[PDF] - Best-Eo rt versus Reservations: A Simple Compa rative PDF Document

SLIDE 1 Best-Eo rt versus Reservations: A Simple Compa rative Analysis Lee Breslau Scott Shenk er Septemb er 2, 1998

SLIDE 2 Context Question: Ho w b est to supp

rt

real-time applications in the Internet? One answ er: Extend Internet a rchitecture to supp

rt

resource reservations

applications

explicitly request enhanced qual- it y

f

service from the net w

rk
net

w

rk

sa ys y es

r

no Status:

lots
f

resea rch, standa rdization activit y and p ro duct development

ho

w ever, widesp read disagreement ab

ut

the wisdom

f

resource reservations remains 1

SLIDE 3 Basic Argument: 1991 Deering The b est-eo rt Internet w

rks

just ne as it is! Why mess with success? Shenk er Sure it w

rks

great fo r data applications, but some audio and video applications need reservations. Deering Mo dern audio and video applications a re adaptive and therefo re don't need reservations. Shenk er Y es, but even some adaptive audio and video applications need reservations to p erfo rm adequately . Deering No, they don't. Shenk er Y es, they do. Deering No, they don't. Shenk er Y es, they do. . . . 2

SLIDE 4 Basic Argument: 1998 . . . Deering No, they don't. Shenk er Y es, they do. Deering No, they don't. Shenk er Y es, they do. . . . 3

SLIDE 5 Goals:

Develop

a simple mo del that captures k ey issues

Increase
ur

understanding

f

the essential features

Info

rm the debate Non-goals:

A

mo del that completely reects realit y

Cha

racterization

f

costs

f

resource reservations

Settle

the debate 4

SLIDE 6 Basic Mo del Link

f

capacit y C sha red b y k

ws

P er

w

utilit y ,

is

a function

f

a

w's

bandwidth sha re b

(0)

=

(1)

= 1

non-decreasing

If k

ws

each receive equal bandwidth total utilit y equals:

V

= k

(

C k ) V a riable load rep resented b y P (k ) 5

SLIDE 7 Basic Mo del (cont.) Best Eo rt

V

B (C ) = P 1 k =1 P (k )k

(

C k ) Reservations

F
r

a certain class

f

utilit y functions, utilit y is maximized b y limiting numb er

f
ws

to k max

V

R (C ) = P k max k =1 P (k )k

(

C k ) + P 1 k =k max +1 P (k )k max

(

C k max ) Discrete mo del allo ws direct computation; con- tinuum version enables examination

f

asymptotic b ehavio r as C increases V R (C )

V

B (C ), but b y ho w much? 6

SLIDE 8 P erfo rmance Measures P erfo rmance gap,

(C

) = V R (C )

V

B (C ) Bandwidth gap,

Ho

w much additional bandwidth must b e added to a b est-eo rt net w

rk

to achieve the same utilit y as a reservation net w

rk?
V

R (C ) = V B (C + (C )) 7

SLIDE 9 Utilit y F unctions {

(b)

Rigid

0.2 0.4 0.6 0.8 1 1 2 3 4 5 Utility Bandwidth

(b)

= fo r b <

b
(b)

= 1 fo r b

b

8

SLIDE 10 Utilit y F unctions {

(b)

(cont.) Adaptive

0.2 0.4 0.6 0.8 1 1 2 3 4 5 Utility Bandwidth

Minimum bandwidth requirement Signicant ma rginal utilit y

ver

a wide range

f

b

able

to adjust to dierent levels

f

net w

rk

service

still

b enet from reservations 9

SLIDE 11 Load Mo dels { P (k ) 3 distributions

P
isson:

P (k ) =

k

e

k

!

Exp
nential:

P (k ) = (1

e
)e
k
Algeb

raic: P (k ) =

+k

z Rep resent a range

f

load mo dels, no claim ab

ut

their validit y 10

SLIDE 12 Results { P

isson

Adaptive P erfo rmance

0.2 0.4 0.6 0.8 1 200 400 600 800 1000 Utility Capacity Reservations Best Effort

Bandwidth Gap

2 4 6 8 10 200 400 600 800 1000 Incremental Capacity Capacity

11

SLIDE 13 Results { Algeb raic Rigid P erfo rmance

0.2 0.4 0.6 0.8 1 200 400 600 800 1000 Utility Capacity Reservations Best Effort

Bandwidth Gap

100 200 300 400 500 100 200 300 400 500 Incremental Capacity Capacity

12

SLIDE 14 Summa ry

f

Results P erfo rmance Gap,

Signicant

fo r small C (i.e., C < L) but quickly converges to zero (except in the algeb raic case) Bandwidth Gap,

P
isson:
!
Exp
nential/Adaptive:
!
Exp
nential/Rigid:
ln

C

Algeb

raic:

/

C Conjecture:

(C

) = (e

1)C

is maximum bandwidth gap 13

SLIDE 15 V a riable Capacit y Given a p rice p er unit bandwidth p, p rovision net w

rk

to maximize total w elfa re: V (C )

pC

Compute capacit y as a function

f

p rice: C (p) T

tal

w elfa re:

W

B (p) = V B (C B (p))

pC

B (p)

W

R (p) = V R (C R (p))

pC

R (p) Price ratio to equalize w elfa re:

(p)

= ~ p p where W R ( ~ p ) = W B (p) 14

SLIDE 16 V a riable Capacit y { Results As p ! 0:

P
isson:
(p)

! 1

Exp
nential:
(p)

! 1

Algeb

raic:

(p)

! , with

>

1 F

r

algeb raic distribution, no matter ho w cheap bandwidth b ecomes, reservation-based net w

rk

retains an advantage

ver

b est-eo rt Conjecture: lim p!0 +

(p)
e

fo r all distributions 15

SLIDE 17 Extensions Sampling

P

erfo rmance va ries

ver

time

Utilit

y ma y b e a function

f

the maximum load exp erienced

F
r

each

w,

assume utilit y is the minimum value tak en

ver

S samples Retry

Rejected
ws

can request service later and receive non-zero utilit y

But

some p enalt y fo r dela y

Mo

del rejected

ws

retrying as additional load 16

SLIDE 18 Extensions { Results P

isson

{ no eect Exp

nential

{ little eect, except with C

L

in sampling extension Algeb raic { signicant change b

th

with C

L

and in asymptotic b ehavio r

(C

) C and

(p)

no longer b

unded

17

SLIDE 19 Conclusions No simple answ er to

ur
riginal

question Over-p rovisioning app ea rs sucient with P

is-

son and Exp

nential

load mo dels Reservations a re useful with Algeb raic distribution What is the nature

f

future Internet load? 18