on this partition b ecome una v ailable for the duration of this op eration The c hoice
bet w een Gpr esent
i
Gp
i
and Gf utur e
i
Gf
i
dep ends on the accuracy of heat o
x
andthe
requiremen ts of an application The presen t and future impact of eac h goal is as follo ws
Gp
Minimize the probabilit y of access to the tertiary storage device for the p ending request
Gf
Service the p ending request with the ob jectiv e to minimize the frequency of access to the
tertiary storage device for the future requests
Gp
Service the p ending request as so on as p ossible
Gf
Service the p ending request with the ob jectiv e to minimize the resp onse time for future
requests
Gp
Service the p ending request to appro ximate an ev en distribution of the load for the presen t
Gf
Service the p ending request in order to ev enly distribute the load for the future requests
In general to satisfy Gp
w e service a request b y utilizing a partition that con tains a ph ysical
replica of o
x
if a v ailable T o satisfy Gp
a request is serviced using the partition with the least
w ait time T o satisfy Gp
a request is serviced using the partition with the longest idle time
As w e assume no prior kno wledge of the sequence of requests for the ob jects in order to satisfy
Gf
Gf
and Gf
a request is serviced b yemplo ying the partition with the least future U sag e
see Equation This distributes the w orkload of an application ev enly across the partitions
maximizing the o v erall pro cessing capabilit y of the system and a v oids the formation of hot sp ots
that ha v e a div erse impact on Gf
Gf
and Gf
Due to this similarit y these goals are com bined
in to one termed Gf
P artition Materialized AT Idle Remaining
id ob jects Time Space
K
o
o
o
K
K
o
o
o
K
K
o
K
T able P artition T able
The rest of this pap er is organized as follo ws Section describ es the data structures main tained
b y the cen tralized sc heduler Section describ es tec hniques for decision making at eachstate
in order to implemen t the alternativ e goals Section describ es the alternativ e state transition
diagrams for the system to visit the dieren t states Section ev aluates the alternativ e decision
making p olicies and state transition diagrams using a sim ulation study Our conclusion and future
researc h directions are con tained in Section Sc heduler and its Data Structures
The sc heduler main tains the status of the tertiary storage device and its queue of request the a v ailabilityof eac h partition and the ph ysical replica of ob jects stored on that partition using
a partition table and the dieren t ob jects in the system and the partitions con taining their
ph ysical replicas using an ob ject table
The sc heduler main tains when the tertiary storage device w ould b e a v ailable to service a re
quest termed Av ailable at Time AT tertiary Using this v ariable and the curren t time termed
NO W the sc heduler can compute the w ait time for this device if NO W AT ter tiar y then
w ait time ter tiar y otherwise wait time ter tiar y AT ter tiar y NOW F or eac h partition K
i
i R the partition table main tains a list of ob jects curren tly
materialized on K
i
when K
i
w ould b e a v ailable to service another request AT K
i
the total time
that K
i
has b een idle since the system generation time and the storage space a v ailable on K
i
see
T able Once a request for an ob ject o
x
is issued if the sc heduler emplo ys an idle partition sa y
K
to service this request then its idle time is adjusted as follo ws
Idle T ime K
Idle T ime K
NOW AT K
If K
has a ph ysical replica of o
x
then its AT is adjusted as follo ws
AT K
NOW T
D isplay
o
x

Ob ject id P artitions Size Heat
o
K
K
o
K
K
K
K o
K
K
T able Ob ject T able
If K
do es not con tain a ph ysical replica of o
x
and is required to materialize it from the tertiary
storage device then
AT K
NOW wait time ter tiar y T
M ater ializ e
o
x
T
Display
o
x
where T
M ater ializ e
o
x
is the time required to read ob ject o
x
from the tertiary storage device In
this case the sc heduler ensures that its a v ailable storage space is greater than the size of o
x
using
the last eld of T able F or eachobject o
x
the ob ject table see T able main tains a list of partitions con taining
aph ysical replica of o
x
size o
x
and heat o
x
This table is used to determine the candidate
partitions that con tain the ph ysical replica of a requested ob ject
Decisions Made at Eac h State
Giv en a request for ob ject o
x
the decisions made at eac h state are as follo ws
A Cho ose one of sev eral idle partitions with a ph ysical replica of o
x
to service this request
B Cho ose one of sev eral busy partitions with a ph ysical replica of o
x
to service this request at
some p oin t in the future
C Cho ose one of sev eral idle partitions to materialize and displa y o
x
D In addition to c ho osing one of sev eral idle partitions to materialize o
x
the sc heduler decides
whic h ob ject of this partition should b e deleted to pro vide sucien t space for o
x
E No decisions are made The request is queued and once a partition b ecomes a v ailable the
sc heduler services this request b y starting from state A see Section for the alternativ estate
transition diagrams

W e start b y describing howstate Bmak es its decision Next Section describ es a tec hnique to
c ho ose b et w een the a v ailable partitions This tec hnique is utilized b y states A C and D Section fo cuses on state D and describ es a tec hnique to determine the ob jects that should b e deleted
Best P artition for State B
Once at state B the sc heduler determines the busy partitions that con tain a ph ysical replica of o
x
Next it c ho oses one of these partitions to service the p ending request This decision impacts Gp
and Gf and has no impact on Gp
and
Gp
If the ob jectiv e is to minimize the resp onse time of
the p ending request Gp
the request should b e queued at the partition with the minim um w ait
time minim um AT K
i
Ho w ev er if the ob jectiv eis to satisfy Gf this request should b e queued
at the partition with the minim um future usage time minim um U sag e K
j
By emplo ying K
j
the system frees other partitions with a higher future usage time to service other requests
The DBA mayw an t to customize state B to asso ciate a dieren tw eightwith eac h goal T o
do so AT and Usage of eac h candidate partition should b e compared using the sp ecied w eigh t
There are t w o problems asso ciated with this First these t wov ariables are in terms of dieren t
units AT is units of time while U sag e is in terms of b oth time and heat Second these v ariables
are based on dieren t scales Our solution to b oth problems is to normalize eac h comp onentas
follo ws
AT
N or maliz ed
K
i

AT K
i
AT
Av g
U sag e
N or maliz ed
K
i

U sag e K
i
Usage
Av g
Both AT
Av g
and U sag e
Av g
are computed b y considering only those partitions that satisfy the
constrain ts of state B and NOT all the partitions in the system Next state B queues this
request at partition K
i
with minim um v alue for
U sag e
N or maliz ed
K
i

Gp
Gf
AT
N or maliz ed
K
i
Both Gp
and Gf are p ositiverealn um b ers ranging in v alue from zero to one These parameters
enable the DBA to sp ecify a dieren tw eigh t for eac h ob jectiv e By c ho osing a v alue close to one
for Gp
and a small v alue for Gf close to zero state B services this request b y emplo ying the
partition with the least w ait time appro ximates Gp

Once at state B all partitions are busy Consequen tly Gp is meaningless Moreo v er Gp is already satised as
the system will not access the tertiary storage device

Once the system decides to en ter state B this request is queued at the c hosen partition sa y
K
x
and AT K
x
is incremen ted with T
D isplay
o
x
Best P artition for States A C and D
Ateac h state A C and D the sc heduler migh t b e required to c ho ose b et w een sev eral partitions
that satisfy the constrain ts of that state F or example once at state A there migh tbe m idle
partitions that con tain a ph ysical replica of o
x
and the system m ust c ho ose one of these partitions
F or eac h state the decision b et w een the a v ailable partitions has an impact on Gp
and Gf and
no impact on either Gp
or Gp
T o satisfy Gp
the sc heduler should emplo y the partition with
the largest idle time to service this request maxim um Idle Time K
j
Ho w ev er in order to satisfy
Gf the sc heduler should emplo y the partition with the least exp ected future usage time minim um
Usage K
i
Once again the DBA can customize eac h state to giveeac h goal a dieren tw eigh t In order
to mak e the idle time and future usage of a partition comparable w e normalize eac h comp onen t
same discussion as Section and utilize the partition with the minim um v alue for
Usage
N or maliz ed
K
i
Gp
Gf
I dl e T ime
N or maliz ed
K
i
Both Gp
and Gf are p ositiv e real n um b ers ranging in v alue from zero to one
Note that w e subtract the t w o normalized comp onen ts from eac h other b ecause their ob jectiv es
conict maximum idle time vs minimum future usage
Best Ob jects for State D
Once at state D the sc heduler mak es t w o decisions the partition sa y K
x
that should materialize
and displa y the requested ob ject and the ob jects that should b e deleted from K
x
to pro vide
enough space to materialize o
x
There are t w o p ossible w a ys of making these decisions
P artitionbased
Use the tec hnique of Section to nd the b est idle partition sa y K
Best
among those
that satisfy the constrain ts of state D
Find the ob jects to b e sw app ed out ie deleted from K
B est
to materialize o
x

Ob jectbased
F or eac h idle partition K
i
that satises the constrain ts of state D do
a Find the ob jects to b e sw app ed out from partition i to materialize o
x
b Store these ob jects in a list sa y O l ist
K
i
The partition K
j
corresp onding to the Olist
K
j
with the minim um FDT v alue is c hosen
to materialize o
x
if O l ist
K
j
consists of q ob jects its FDT is
P
q
i
FDT o
i

Figure presen ts an algorithm to determine the b est ob jects to b e deleted from a sp ecic
partition this algorithm is used b y Step of the partitionbased strategy and Step a of the
ob jectbased strategy The inputs to this algorithm are a partition K
i
the amoun tof
storage space required ie size of the ob ject to b e materialized and an empt y list The output
of this algorithm is a list of ob jects to b e replaced these ob jects are returned b y inserting them
in to the input empt y list Giv en a partition this algorithm c ho oses ob jects with the least future
displa y time as the candidate ob jects to b e replaced
The ob jectbased strategy c ho oses the b est set of ob jects to b e replaced globally and emplo ys
the partition that con tains these ob jects to service the p ending request On the other hand the
partitionbased strategy c ho oses the b est partition to service a request and replaces the b est ob jects
in that partition The c hoice b et w een these t w o strategies is application dep enden t and the DBA
mayw an t to customize the system to strik e a compromise b et w een these t w o strategies T odoso w e dene the follo wing strategy
F or eac h idle partition K
i
that satises the constrain ts of state D do
a Find the ob jects to b e sw app ed out from partition i to materialize o
x
b Store these ob jects in a list sa y Olist
K
i
Cho ose the partition sa y K
j
with the minim um v alue for
FDT
N or maliz ed
K
j

G
obj ect based
G
par tition based
FDT
N or maliz ed
Olist
K
j

Both G
obj ect based
and G
par tition based
are p ositiv e real n um b ers ranging in v alue from zero to
one W e normalize the FDT of a partition and its ob jects in order to mak e them comparable

Intr a Partition Best Obje ct K S
x
O
List

Determine the b est candidate ob jects to b e sw app ed out from partition K partition K con tains the ph ysical replica of q ob jects Min MaxFDT
MinCand Null
for i to q do
CandList DelList Null
i ary exhausted F ALSE
i ary candidate is found or it either is w orthless or do es not exist while NOT i ary exhausted do
for all i ary ob jects in K i ary ob jects in DelList calculate the FDT O
i ar y
C andF D T min FDT O
i ar y
C andList S
O
i ar y
wher eF DT O
i ar y
C andF D T if C andList Null OR C andF D T Min then
i ary exhausted TR UE i ary candidate do es not exist or it is w orthless else i ary candidate exists for eac h O
List
in CandList
if Siz e O
List
Remaining S pace K S
x
then
D el List O
List
DelList C andList C andList O
List
end if if C andList Nullthen i ary candidate is found MinCand CandList
Min CandFDT
i ary exhausted TR UE
end if end else end while end for return the rst elemen t O
List
of MinCand
Figure Cho osing ob jects to b e replaced

A B C D E
Figure MT A state transition diagram for Gp Alternativ e State T ransition Diagrams
In this section w e describ e three alternativ e state transition diagrams for visiting the dieren t
states W e use the follo wing terminology Once at a state eg A if no partitions satisfy the
constrain ts of that state eg no partition is idle the state has faile d Once at a state fails the
system pro ceeds to test the constrain ts of another state This section describ es the state that
initiates the transition and the order in whic h the dieren t states are visited ie the state
tr ansition diagr am emplo y ed b y the sc heduler
Dieren t transition diagrams satisfy dieren t goals In this section w e describ e three dieren t
state transition diagrams Minim um T ertiary Access transition diagram MT A to satisfy Gp
Minim um Resp onse Time transition diagram MR T to satisfy Gp
FleXible T ransition diagram
FXT to appro ximate GfW e do not describ e a state transition diagram for Gp
b ecause at this
poin t in time w e consider it unrealistic for a system ie w e cannot en vision an application that
w ould compromise either the resp onse time or throughput of the system to distribute the w orkload
ev enly for a single request
MTA p essimistic Figure sho ws the state transition diagram for Gp
minim um frequency of accesses to the tertiary
storage device Once a request is issued it visits state A If A fails state B is the next b est c hoice
b ecause the ob jectiv e is to service this request without accessing the tertiary storage device ev en
if it results in a long w ait time If B fails the subsequen t states are C and D whic h result in an
access to the tertiary storage device When D fails the request is queued un til a busy partition
b ecomes a v ailable state E Once a partition b ecomes a v ailable the sc heduler services this request
b y starting from state A This enables the sc heduler to determine if another request has materialized
o
x
on a dieren t partition and if so utilizes this partition to service the p ending request
MT A is p essimistic b ecause it allo ws at most one ph ysical copyofeac h ob ject in the system
If an ob ject is accessed v ery frequen tly the partition con taining its ph ysical copyma y b ecome hot

A
C D E
B
Figure MR T state transition diagram for Gp
and the b ottlenec k for the en tire system This is a consequence of visiting state B b efore C and
D Moreo v er state B mak es no decisions b ecause at most one busy partition con tains the ph ysical
replica of o
x
MRT optimistic Figure con tains the transition diagram that minimizes the service time of a request Giv en
a request the system starts its tra v ersal with state A If A fails it decides b et w een states B
and C This is done as follo ws It prob es state B for the busy partition that will service this
request B returns either K
B
or indicates the failure of this state Next it prob es state
C for an idle partition that will b e used to materialize the requested ob ject and displa y it This
state also returns either K
C
or If b oth states return a v alid partition the system determines
the state that results in a lo w er resp onse time and pro ceeds to that state ie if AT K
B
T
M ater ializ e
o
x
w ait time ter tiar y then go to state B otherwise go to state C If C returns and B returns a candidate partition then the system pro ceeds to state B If B returns the
system pro ceeds to state C In this case if state C also fails the system en ters state D Finally if
D also fails the request is queued at state E Once a partition b ecomes a v ailable the system tries
to service this request b y starting from state A
MR T is optimistic b ecause it uses the tertiary storage device to materialize additional ph ysical
replicas of o
x
risking the p ossiblitiy of the additional replicas not getting accessed in the future
and a request during T
M ater ializ e
o
x
to access the tertiary storage device and w ait for a longer
in terv al of time Note that the decision making p olicy emplo y ed b y states B and C see Sections and impacts the decision b et w een these t w o states

A
B C
D E
Figure FXT state transition diagram for Gf
FXT A Flexible V ersion of MR T Figure sho ws the state transition diagram for Gf termed FXT It is almost iden tical to MR T
except that it is more optimistic Once state A fails FXT decides b et w een states B C and D It
prob es eac h state for a candidate partition Assuming that eac h state succeeds and returns a v alid
partition termed K
B
K
C
and K
D
resp ectiv ely the sc heduler determines if it is faster to w ait for
a busy partition that con tains a ph ysical replica of the requested ob ject to b ecome a v ailable state
B or to materialize the requested ob ject either state C or D If it is faster to pro ceed to state B
then it do es so Otherwise it decides b et w een states C and D based on the exp ected usage time of
eac h candidate partition If Usage K
C
Usage K
D
it pro ceeds to state C otherwise it pro ceeds
to state D The justication for this is as follo ws K
C
could ha v e man y frequen tly accessed ob jects
a high usage time while K
D
con tains man y ob jects with a lo w frequency of access In this case
FXT replace the least frequen tly accessed ob jects with those that are accessed more frequen tly FXT is more optimistic than MR T b ecause if the deleted ob ject is accessed in the near future
it m ust b e materialized from the tertiary storage device This w ould result in b oth a high resp onse
time and a lo w system throughput Moreo v er the tertiary storage device ma y b ecome a b ottlenec k
for the system diminishing the o v erall pro cessing capabilit y of the system Once again the DBA s
c hoice of v alues for input parameters of states C and D impacts the candidate partition pro duced
b y eac h state and the o v erall decision to visit either state C or D P erformance Ev aluation
W e quan tied the p erformance tradeos asso ciated with the alternativ e state transition diagrams
and parameters using a sim ulation mo del of a parallel information system and a general purp ose

w orkload This mo del is implemen ted using the CSIM Sc h sim ulation language W e start
b y describing the sim ulation mo del Next w e presen t the p erformance results obtained from the
system
Sim ulation Mo del
Our sim ulation mo del consisted of v e main elemen ts the Displa y Station Cen tralized Sc hed
uler In terconnection Net w ork Pro cessor and T ertiary Storage Eac h Displa y Station
consists of a terminal whic h generates the w orkload of the system Eac h Pro cessor consists of a
CPU some RAM and a single disk driv e with a megabit p er second bandwidth B
D isk
m bps The T ertiary Storage device pro vides a megabit p er second bandwidth B
T er tiar y
m bps The In terconnection Net w ork mo dels a fully connected net w ork with a one millisecond
latency time The Cen tralized Sc heduler consists of an Ob ject Manager a P artition Manager and
aT ertiary Manager These comp onen ts main tain the data structures describ ed in Section Eac h Displa y Station s request is rst dispatc hed to the Cen tralized Sc heduler The Sc heduler
services this request based on its customized state transition diagram MT A MR T FXT and
the v alue of parameters Gp
Gp
Gf G
obj ect based
and G
par tition based
A user emplo ys a displa y station to request an ob ject W e assume that a displa y station can
displa y only one ob ject at a time In our exp erimen ts w ev aried the n um b er of displa y stations
from one to in order to v ary the system load W e assumed a closed system where once a displa y
station issues a request it do es not issue another un til the rst one is serviced W e also assume
a zero think time b et w een the requests This parameter w as c hosen in order to stress the system
and in v estigate its limitations
The database consisted of a single media t yp e The bandwidth requiremen t of this media t yp e
is megabits p er second M The system consisted of pro cessors P resulting in
partitions R A ttac hed to eac h pro cessor is a one gigab yte disk driv e The total storage
capacit y of the system is gigab ytes In all exp erimen ts w e assumed equisized ob jects and did
not analyze the impact of this v ariable
The exp erimen tal design of this study w as three dimensional Its axes where the m ultipro
gramming lev el of the system the size of the database and the distribution of access to the
ob jects in the database uniform vs exp onen tial The m ultiprogramming lev el of the system is
This is a part of our future researc h direction

Figure Small database Mean is a fraction of the n um b er of ob jects in the database
con trolled using the n um b er of displa y stations In this study w e analyzed t w o dieren t database
sizes small and large The size of the small database is of the total storage capacit y of the
system and can b e materialized on the disks across the dieren t partitions rendering the tertiary
storage device redundan t The size of the large database is v e times that of the storage capacit y
of the system W e analyzed these t w o dieren t database sizes in order to understand the tradeos
asso ciated with our p olicies In particular w ew ondered whether our p olicies are redundan t for
a database that is small enough to b ecome disk residen t As demonstrated in Section it is
b enecial to use the tertiary storage device ev en for small databases
P erformance Results
W e presen t our p erformance results for eac h database size in turn Unless stated otherwise in
these exp erimen ts state D w as customized with the ob jectbased replacemen t p olicy ie
G
par tition based
and G
obj ect based
and states A B and C w ere customized to
giv e a higher priorit y to the presen t instead of the future ie Gp
Gp
Gf F or
the large database w e analyze the impact of using dieren tv alues for these parameters Due to the
general nature of our w orkload these parameters do not ha v e an impact on the o v erall p erformance
of the system
In all exp erimen ts w e use the throughput of the system to compare the alternativ e transition
diagrams
Small Database

In this exp erimen t the database consisted of ob jects eac h megab ytes in size T
D isplay
seconds The total size of the database w as of the storage capacit y of the system
W e analyzed the throughput of the system as a function of the n um b er of users in the system for
t w o dieren t distributions of access sk ew ed and uniform see Figure In these exp erimen ts w e
tried to sim ulate a system that has b een op erating for a while with the en tire database already
materialized on the disk driv es T oac hiev e this w e emplo y ed a greedy algorithm that assigns the
ob jects with the ob jectivetoev enly distribute the w orkload of an application across the partitions
The maxim um theoretical pro cessing capabilit y of the system is displa ys p er min ute This is
a theoretical upp er b ound b ecause it assumes no access to the tertiary storage device and a uniform distribution of access to the partitions in the system
With an exp onen tial distribution of access to the ob jects mean of the n um b er of ob jects
in the database ie MR T and FXT outp erform MT A b ecause at m ultiprogramming lev els
higher than these t wotec hniques utilize the remaining of eac h disk driv e to materialize
the frequen tly accessed ob jects on sev eral partitions By doing so they a v oid a single partition
from b ecoming the b ottlenec k for the en tire system maximizing the o v erall p erformance of the
system MT A cannot utilize the remaining of the system s storage capacit y b ecause it a v oids
the sc heduler from accessing the tertiary storage device Consequen tly the original assignmen tof
ob jects to partitions remains unc hanged and the partition con taining the most frequen tly accessed
ob ject b ecomes a b ottlenec k A t high m ultiprogramming lev els FXT outp erforms MR T Because
it replaces the least frequen tly accessed ob jects with those that are accessed more frequen tly in
order to maximize the usefull utilization of the disk space MR T cannot b eha v e this w a y b ecause
once the storage capacit y of the system is exhausted causing state C to fail it en ters state B at
all times and a v oids b oth state C and D
A t high m ultiprogramming lev els the throughput of the system with MR T and FXT is displa ys and is increasing These strategies do not attain the maxim um pro cessing capabilit y of the
system b ecause the bandwidth of the tertiary storage device is lo w er than that of a partition
consequen tly when a partition is required to materialize the frequen tly accessed ob ject it sits idle
for some duration of time
With a uniform distribution of access MT A results in a p erformance almost iden tical to MR T

This access pattern distributes the w orkload of the application ev enly across the partitions and
This algorithm is as follo ws it sorts the ob jects based on their frequency of access assigns one ob ject at a
time to the partitions in a roundrobin manner
Indeed the throughput of MT A with a uniform distribution of access is higher than that with an exp onen tial
distribution compare Figure a with b

minimizes the probabilit y of a b ottlenec k partition The p erformance of the system with MR Tis
sligh tly higher b ecause it utilizes the remaining of the disk storage to minimize the w ait time
at state B
A t high m ultiprogramming lev els FXT exhibits a thrashes b eha vior causing the throughput
of the system to drop The explanation for this b eha vior is as follo ws FXT decides b et w een states
B C and D Similar to MR T it utilizes the remaining of the disk storage to replicate sev eral
ob jects m ultiple times b y visiting state C A t some p oin t the storage capacit y of the system is
exhausted Once m ultiple requests collide and comp ete for the same partition due to the random
nature of the w orkload FXT en ters state D b ecause its faster to materialize an ob ject on an
idle partition with insucien t storage device as compared to the w ait time at state B Once at
this state it deletes the ph ysical replica of an ob ject sa y o
y
from an idle partition in fa v or of
an additional replica of the requested ob ject o
x
If this is the only ph ysical replica of o
y
in
the system then deleting it is clearly a mistak e b ecause o
y
will b e accessed at some p ointinthe
future due to a uniform distribution of access In this case once o
y
is accessed the system has to
materialize it from the tertiary storage device whic his slo w degrading the o v erall p erformance of
the system As w e increase the m ultiprogramming lev el state D b ecomes more attractiv e b ecause
when a partition sa y K
i
materializes ob ject o
y
the requests referencing the ph ysical replica of
other ob jects stored on K
i
w ait for a longer in terv al of time at state B This causes the system
to service a larger fraction of requests b y materializing ob jects from the tertiary storage device
reducing the o v erall throughput of the system
Large Database
In this exp erimen t the database consisted of ob jects eac h megab ytes in size T
D isplay
seconds The total size of the database w as v e times the storage capacit y of the system
W e analyzed the impact of b oth the alternativ e state transition diagrams and parameters on the
o v erall p erformance of the system W e do not presen t all the obtained results b ecause they sho w
the same observ ation rep eatedly Instead w e presen t the results for three dieren t system loads a
ligh t system load m ultiprogramming lev el a mo derate system load m ultiprogramming lev el
and a hea vy system load m ultiprogramming lev el F or eac h system load w e analyze
the throughput of the system for the alternativ e transition diagrams and parameters as a function
of the degree of sk ew to the ob jects in the database W e analyzed four dieren t degrees of sk ews
sim ulated using an exp onen tial distribution with the follo wing means

and
of the
n um b er of ob jects in the database ie the mean w as v aried from to As the mean

Figure Large database Mean is a fraction of the n um b er of ob jects in the database
of this distribution b ecomes smaller the access to the ob jects b ecomes more sk ew ed Figure compiles the obtained results in three dieren t graphs Eac h graph corresp onds to a dieren t
system load The xaxis of these graphs corresp onds to the mean of the exp onen tial distribution
ie degree of sk ew These exp erimen ts w ere conducted assuming a system whose disk driv es
con tain the ph ysical replica of no ob jects the greedy algorithm of Section w as not emplo y ed
Unlik e the small database the large database forces the alternativ e state transition diagrams to
visit b oth states C and D A general trend in these gures is that MR T FXT and MT A result in an
iden tical p erformance when the distribution of access is close to uniform As the distribution of
access to the ob jects b ecomes more sk ew ed MR T and FXT outp erform MTAb y a wider margin
Consider eac h case in turn With a lo wdegreeofsk ew most of the requests cause the alternativ e
state transition diagram to en ter state D in order to materialize the requested ob ject resulting in
a high frequency of access to the tertiary storage device Consequen tly the tertiary storage device
b ecomes a b ottlenec k and determines the full pro cessing capabilit y of the system If ev ery request
resulted in an access to the tertiary storage device the throughput of the system w ould ha v e b een
displa ys p er min ute
W e observ ed a throughput of displa ys p er min ute for all system loads
b ecause ev ery no w and then a request observ es a hit ie nds the requested ob ject disk residen t
Withahigh degreeofsk ew b oth MR T and FXT outp erform MT A b ecause MT A allo ws
at most one ph ysical replica of an ob ject in the en tire system it tries to minimize the frequency of
If none of the requests accessed the tertiary storage device the maxim um pro cessing capabilit y of the system
w ould ha v e b een displa ys p er min ute

access to the tertiary storage device The partition con taining the most frequen tly accessed ob ject
b ecomes a b ottlenec k and determines the full pro cessing capabilit y of the system the pro cessing
capabilit y of a partition is at most displa ys p er min ute MR T and FXT replicate this ob ject on
sev eral dieren t partitions maximizing the o v erall pro cessing capabilit y of the system
In general MT Apro vides a b etter p erformance with a mo derate degree of sk ew as com pared to either a high or a lo w degree of sk ew This is b ecause state D materializes the
frequen tly accessed ob jects on dieren t partitions resulting in a more ev en distribution of the load
across the partitions
W e analyzed the p erformance of the system with v arious v alues for Gp
Gp
Gf G
obj ect based
and G
par tition based
More sp ecically w e analyzed v alues that either enable or disable a certain
functionalit y Due to the general nature of our w orkload these c hoices ha v e a marginal impact
on the o v erall throughput of the system and the obtained results are almost iden tical to that of
Figure Conclusion and F uture Researc h Directions
In this pap er w e describ ed virtual data replication as a tec hnique to supp ort sim ultaneous displa y
of sev eral m ultimedia ob jects to dieren t users Wedev elop ed no v el tec hniques to manage the
ph ysical replica of m ultimedia ob jects These tec hniques determine the partition emplo y ed to
displa y an ob ject the partition that materialize the ph ysical replica of ob ject and services a
request and the ob jects sw app ed out in order to mak e ro om for the requested ob ject
Once a request for an ob ject is issued w e iden tied v e p ossible states in the system and
a exible decision making p olicy for eac h of these states In addition w e dev elop ed three state
transition diagrams for the sc heduler MT A MR T and FXT Both the decision making p olicies and
the state transition diagrams appro ximate dieren t ob jectiv es enabling the database administrator
to customize the system to satisfy sp ecic requiremen ts of an application
W e used a sim ulation study to quan tify the tradeos asso ciated with the alternativ estate
transition diagrams and p olicies Due to the general nature of our w orkload the alternativ e decision
making p olicies at eac h state ha v e marginal impact on the o v erall p erformance of the system ie
these p olicies are appropriate for a sp ecic application and not an arbitrary w orkload Ho w ev er
the alternativ e state transition diagrams ha v e a signican t impact on the o v erall p erformance of
the system In general our results demonstrate that MR T is a sup erior strategy as compared to

b oth MT A and FXT The remaining results can b e summarized as follo ws
F or a database that is small enough to b ecome disk residen t across the partitions
MR T is sup erior to b oth MT A and FXT This is b ecause MR T utilizes the full storage
capacit y of the system to minimize the w ait time
MT A minimizes the n um b er of accesses to the tertiary storage device Ho w ev er it al
lo ws at most one ph ysical replica of an ob ject in the system If an ob ject is accessed
frequen tly the partition con taining it b ecomes a b ottlenec k reducing the o v erall pro
cessing capabilit y of the system MR T and FXT can replicate this ob ject m ultiple times
a v oiding the formation of a b ottlenec k
With a uniform distribution of access to the ob jects FXT exhibits a thrashing b eha vior
where ob jects are sw app ed in and out v ery frequen tly causing the tertiary storage device
to b ecome a b ottlenec k As the m ultiprogramming lev el is increased the thrashing
b eha vior b ecomes more sev ere resulting in a v ery lo w system p erformance
for a large database its size is v e times that of the storage capacit y of the system
When the w orking set of the terminals exceeds the storage capacit y of the system eg
uniform distribution of access to the ob jects the alternativ e strategies pro vide an iden
tical p erformance regardless of the m ultiprogramming lev el of the system This is
b ecause the tertiary storage device b ecomes a b ottlenec k and determines the full pro
cessing capabilit y of the system
When the w orking set of the terminals is smaller than the storage capacit y of the system
eg a sk ew ed distribution of access to the ob jects MR T and FXT outp erform MT A
This is b ecause these strategies can replicate the frequen tly accessed ob jects m ultiple
times a v oiding a partition from b ecoming a b ottlenec k
MR T and FXT result in an iden tical p erformance
A t rst glance one migh tbe con vinced that b oth the tertiary storage device and the p olicies
dev elop ed in this study are redundan t for a small database Ho w ev er as demonstrated in Sec
tion MR T can transform a static system in to a dynamic one that maximizes the utilization
of the disk space and enhances the o v erall p erformance of the system
W e b eliev e that virtual data replication is a promising area of researc h that can enable parallel
database managemen t systems to supp ort realtime displa yofm ultimedia data and in tend to

extend this study in sev eral w a ys First the ob ject replacemen t p olicy emplo y ed b y state D can
result in fragmen tation of the disk space This w as not observ ed in the ev aluation section of the
pap er b ecause w e assumed that the database consists of equisized ob jects When the disk space
is fragmen ted an ob ject cannot b e stored in a noncon tiguous manner b ecause up on its retriev al
the system incurs exp ensiv e seek op erations reducing B
D isk
and resulting in hiccups W ein tend to
in tro duce more sophisticated ob ject replacemen t p olicies that a v oid fragmen tation of the disk space
Second when the system resources are committed ie the n um b er of requests exceeds the n um ber
of partitions w ein tend to design sc heduling p olicies that analyze the queue of requests and reserv e
partitions in a manner that maximizes the o v erall p erformance of the system this should minimize
the impact of the thrashing b eha vior for FXT and further enhance the p erformance of the system
for b oth MR T and MT A Third w ein tend to in v estigate sev eral optimization tec hniques use a
partition to service m ultiple requests for an ob ject b ym ultiplexing the stream of data to dieren t
terminals use a v ariation of the rst optimization to o v erlap the displa y of a frequen tly accessed
ob ject with its materialization on a dieren t partition since the bandwidth of the tertiary storage is
lo w er than that of a partition F ourth for a system with h undreds and thousands of pro cessors the
cen tralized sc heduler ma y b ecome a b ottlenec k It w as essen tial to assume a cen tralized sc heduler
in this study in order to understand the tradeos asso ciated with the alternativ es state transition
diagrams W ein tend to replace the prop osed cen tralized p olicies with no v el distributed sc heduling
algorithms
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Disks RAID In Pr o c e e dings of the A CM SIGMOD Intl Conf Ma y Sc h H Sc h w etman CSIM A CBased Pro cessOrien ted Sim ulation Language T ec hnical
Rep ort PP Micro electronics and Computer T ec hnology Corp oration Sto M R Stonebrak er The case for SharedNothing In Pr o c e e dings of the Data
Engine ering Confer enc e IEEE

Asset Metadata

Creator Ghandeharizadeh, Shahram (author), Shahabi, Cyrus (author)

Core Title USC Computer Science Technical Reports, no. 600 (1995)

Alternative Title Management of virtual replicas in parallel multimedia information systems (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 25 pages (extent), technical reports (aat)

Language English

Unique identifier UC16270210

Identifier 95-600 Management of Virtual Replicas in Parallel Multimedia Information Systems (filename)

Legacy Identifier usc-cstr-95-600

Format 25 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)

Access Conditions The author(s) retain rights to their work according to U.S. copyright law. Electronic access is being provided by the USC Libraries, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright.

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)

Linked assets

Computer Science Technical Report Archive