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' $ Throughput-Comp etitiv e Admission Con trol for Con tin - - PowerPoint PPT Presentation
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' $ Throughput-Comp etitiv e Admission Con trol for Con tin uous Media Databases Minos N. Garofalakis (Univ. of Wisc onsin { Madison) Y annis E. Ioannidis (Univ. of Wisc onsin { Madison) Ban u Ozden (Bel l
SLIDE 1' & $ % Throughput-Comp etitiv e Admission Con trol for Con tin uous Media Databases Minos N. Garofalakis (Univ.
f
Wisc
nsin
{ Madison) Y annis E. Ioannidis (Univ.
f
Wisc
nsin
{ Madison) Ban u
Ozden
(Bel l L ab
r
atories) Avi Silb ersc hatz (Bel l L ab
r
atories) Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 1
SLIDE 2' & $ % Outline
In
tro duction and Motiv ation
Problem
F
rm
ulation
Con
tributions 1. Algorithms and Theoretical Results 2. Exp erimen tal V alidation
Conclusions
Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 2
SLIDE 3' & $ % In tro duction and Motiv ation
Continuous
Me dia : Real-time resource requiremen ts for deliv ery
i
MPEG-1 clip Ci
stream( C )
duration 1.5 Mbps
Eectiv
e resource managemen t for
n-demand
supp
rt
Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 3
SLIDE 4' & $ % In tro duction and Motiv ation (con t.)
A
dmission Contr
l
: pro vide service guaran tees for accepted streams
Admission Control
B A N D W I D T H
reject T I M E accept
On-line
decision making { non-preemptiv e!
Crucial
for high serv er utilization Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 4
SLIDE 5' & $ % Problem F
rm
ulation
Study
the implications
f
the
n-line
nature
f
admission con trol
Admission
Con trol Ob jectiv e: Maximize total serv er throughput
v
er a sequence
f
requests
Metric:
Comp etitive r atio , i.e., b
und
n
w
rst-case
b eha vior
v
er an y p
ssible
sequence { v ery robust! Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 5
SLIDE 6' & $ % Problem F
rm
ulation (con t.)
Admission Control
ti li ri
time
B
accept reject
l
max = max i fl i g , l min = min i fl i g ,
=
l max l min
r
max = max i fr i g ,
=
r max B
Comp
etitiv e ratio
f
algorithm A = sup seq uences P O P T l i r i P A l i r i
W
an t small (i.e., close to 1) ratios Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 6
SLIDE 7' & $ % Our Con tributions
Comp
etitiv e ratio
f
con v en tional, \greedy" adm. con trol is
1
Lo
w er b
unds
f
log
1
n
the comp etitiv e ratio
f
an y deterministic
r
randomized strategy
No
v el strategies, based
n
Bandwidth Pr ep artitioning with ratios
f
O (log ) (i.e., near-optimal) for large B
Strategies
can easily b e adapted to accommo date clip p
pularities
to impro v e a v erage case
Exp
erimen tal v alidation Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 7
SLIDE 8' & $ % Con v en tional Wisdom: \Greedy" Admission Con trol
Work-Conserving
str ate gy (W C ): admit incoming request if 9 sucien t bandwidth, reject
therwise
time
t2 t1
B
Theorem: W C is 1+ 1
comp
etitiv e Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 8
SLIDE 9' & $ % Lo w er Bounds
n
Comp etitiv eness Theorem: An y deterministic
r
randomized
n-line
admission con trol strategy has a comp etitiv e ratio
f
log
1
Exp
nen
tial gap w.r.t. W C | lots
f
space for impro v emen t! Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 9
SLIDE 10' & $ % The Basic Idea: Simple Prepartitioning
Idea:
isolate requests with large length dierences so that short requests cannot monop
lize
the serv er Simple Bandwidth Prepartitioning (S B P ): 1. Divide bandwidth B in to dlog e partitions,
f
size B dlog e eac h 2. Sc hedule requests with lengths in [2 i1
l
min ; 2 i
l
min ) in the i th partition using W C ( Note that
2
within e ach p artition ) Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 10
SLIDE 11' & $ % S B P Example
1
log∆
B
log∆
B
log∆ t
B
log∆
B
t2
Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 11
SLIDE 12' & $ % Reducing F ragmen tation: Do wn-shift Prepartitioning
Idea:
again, prohibit short requests from monop
lizing
the serv er but also allo w long requests to \steal" from lo w er partitions Do wn-shift Bandwidth Prepartitioning (D B P ): 1. Divide bandwidth B in to dlog e partitions jB i j = B dlog e 2. Sc hedule requests with lengths in [2 i1
l
min ; 2 i
l
min ) in B 1 [ : : : [ B i using W C
Ma
jor b enet: reduce eects
f
bandwidth fragmen tation due to prepartitioning Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 12
SLIDE 13' & $ % D B P Example
∆
B
log∆
B
t2 t1 log∆
B
log∆
B
t log
2
Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 13
SLIDE 14' & $ % Comp etitiv eness
f
Bandwidth Prepartitioning Theorem: (a) Assuming
=
r max B < 1 dlog e , S B P and D B P are O
log
1log
comp
etitiv e (b) If
<
1 2dlog e , then S B P and D B P are O (log )
comp
etitiv e
Realistic
assumptions. E.g., if r max = 8 Mbps, l max = 120
l
min , then r max
d
log e = 56 Mbps ( << B )
F
r
reasonably large B , S B P and D B P are ne ar-optimal Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 14
SLIDE 15' & $ % Better Av erage Case: P
pularit
y-based Prepartitioning
Idea:
emplo y clip p
pularities
to dene partition sizes (simple S B P
r
D B P ma y underutilize the serv er)
p
j = cum ulativ e p
pularit
y
f
clips with length l j
P
L i = f (p j ; l j ) j l j 2 [2 i1
l
min ; 2 i
l
min ) g P
pularit
y-based Bandwidth Prepartitioning (P B P ):
Same
as D B P , but dene the size
f
the i th partition as: jB i j = f (P L i ) P i f (P L i )
B
for some function f Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 15
SLIDE 16' & $ % Exp erimen tal Results
Goal:
Prepartitioning w as based
n
comp etitiv e (w
rst-case)
analysis | what ab
ut
a v erage-case?
W
C vs. P B P ( results sho wn with f (P L i ) = P P L i p j
l
j )
A
rrival Pr
c
ess : P
isson
, Burst y , P
isson
+ Short Bursts { capture short-term
v
erloads (e.g., 6
'clo
c k news)
Popularities
: Zipan L ength-Popularity Corr elation : P
sitiv
e , Negativ e , Random
Metric
: fraction
f
serv er capacit y utilized sc heduled P l i
r
i B
sim
ulation time Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 16
SLIDE 17' & $ % Exp erimen tal Results (con t.)
P
isson
Arriv als
Burst
y Arriv als, Random Correlation
0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 2.5 3 Fraction of Server Capacity Used Request Arrival Rate Poisson Arrivals, z=0.6, Random Correlation PBP WC 0.2 0.4 0.6 0.8 1 50 100 150 200 250 300 Fraction of Server Capacity Used Burst Separation Bursty Arrivals, Batch Size=40, z=0.6, Random Correlation PBP WC
Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 17
SLIDE 18' & $ % Exp erimen tal Results (con t.)
Burst
y Arriv als, Negativ e Correlation
P
isson+Short
Bursts
0.2 0.4 0.6 0.8 1 50 100 150 200 250 300 Fraction of Server Capacity Used Burst Separation Bursty Arrivals, Batch Size=40, z=0.6, Negative Correlation PBP WC 0.2 0.4 0.6 0.8 1 0.01 0.02 0.03 0.04 0.05 0.06 Fraction of Server Capacity Used lambda(short) Poisson + Short Burst Arrivals, lambda(long)=0.7 PBP WC
Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 18
SLIDE 19' & $ % Conclusions and F uture W
rk
Comp
etitiv e analysis for admission con trol in Con tin uous Media DBs: 1. Con v en tional W C has comp etitiv e ratio linear in
=
l max l min 2. Lo w er b
unds
f
(log ) for an y deterministic
r
randomized strategy 3. Prepartitioning strategies { near-optimal for sucien tly large bandwidth 4. Exploit kno wledge
f
p
pularities
for go
d
a v erage-case p erformance 5. Exp erimen tal v alidation
Incorp
rate
ther
resources (e.g., memory)
On-line
load balancing in distributed con tin uous media serv ers Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 19
SLIDE 20' & $ % Comp etitiv e Ratio: F
rmal
Denition
:
request sequence
V
A ( ) P S A l i
r
i : total \b enet"
f
A
v
er
(A)
= 8 > > < > > : sup A
;
V A
(
) V A ( ) , if A is deterministic sup A
;
V A
(
) E A [V A ( )] , if A is randomized Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 20
SLIDE 21' & $ % Exp erimen tal Results: More Details
P
isson:
arriv al rate
Burst
y: short bursts
f
request batc hes arriving at displacemen ts
f
burst sep ar ation
P
isson+Bursts:
p
isson
arriv al
f
long requests ( l
ng
) with bursts
f
short requests ( shor t ) System P arameter V alue Serv er Bandwidth Capacit y 100 c hannels / 100{250 Mbps Request Lengths 5 min utes { 150 min utes Request Rates (V ariable Bandwidth Case) 500 Kbps
8
Mbps Zipan P
pularit
y Sk ew (z ) 0.0
2.0
Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 21
SLIDE 22' & $ % Related W
rk
On-line
A lgorithms: On-line In terv al Sc heduling , On-line circuit routing
Shar
e d Vide
-on-Demand
[Aggarw al et al., ESA'95] Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 22
