Close
About
FAQ
Home
Collections
Login
USC Login
Register
0
Selected
Invert selection
Deselect all
Deselect all
Click here to refresh results
Click here to refresh results
USC
/
Digital Library
/
Computer Science Technical Report Archive
/
USC Computer Science Technical Reports, no. 653 (1997)
(USC DC Other)
USC Computer Science Technical Reports, no. 653 (1997)
PDF
Download
Share
Open document
Flip pages
Contact Us
Contact Us
Copy asset link
Request this asset
Transcript (if available)
Content
T rading Memory for Disk Bandwidth in VideoonDemand Serv ers
W eifeng Shi
Computer Science Departmen t
Univ ersit y of Southern California
Los Angeles California wfshicsusce du
Shahram Ghandeharizadeh
P anasonic T ec hnologies Inc
Researc h W a y
Princeton New Jersey shahr amr ese ar chp anasonicc om
June
Abstract
In a VideoonDemand serv er requests from dif
feren t clien ts are indep enden t of eac h other and
ma y arriv e at random time Commercial systems
ma y con tain h undreds to thousands of clien ts
and th us pro viding an individual stream for eac h
clien t ma y require v ery high disk bandwidth in
the serv er Therefore the disk bandwidth maybe come a b ottlenec k resource restricting the n um
ber of concurren t displa ys in the system In this
pap er w e prop ose a sc heme that trades memory
for disk bandwidth and strik es a balance in or
der to prev en t either memory or disk bandwidth
from b ecoming a b ottlenec k resource Moreo v er
w e obtain the balance p oin t of trading memory
for disk bandwidth whic h leads to the most cost
eectiv e system conguration
In tro duction
During the past few y ears adv ances in comput
ing and comm unication tec hnologies ha vemade it
feasible to implemen t a VideoonDemandV OD
serv er whic h can pro vide con tin uous deliv ery of
thousands of video streams to dieren t clien ts
Video is quite dieren t from con v en tional data
t yp es lik e text and image First video ob jects
are t ypically large in size and ha v e high bit rate
This researc h w as supp orted in part b y a Hewlett
P ac k ard unrestricted cashequipmen t gift and the Na
tional Science F oundation under gran ts IRI and
IRI NYI a w ard
F or example a t w o hour MPEG enco ded video
ma y require Gigab ytes GB of storage and
Megabits per second Mbps of bandwidth for
its displa y Second video data needs to be re
triev ed and deliv ered to clien t at a presp ecied
rate otherwise the displa y ma y observ e disrup
tions and dela ys
W e consider a V OD arc hitecture depicted in
Figure The serv er includes a n um ber of disks
. . .
Clients
Network
Disks
Buffer Pool
Server
...
Figure At ypical arc hitecture of a V OD system
and a buer p o ol W e assume there is no net
w ork constrain ts Eac h video is strip ed in to equi
sized data blo c ks The size of eac h blo c k is de
noted as B and the data blo c ks are assigned
to the disks in a roundrobin manner to bal
ance the load imp osed bya displayev enly across
the a v ailable disks GZS
LS TPBG Figure sho ws an example of striping video X
o v er disks The buer pool is also divided
in to frames of size B W e assume an en viron
X X X X X X X X 01 2 3 45 6 7
. . . . . . . . . . . .
Figure An example of data striping
men t where all video ob jects ha vethe same con
stan t bandwidth requiremen t this assumption
will b e relaxed as part of our future researc h di
rections T o guaran tee a con tin uous displa y a
certain amoun t of disk bandwidth referred to
as a disk str e am m ust be reserv ed Eac h disk
stream ma y serv e one or as w e shall see later
more displa ys W e adopt the cyclebased ap
proac h A OG NY R V TPBG that re
triev es data blo c ks in to memory at regular time
in terv als Eachactiv e disk stream stages one data
blo c k in to the buer pool during one cycle and
transmits the blo c k to the clien t b y the end of
the cycle The displa y of this blo c k starts from
the b eginning of next cycle and lasts for one cy
cle This paradigm ensures a con tin uous displa y
of eac h video
The pla ybac k requests for videos from dieren t
clien ts are indep endentof eachother and mayar riv e at random time and therefore a new video
displa y could be started to satisfy eac h request
In a commercial V OD system whichmaycon tain
thousands of activ e clien ts EET this indi
vidual service ma y lead to v ery high disk band
width requiremen t in the serv er Th us the disk
bandwidth as opp osed to disk storage capacit y is the more scarce resource restricting the n um
ber of concurren t displa ys in the system There
ha v e b een sev eral studies on buer sharing tec h
niques to o v ercome the disk bandwidth restric
tion DDM
DS KR T ORS ORS
RZ The basic idea of buer sharing is that
if there are t w o clien ts requesting the same video
but not at the same time the serv er can serv e the
latter one b y using the data whic h is read in to the
buer pool on b ehalf of the former one There
fore the referred video is read from disk only once
while the system supp orts t w o sim ultaneous dis
pla ys An example of buer sharing is sho wn in
Figure where t w o displa ys D
and D
of video
X are supp orted b y one single disk stream In the
curren t cycle the t w o displa ys are at p osition X XXXXX
3 45678
. . . . . .
XXXXXX
456789
. . . . . .
current cycle:
next cycle:
D
1 D
2
D
1 D
2
Figure An example of buer sharing
and resp ectiv ely and they will mo v e to p osition
and in the next cycle If t w o displa ys are ref
erencing the same video with the p osition p and
p p p resp ectiv ely then the distance be t w een them is dened as p p In this example
the distance is blo c ks Note that although the
p ositions of D
and D
are c hanging as a func
tion of time the distance b et w een them remains
constantun til one displa y ends By retaining the
blo c ks bet w een them in buer pool to co v er the
distance D
can be supp orted without an y disk
access
Ideally a buer sharing tec hnique should en
hance the o v erall p erformance of a system Ho w
ev er all the existing buer sharing tec hniques
ma y exhaust the a v ailable buer space degrading
the system p erformance T o illustrate assume a
serv er that consists of a disk driv e with su
cien t bandwidth to pro vide v e disk streams and
enough buer space to stage v e data blo c ks
in memory Without buer sharing Figure a
the serv er can supp ort v esim ultaneous displa ys
since eac h displa y needs one disk stream and one
buer blo c k With buer sharing there could b e
excessiv e use of buer space for sharing purp ose
and therefore mak e the buer p o ol b ecome a b ot
tlenec k In the w orst case sho wn in Figure b
the en tire buer space is used to enable shar
ing bet w een t w o displa ys of Y Other requests
are queued due to lac k of buer space although
there are four idle disk streams in the system
The queued requests mayha v e to w ait for hours
b efore one of the activ e displa ys nishes
Another imp ortan t issue in V OD systems is
costeectiv eness F or a commercial system cost
Y
54
Z
0
W
15
X
10
Y
50
Y
54
Y
53
Y
52
Y
51
Y
50
.
.
.
X
Z
W
waiting queue
Figure a without buer sharing Figure b with buer sharing
Figure Buer sharing could degrade the system p erformance
eectiv eness is critical Buer sharing is essen
tially a metho d of trading memory for disk band
width Since memory is not a free resource it
is imp ortantto study ho w m uchmemoryshould
be traded for disk bandwidth for example ho w
to decide the size of the buer pool whic h can
bring the o v erall system cost do wn to the mini
m um T o the b est of our kno wledge no study has
addressed this issue b efore ev en though it has a
substan tial impact on the costeectiv eness of the
buer sharing tec hnique
In this pap er w ein tro duce the concept of dis
tancethr eshold denoted d
t
whic h is a threshold
on the n um ber of blo c ks bet w een t w o adjacen t
displa ys referencing the same video None of the
existing studies ha v e prop osed this concept be fore If the distance b et w een t w o displa ys exceeds
d
t
then they are not allo w ed to share one disk
stream b y using memory In fact the v alue of d
t
denes ho wm uc h memory could b e used to trade
for disk bandwidth W e further presen t the c on
tr ol le d buer sharing CBS sc heme whic h pr e
vents the buer p o ol from b ecoming a b ottlenec k
while reducing the disk bandwidth requiremen t
eectiv ely in V OD systems The CBS sc heme
consists of t w o parts a buer managemen t al
gorithm with the concept of distance threshold
terme d BMDT algorithm and a conguration
planner whic h tak es d
t
as one of its input param
eters and outputs the corresp onding buer and
disk bandwidth requiremen ts These t w o parts
w ork together to guaran tee there is no b ottlenec k
resource either buer space or disk bandwidth
in the system Moreo v er w e obtain the optimal
d
t
v alue whic h leads to the most costeectiv e sys
tem conguration W e also pro v e that the opti
mal d
t
v alue is only related to the cost of mem
ory and disk bandwidth and is indep enden t of
the arriv al rate of requests the access frequency
distribution and the access frequency of eac hin dividual video
The rest of this pap er is organized as follo ws In
Section w e describ e the related w ork In Sec
tion w e presen t the CBS sc heme In Section
w e explain ho w to c ho ose the optimal v alue
for distance threshold to ac hiev e the lo w est sys
tem cost Exp erimen tal results are presen ted in
Section The conclusions and future researc h
directions can b e found in Section Related W ork
Except buer sharing there are t w o other ap
proac hes to o v ercome the IO b ottlenec k
b atching DSS WSY in this metho d
requests are dela y ed un til they can be
merged with other requests for the same
video These merged streams then form one
ph ysical stream from the disk and consume
only one set of buers Only on the net w ork
will the streams split at some p oin t for deliv
ery to the individual clien t Although batc h
ing do es not require additional resources it
ma y result in longer w aiting time whic h is
unacceptable in some circumstances F oxex ample when p erforming the V CR functions
clien ts usually exp ect to get the resp onse im
mediately and ev en a few seconds w aiting
seems to b e undesirable
adaptive piggyb acking GLM in this ap
proac h streams for the same video are ad
justed to go slo w er or faster b y a few p ercen t
suc h that it is imp erceptible to the view er
and the streams ev en tually merge and form
one ph ysical stream from the disks
Batc hing and adaptiv e piggybac king are orthogo
nal to buer sharing and w e will not in v estigate
them an y further in this pap er
Con trolled Buer Sharing
Sc heme
In this section w e presen t the con trolled buer
sharing CBS sc heme The CBS sc heme con
sists of t w o parts the BMDT algorithm and the
conguration planner These t w o parts w ork to
gether to guaran tee that there is no b ottlenec k
resource in the system
Sharing pair and merging pair
F or an y video ob ject Xthere ma y exist m ultiple
displa ys of X at dieren t p ositions concurren tly Giv en the distance threshold d
t
w e dene a g r oup
of video X as a sequence of displa ys D
D
D
n
where D
i
i n is displa ying video
X this sequence is ordered in terms of de
creasing p osition of eac h displa y the distance
bet w een D
i
and D
i i n do es not ex
ceed d
t
there is no displa yof X that is ahead
of D
within the distance of d
t
and there is no
displayof X that is few er than d
t
blo c ks b ehind
D
n
F or eac h pair of D
i
D
i i n in the sequence D
i
is called pr eceding displ ay of
D
i
and D
i
is the succeeding displ ay of D
i
Figure sho ws an example of a group of video X
consisting of four displa ys
XXXX
6789
. . .
X
10
D D 4 D D 2 1 3
. . . X
11
X
12
Figure A group of video X d
t
Consider a pair of preceding and succeeding
displa ys in a group If the succeeding displa y is
b eing serv ed from the buer pool without an y
disk access w e call the t w o a shar ing pair In
this case the data blo c ks b et w een this pair m ust
b e retained in buer p o ol to supp ort the con tin
uous data deliv ery to the succeeding displa y and
cannot be discarded when buer replacemen t is
necessary The buer requiremen t of a sharing
pair is determined b y the distance b et w een them
On the other hand if the succeeding displa y is
b eing serv ed b y a disk stream then if some of
the blo c ks b et w een them are buer p o ol residen t
these blo c ks can b e discarded W e call these t w o
displa ys a mer g ing pair A merging pair could
ev olv e to become a sharing pair when all the
blo c ks bet w een this pair are a v ailable in buer
p o ol An example of sharing pair and merging
pair is sho wn in Figure Figure sho ws the
XXXXX
34567
. . .
X
10
D D D D
2 1 3 4
. . .
sharing pair: ( D 2 , D3 ) , ( D 3 , D4 )
merging pair: (D1 , D2 )
: data block not available in buffer pool
Figure Sharing pair and merging pair d
t
mapping bet w een disk streams and displa ys of
the example in Figure Note that disk stream
j supp orts three sim ultaneous displa ys D
D
and D
b ecause the t w o sharing pairs are con
nected to eac h other In fact if a video is p opular
enough then it ma yha v e a large n um ber of con secutiv e blo c ks retained in the buer pool ie
man y sharing pairs of this video are connected
D
D
D
D 2
1
3
4
i
j
.
.
.
.
.
.
Disk stream Display
Figure Mapping b et w een disk streams and dis
pla ys
together b ecause of the frequen t access on it
When this happ ens one single disk stream will
supp ort man y displa ys of the same video
Note that the denition of a sharing or merg
ing pair is based on the preceding and succeed
ing displa ys whic h are dened within a group
Therefore the distance bet w een a sharing or
merging pair do es not exceed d
t
BMDT algorithm
A system m ust satisfy the buer requiremen tofa
sharing pair to ensure con tin uous displayof this
pair Moreo v er eac h activ e disk stream will read
one new data blo c k in to buer pool during eac h
cycle Let M be the size of buer pool in terms
of the n um ber of blo c ks d
s
be the sum of the
distances b et w een eac h sharing pair ie the total
n um ber of buer blo c ks required b y all sharing
pairs d
m
be the n um ber of buers o ccupied b y
merging pairs and S b e the n um b er of activ e disk
streams Then the buer constrain t
d
s
S M
m ust b e satised to guaran tee the con tin uous dis
pla y for eac h clien t The v ariable d
m
do es not
app ear in inequalit y b ecause those buers o c
cupied b y merging pairs are not mandatory to
pro vide con tin uous displa ys The upp er b ound
of d
m
is M d
s
S Whenev er d
m
exceeds this
b ound some buers o ccupied b y merging pairs
will b e discarded to reduce the v alue of d
m
to b e
within its upp er b ound In addition there also
exists disk bandwidth constrain t whic h can be
expressed as
S I
where I is the maxim um n um b er of disk streams
the system can supp ort Inequalit y limits the
n um b er of activ e disk streams based on the a v ail
able ph ysical IO resources in the system The
system should manage the buer and disk band
width resources in the presence of new requests
activ e displa ys ending and exiting the system or
merging pairs ev olving to sharing pairs
W e prop ose the BMDT algorithm as follo ws
Applied in a system congured according to the
planner Section this algorithm guaran tees
that there will b e no rejected requests ie eac h
request is serv ed immediately up on its arriv al in
the serv er see the result in Section The
BMDT algorithm is applied at the end of eac h
cycle The admission con trol is implied in this
algorithm so that the con tin uous displa y for eac h
clien t is guaran teed
F ree the disk stream whic h already reac hed
the end of a displa y Ev olveas man y of the merging pairs to shar
ing pairs and free the disk stream of the
succeeding displa y while a all the blo c ks
bet w een the merging pair are a v ailable in
buer and b inequalit y is satised
Inequality is a condition of this step be cause ev olving merging pairs to sharing ones
increases the v alue of d
s
and impacts this in
equalit y Admit as man y of the new requests while
b oth inequalit y and are satised
Inequalities and are in v olv ed b ecause
a new displayma y need b oth buer and disk
bandwidth resources
P erform buer replacemen t and allo cation
algorithm
The buer replacemen t and allo cation algo
rithm in step is further detailed as follo ws It
will decide whic h buer should b e discarded when
buer replacemen t is necessary F ree the buers whichha v e no p oten tial for
sharing
This step discards all the buers whic h do
not fall in b et w een mergingsharing pair ie
no displa y will get data from these buers in
the future
While d
s
d
m
S M Do
i c ho ose the merging pair with the
longest distance as the victim
ii free those buers that fall in bet w een
this merging pair
iii decremen t d
m
b y the n um b er of buers
freed in ii This step will discard the buers that fall
in b et w een the victim merging pair to create
buer space for either sharing pairs or new
displa ys
Assign one free buer to eac h activ e disk
stream
This step sp ecies the address to whic h the
new data blo c k will go
So far the BMDT algorithm is complete Ho w
ev er setting a threshold for buer sharing solely
migh t not prev en t the undesirable condition
sho wn in Figure b If the buer p o ol is to o small
it could still form a b ottlenec k if the buer p o ol
is to o large some buer space ma y be w asted
W e need to quan tify ho w m uc h buer space is
actually required Moreo v er in the presence of
BMDT the IO requiremen t will b e reduced and
therefore w e also need to quan tify howm uc h disk
bandwidth is actually needed
Conguration planner
The conguration planner computes the buer
and disk bandwidth requiremen t based on a n um
ber of input parameters It is applied staticly
at the system design time After the system is
congured according to the planner the BMDT
algorithm is dynamically applied at the system
runtime The planner and the BMDT algorithm
constitute the CBS sc heme
The input to the planner includes the arriv al
rate of requests the access frequency distribu
tion the n um ber of videos a v ailable the system
utilization factor and the distance threshold d
t
The output is the n um ber of buer blo c ks and
the n um ber of disk streams required Except d
t
all the input parameters reect the c haracteris
tic of the system itself Theoretically the planner
could tak e an y v alue of d
t
as its input Dier
en t d
t
v alues will lead to dieren t buer and disk
bandwidth requiremen ts and therefore the sys
tem cost will be dieren t In the next section
Section w e will describ e howto c ho ose the op
timal d
t
v alue whic h brings the system cost do wn
to the minim um
Assume the request arriv al pro cess follo ws P ois
son distribution with rate Let V denote the
n um ber of dieren t videos in the system As
sume the length of eac h video is l and let be
l
Up on arriv al of a request to the system the clien t
choosestow atchvideo j j V with proba
bilit y p
j
Therefore for eac h video j j V the request arriv al follo ws a P oisson pro cess with
rate j
where j
p
j
and
P
V
j j
Then
the exp ected n um b er of displa ys that the system
m ust supp ort is
m and the exp ected n um ber of displa ys that refer
ence video j is
m
j
j
Consider the disk bandwidth requiremen t rst
Without an y buer sharing m is also the ex
p ected n um ber of disk streams in the system
No w consider m
the exp ected n um ber of disk
streams in a system emplo ying BMDT algorithm
Let t
p
denote the length of a cycle then the time
in terv al b et w een a sharing pair should not exceed
d
t
t
p
According to P oisson pro cess the proba
bilityof t w o requests for video j arriving within
d
t
t
p
is
p
s
j
e
j
d t t p
Let I
j
b e a random v ariable denoting the n um ber
of disk streams whic h are retrieving the data of
video j W e already kno w the exp ected n um ber
of displa ys of video j is m
j
Let D
D
D
m
j
denote these m
j
displa ys F rom Equation w e
knowthe probabilit y that D
i
and D
i i
m
j
are bridged up to form a sharing pair is p
s
j
therefore the probabilit y that there is no bridge
bet w een D
i
and D
i i m
j
is p
s
j
If
there are only one out of m
j
displa ys serv ed from
disk it means all these m
j
displa ys are bridged
up Let P I
j
k b e the probabilit y that k out of
m
j
displa ys are serv ed from disk while the other
m
j
k displa ys b eing serv ed from the buer p o ol
Then w e get P I
j
p
m
j
s
j
since there are
totally m
j
bridges If there are t w o out of
m
j
displa ys serv ed from disk it means there are
m
j
bridges among the m
j
displa y pairs and
there is only one displa y pair whic h is not bridged
up There are totally
m
j
com bination
of the pair with no bridge Then weha v e P I
j
m
j
p
m
j
s
j
p
s
j
By generalizing
the computation w eha v e
P I
j
k
m
j
k p
m
j
k
s
j
p
s
j
k
and the exp ected v alue of I
j
can b e expressed as
E I
j
m
j
X
k k P I
j
k
E I
j
is actually the exp ected n um ber of disk
streams whic h are displa ying video j Then the
exp ected n um b er of disk streams in a system em
plo ying BMDT is
m
V
X
j E I
j
No w Consider the buer requiremen t of the
system Without an y buer sharing eac h dis
pla y needs one buer and the exp ected n um ber
of required buers w is
w m
The measuremen t of buer requiremen t under
BMDT can be ac hiev ed as follo ws First con
sider the sharing pairs of video j Let d
j
be a
random v ariable denoting the distance bet w een
a sharing pair of video j If d
j
k it means
that the time in terv al b et w een the sharing pair is
less than k t
p
but greater than k t
p
The
probabilityof d
j
k can b e expressed as
P d
j
k e
j
k t p
e
j
k t p
where k d
t
Since w e are considering
the buers o ccupied b y a sharing pair of video
j the probabilit y that this sharing pair requires
k buers is
P d
j
k jd
j
d
t
P d
j
k d
j
d
t
P d
j
d
t
where the ev en t d
j
d
t
means this is a sharing
pair Since k d
t
the ev en t d
j
k implies
d
j
d
t
therefore P d
j
k d
j
d
t
P d
j
k F rom Equation w e kno w P d
j
d
t
p
s
j
Then Equation can b e rewritten as
P d
j
k jd
j
d
t
P d
j
k p
s
j
Nowweha v e the exp ected n um b er of buers o c cupied b y one sharing pair of video j as follo ws
E d
j
d t
X
k
k P d
j
k jd
j
d
t
F rom Equation w e obtain the exp ected n um
b er of disk streams of video j E I
j
then the ex
p ected n um b er of displa ys whic h are serv ed from
the buer pool is m
j
E I
j
So the exp ected
n um ber of buers required b y sharing pairs of
video j is
b
j
m
j
E I
j
E d
j
and the exp ected n um ber of buers required b y
all sharing pairs in the system is
b V
X
j
b
j
Besides the buer requiremen t of sharing pairs
eac h activ e disk stream will read one new data
blo c k in to the buer pool during eac h cycle as
w e explained previously therefore the exp ected
n um ber of buers required b y the whole system
is
w
b m
Equation and are the solution of the
exp ected n um ber of disk streams and the ex
p ected n um b er of buer blo c ks Giv en the system
utilization factor w e ma y further get the actual
n um b er of disk streams and buer blo c ks through
a simple m ultiplication F or example if the ex
p ected n um ber of disk streams is and the
utilization factor is then the system should
b e congured with disk streams
Exp erimen tal results see Section sho ws that
if a system is congured according to this planner
and the BMDT algorithm is applied at the sys
tem runtime then there will be no b ottlenec k
resources in the system
Cho osing the Optimal Dis
tance Threshold
F rom Section the buer and disk bandwidth
requiremen ts are impacted bythe v alue of d
t
If d
t
is to o large more buer space ma y b e needed to
enable sharing increasing the memory cost On
the other hand a small v alue of d
t
ma y discour
age sharing all together causing the disk cost to
b ecome signican t In a real system it is imp or
tantto c ho ose the optimal d
t
v alue that minimizes
the system cost with resp ect to memory and disk
resources
Let M
denote the cost of memory for eachdata
blo c k and I
denote the cost of a disk stream I
can b e obtained through the cost of one disk driv e
and the n um b er of disk streams it supp orts F or
example if one disk driv e costs and it can
supp ort as man y as disk streams then I
will
be W e found the optimal d
t
v alue is
I
M
when it is an in teger v alue The discussion for
I
M
as a real n um b er is at the end of this section
The formal pro of is as follo ws
Let a
i
denote the n um b er of displa ys that are i
blo c ks apart from the immediate prior displa ys of
the same video When i do es not exceed d
t
the
cost of these a
i
displa ys is a
i
i M
b ecause they
are all serv ed from buer p o ol with no disk access
When i is greater than d
t
the displa ys m ust be
serv ed from disk and they eachcost I
M
due
to the requiremen ts of one disk stream and one
buer Then the cost of the whole system C can
b e expressed as
C d t
X
i a
i
i M
m d t
X
i
a
i
I
M
Let d
opt
be
I
M
assuming it is an in teger then
C
opt
d opt
X
i a
i
i M
m d opt
X
i a
i
I
M
F or those d
t
v alues greater than d
opt
the dier
ence b et w een C and C
opt
is
C C
opt
d t
X
i d opt
a
i
i M
d t
X
i d opt
a
i
I
M
whic h can b e rewritten as
C C
opt
d t
X
i d opt a
i
i M
d
opt
M
M
The v alue is no less than zero and demonstrates
that the system cost do es not decrease with those
d
t
v alues greater than d
opt
In realit y C C
opt
only when d
t
is equal to d
opt
This is b ecause
eac h displa y needs buer blo c k without sharing
T ak e a simple example where d
opt
and t w o
displa ys of X ha v e a distance of blo c ks If d
t
is
set to d
opt
then the cost for these t w o displa ys is
c I
M
b ecause eac h of them needs one
disk stream and one buer blo c k If d
t
is set to
d
opt
then they can share one disk stream The
cost of the preceding displayis I
M
and the
cost of the succeeding one is M
Therefore the
total cost of the t w o displa ys is c
I
M
Ob viously c c
since
I
M
No w consider those d
t
v alues less than d
opt
F or
these v alues the dierence b et w een C and C
opt
is
C C
opt
d opt
X
i d t a
i
I
M
d opt
X
i d t a
i
i M
whic h can b e rewritten as
C C
opt
d opt
X
i d t a
i
d
opt
M
M
i M
This v alue is greater than b ecause i d
opt
It
completes the pro of that the system with the dis
tance threshold of d
opt
ac hiev es the lo w est system
cost
In this pro of w e applied the same d
t
v alue on
eac h video Similarly it can also be pro v ed that
applying an y d
t
v alue other than d
opt
or d
opt
on an y video in the system will lead to a system
cost higher than C
opt
the pro of is similar to the
ab o v e and is eliminated here due to lac k of space
F rom the pro cedure of the ab o v e pro of it is
sho wn that the optimal d
t
v alue is impacted only
b y the cost of memory and disk stream and in ter
estingly it is indep enden t of the arriv al rate of re
quests the access frequency distribution and the
access frequency of eac h individual video the ex
perimen tal results in Section also demonstrate
this
The optimal d
t
v alue
I
M
indicates that one disk
stream is equiv alentto d
opt
memory blo c ks as far
as cost is concerned When using a d
t
v alue larger
than d
opt
some displa ys ma y be serv ed from
the buer p o ol b y using d
t
memory blo c ks eac h
whic h cost more than serving them directly from
disk streams On the other hand when using a
d
t
v alue smaller than d
opt
some displa ys with the
distance of d
t
from their immediate prior displa y
will be serv ed b y disk streams while otherwise
they could b e serv ed from the buer p o ol and cost
less Essen tially d
opt
denes a balance p oin t of
trading memory for disk bandwidth whic h leads
to the most costeectiv e system conguration
In the extreme case where memory is v ery c heap
ie M
becomes v ery small d
opt
ma y go to in
nit y whic h means the en tire video could b e re
tained in memory for sharing bet w een dieren t
clien ts
When
I
M
is not an in teger w e rst congure
the system according to the planner b y taking
b
I
M
c as the distance threshold and compute the
system cost m
I
w
M
Then w e congure
the system using d
I
M
e and compute the system
cost in this case The optimal d
t
will b e the v alue
whic h results in the lo w er cost
Exp erimen tal Results
In this section w e presen t the exp erimen tal re
sults W e consider a commercial V OD system
with thousands of concurren t displa ys Clien t re
quests are issued using a P oisson pro cess If a
request arriv es when the system cannot admit it
then it will b e rejected The system con tains MPEG enco ded videos with eac h video requir
ing Mbps for its con tin uous displa y Eac h video
is min utes long The length of eac h cycle is seconds and the size of a data blo ckis MBThe
frequencies for requesting v arious videos followa
Zipf distribution
with parameter sho wn in
Figure whic h has been sho wn to matc h with
the empirical data from video ren tal stores in a
particular w eek DSS The system utilization
20 40 60 80 100
0
2
4
6
8
10
12
Video Index
Access freq.[%]
0
Figure Access frequency distribution Zipf
with parameter factor is set to W e start with exp erimen ts whic h compare
the p erformance of dieren t buer sharing tec h
niques The v alue of I
and M
is set to be
and resp ectiv ely according to the
mark et price F or example one Seagate Bar
racuda STWB disk driv e is ab out and
can pro vide disk streams in our exp erimen ts
Th us I
is around M
is the cost for MB memory in our exp erimen ts First wecom pute the optimal d
t
v alue whic h is d
e in
our case No w consider the arriv al rate of In a Zipf distribution if the videos are sorted according
to the access frequency then the access frequency for the
i
th
video is giv en b y f i c
i
where is the parameter
for the distribution and c is the normalization constan t
requests per min ute W e congure the system
according to the planner in Section Then
under the same system conguration w e p erform
three exp erimen ts using dieren t buer manage
men t tec hniques the CBS sc heme buer
sharing without an y distance threshold and no
buer sharing at all Eac h exp erimen t is run for
hours W e measure the system throughput in
eac h exp erimen t The exp erimen ts for other ar
riv al rates are conducted b y follo w
ing the same steps It could happ en that t wore quests for the same video arriv e within one cycle
ho w ev er the c hance is v ery lo w less than in
all the exp erimen ts and is neglected in our study The results presen ted in Figure sho w that the
30 40 50 60 70
0
2000
4000
6000
8000
Arrival rate [requests/minute]
Max. number of concurrent displays
20
sharing
without
any threshold
no sharing
CBS
scheme
Figure System p erformance with dieren t
buer managemen ttec hniques
CBS sc heme ac hiev es the best p erformance and
buer sharing without an y distance threshold is
ev en w orse than no buer sharing at all due to the
exhausted buer usage W e also monitor the p er
cen tage of requests whic h are rejected due to lac k
of buer space andor disk bandwidth in eac h
exp erimen t The results are sho wn in Figure The CBS sc heme do es not app ear in Figure b ecause there is no request rejected in the exp er
imen ts using CBS This demonstrates that there
is no b ottlenec k in a system emplo ying CBS
W e then study the c haracteristic of the optimal
d
t
v alue
In Section it is pro v ed that the optimal d
t
v alue is determined b y the ratio bet w een I
and
M
T o v erify this w e x I
at and v ary
the M
v alue to be and re
30 40 50 60 70
0
20
40
60
80
Arrival rate [requests/minute]
Rejected requests [%]
20
sharing
without
any threshold
no sharing
100
Figure Refused requests in dieren t buer
managementtec hniques
5 10 15 20 25
0.7
0.8
0.9
1
Distance threshold
System cost
0
: M = 10, I = 92
$$
: M = 8, I = 92
$$
: M = 6, I = 92
$$
Figure Optimal d
t
v alue with dieren tmem ory price
sp ectiv ely The arriv al rate is requests per
min ute The system is congured for eac h d
t
v alue from to according to the planner The
system cost m
I
w
M
is measured in eac h
case and depicted Figure as compared with
the case of d
t
Note that when d
t
there
is no sharing and the system cost is mark ed as In Figure the lo w est system cost is ac hiev ed
when d
t
is and with the M
v alue as
and resp ectiv ely whic h ex
actly v eried our study on ho wtoc ho ose the op
timal v alue
Figure sho ws the system cost under dieren t
arriv al rates and distance threshold v alues The
v alue of I
and M
are and resp ec
tiv ely W e try three dieren t arriv al rates and F or eac h arriv al rate w e congured
the system according to the planner b y using v ar
ious distance threshold The result in Figure
5 10 15 20 25
0.7
0.8
0.9
1
Distance threshold
System cost
0
=30
threshold = 12
λ
=50 λ
=70 λ
Figure Optimal d
t
in systems with dieren t
arriv al rate
sho ws the lo w est system cost is ac hiev ed when
d
t
for ev ery arriv al rate and demonstrates
that the optimal d
t
v alue is indep enden t of the
arriv al rates
W e also study the relationship b et w een the op
timal d
t
v alue and the access frequency distribu
tion Still I
and M
The ar
riv al rate is xed at requests p er min ute Ex
cept the Zipf with parameter whic h matc hes
w ell with the empirical data on video ren tal w e
try t w o other parameters and whic h
are sligh tly more sk ew ed than that of parame
ter The actual customer demand ma ybe
more sk ew ed than the empirical ren tal frequen
cies b ecause video stores can sto c k only a limited
n um b er of copies of p opular videos and customers
who wish to ren t a p opular video ma y b e forced to
ren t a less p opular video F or eac h distribution
the system is congured according to the planner
b y using v arious distance threshold The system
cost in eac h case is measured and presen ted in
Figure whic hsho ws that the optimal d
t
is in
dep enden t of the access frequency distribution
A misconception ab out distance threshold is
that setting a dieren t threshold for the p opu
larvideosw ould reduce the system cost In fact
using a d
t
v alue either larger or smaller than the
optimal v alue on p opular videos will increase the
system cost W e p erform the exp erimen ts in the
follo wing approac h First w e pic k up the most
p opular videos in the system F or other videos
wex d
t
at which isthe optimalv alue Then
for eac h n um ber from to w e congure the
5 10 15 20 25
0.7
0.8
0.9
1
Distance threshold
System cost
0
Zipf (0.271)
Zipf (0.135)
Zipf (0.012)
threshold = 12
Figure Optimal d
t
in systems with dieren t
access freq distribution
5 10 15 20 25 30
0.7
0.75
0.8
0.85
0.9
0.95
1
Distance threshold for popular videos
System cost
1
Figure Optimal d
t
is indep enden t of video
p opularit y
system sp ecially b y applying this n um ber as the
distance threshold on the p opular videos In
all cases the arriv al rate is and the access fre
quency is Zipf with parameter Figure sho ws the system cost vs the threshold applied
on the p opular videos It is clear that only when
the threshold applied on p opular videos is do es
the system reac h the lo w est cost This result
sho ws the optimal d
t
v alue is indep enden t of the
access frequency of the individual video
Conclusions and F uture Re
searc h Directions
Buer sharing could b e eectiv e to reduce the IO
requiremen t in V OD systems Ho w ev er the ex
isting buer sharing tec hniques ma y exhaust the
a v ailable memory space to form new b ottlenec k
In this pap er w e in tro duced the concept of dis
tance threshold and presen ted the CBS sc heme
whic h guaran tees there is no b ottlenec k resource
either memory or disk bandwidth in the system
Moreo v er w e obtained the optimal v alue of dis
tance threshold whic h minimizes the system cost
This optimal v alue is indep enden t of the arriv al
rate of requests the access frequency distribution
and the access frequency of eac h individual video
Presen tly w e are pursuing t w o researc h direc
tions First w e are extending the CBS sc heme
to mixed media t yp es ie there could b e videos
of dieren t bit rates in the system Second w e
are attempting to supp ort V CR functions in the
presence of con trolled buer sharing There are
some c hallenging and in teresting problems related
to this issue
References
A OG DP Anderson Y Osa w a and R Go vin
dan A File System for Con tin uous Media
A CM T r ansactions on Computer Systems No v em b er
DDM
A Dan D Dias R Mukherjee
D Sitaram and R T ew ari Buering and
Cac hing in LargeScale Video Serv ers In
Pr o c of COMPCON DS A Dan and D Sitaram Buer man
agemen t p olicy for an ondemand video
serv er US Patent No No v em
b er DSS A Dan D Sitaram and P Shahabuddin
Sc heduling P olicies for an OnDemand
Video Sev er with Batc hing In Pr o c e e d
ings of the A CM Multime dia pages EET Ele ctr onic Engine ering Times page
Marc h
GLM L Golub c hik J Lui and R Mun tz Re
ducing IO Demand in VideoOnDemand
Storage Serv ers In Pr o c e e dings of the
A CM SIGMETRICS pages GZS
S Ghandeharizadeh R Zimmermann
W Shi R Rejaie D Ierardi and TW
Li Mitra A Scalable Con tin uous Media
Serv er Kluwer Multime dia T o ols and Ap
plic ations KR T M Kamath K Ramamritham and
D T o wsleyCon tin uous Media Sharing in
Multimedia Database Systems In Pr o
c e e dings of the th International Confer
enc e on Datab ase Systems for A dvanc e d
Applic ations pages
LS P Lougher and D Shepgerd The Design
of a Storage Serv er for Con tin uous Media
The Computer Journal sp e cial issue on
multime dia F ebruary NY RT Ng and J Y ang Maximizing
Buer and Disk Utilizations for News
OnDemand In Pr o c e e dings of the In
ternational Confer enc e on V ery L ar ge
Datab ases Septem b er
ORS B
Ozden R Rastogi and A Silb er
sc hatz Demand P aging for Videoon
demand Serv ers IEEE International Con
fer enc e on Multime dia Computing and
SystemsMa y ORS B
Ozden R Rastogi and A Silb er
sc hatz Buer Replacemen t Algorithms
for Multimedia Databases IEEE Inter
national Confer enc e on Multime dia Com
puting and Systems June R V P Rangan and H Vin Ecien t Storage
T ec hniques for Digital Con tin uous Me
dia IEEE T r ansactions on Know le dge
and Data Engine ering August
RZ D Rotem and JL Zhao Buer Man
agemen t for Video Database Systems In
Pr o c e e dings of International Confer enc e
on Datab ase Engine ering pages
Marc h
TPBG FA T obagi J P ang R Baird and
M Gang Streaming RAIDA Disk Ar
ra y Managemen t System for Video Files
In First A CM Confer enc e on Multime dia August WSY J W olf H Shac hnai and P Y u D ASD
Dancing A Disk Load Balancing Op
timization Sc heme for VideoonDemand
Computer Systems In Pr o c e e dings of the
A CM SIGMETRICS and Performanc e May
Abstract (if available)
Linked assets
Computer Science Technical Report Archive
Conceptually similar
PDF
USC Computer Science Technical Reports, no. 659 (1997)
PDF
USC Computer Science Technical Reports, no. 627 (1996)
PDF
USC Computer Science Technical Reports, no. 628 (1996)
PDF
USC Computer Science Technical Reports, no. 650 (1997)
PDF
USC Computer Science Technical Reports, no. 623 (1995)
PDF
USC Computer Science Technical Reports, no. 590 (1994)
PDF
USC Computer Science Technical Reports, no. 864 (2005)
PDF
USC Computer Science Technical Reports, no. 634 (1996)
PDF
USC Computer Science Technical Reports, no. 791 (2003)
PDF
USC Computer Science Technical Reports, no. 612 (1995)
PDF
USC Computer Science Technical Reports, no. 625 (1996)
PDF
USC Computer Science Technical Reports, no. 630 (1996)
PDF
USC Computer Science Technical Reports, no. 615 (1995)
PDF
USC Computer Science Technical Reports, no. 685 (1998)
PDF
USC Computer Science Technical Reports, no. 610 (1995)
PDF
USC Computer Science Technical Reports, no. 629 (1996)
PDF
USC Computer Science Technical Reports, no. 618 (1995)
PDF
USC Computer Science Technical Reports, no. 619 (1995)
PDF
USC Computer Science Technical Reports, no. 598 (1994)
PDF
USC Computer Science Technical Reports, no. 600 (1995)
Description
Weifeng Shi and Shahram Ghandeharizadeh. "Trading memory for disk bandwidth in video-on-demand servers." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 653 (1997).
Asset Metadata
Creator
by Weifeng Shi and Shahram Ghandeharizadeh
(author)
Core Title
USC Computer Science Technical Reports, no. 653 (1997)
Alternative Title
Trading memory for disk bandwidth in video-on-demand servers (
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
12 pages
(extent),
technical reports
(aat)
Language
English
Unique identifier
UC16271021
Identifier
97-653 Trading Memory for Disk Bandwidth in Video-on-Demand Servers (filename)
Legacy Identifier
usc-cstr-97-653
Format
12 pages (extent),technical reports (aat)
Rights
Department of Computer Science (University of Southern California) and the author(s).
Internet Media Type
application/pdf
Copyright
In copyright - Non-commercial use permitted (https://rightsstatements.org/vocab/InC-NC/1.0/
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
Coverage Temporal
1991/2017
Repository Email
csdept@usc.edu
Repository Name
USC Viterbi School of Engineering Department of Computer Science
Repository Location
Department of Computer Science. USC Viterbi School of Engineering. Los Angeles\, CA\, 90089
Publisher
Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA
(publisher)
Copyright
In copyright - Non-commercial use permitted (https://rightsstatements.org/vocab/InC-NC/1.0/