Best-E�o rt versus Reservations: A Simple Compa rative Analysis Lee Breslau Scott Shenk er Septemb er 2, 1998
Context Question: Ho w b est to supp o rt real-time ap- plications in the Internet? One answ er: Extend Internet a rchitecture to supp o rt resource reservations applications explicitly request enhanced qual- � it y of service from the net w o rk net w o rk sa ys o r y es no � Status: lots of resea rch, standa rdization activit y and � p ro duct development ho w ever, widesp read disagreement ab out � the wisdom of resource reservations remains 1
Basic Argument: 1991 The b est-e�o rt Internet w o rks just Deering �ne as it is! Why mess with success? Sure it w o rks great fo r data applica- Shenk er tions, but some audio and video applica- tions need reservations. Mo dern audio and video applications Deering a re and therefo re don't need reser- adaptive vations. Y es, but even some adaptive audio Shenk er and video applications need reservations to p erfo rm adequately . No, they don't. Deering Y es, they do. Shenk er No, they don't. Deering Y es, they do. Shenk er . . . 2
Basic Argument: 1998 . . . No, they don't. Deering Y es, they do. Shenk er No, they don't. Deering Y es, they do. Shenk er . . . 3
Goals: Develop a mo del that captures k ey simple � issues Increase our understanding of the essential � features Info rm the debate � Non-goals: A mo del that completely re�ects realit y � Cha racterization of costs of resource reser- � vations Settle the debate � 4
Basic Mo del Link of capacit y sha red b y �o ws C k P er �o w utilit y , is a function of a �o w's band- � width sha re b (0) = 0 � � ( 1 ) = 1 � � non-decreasing � If �o ws each receive equal bandwidth total k utilit y equals: C = ( ) V k � � k V a riable load rep resented b y P ( k ) 5
Basic Mo del (cont.) Best E�o rt C ( C ) = 1 ( k ) k ( ) V P � � P B =1 k k Reservations F o r a certain class of utilit y functions, util- � it y is maximized b y limiting numb er of �o ws to k max k C max ( C ) = ( k ) k ( ) + V P � � P R =1 k k C 1 ( k ) k ( ) P � P max = k +1 k k max max Discrete mo del allo ws direct computation; con- tinuum version enables examination of asymp- totic b ehavio r as C increases V ( C ) V ( C ), but b y ho w much? � R B 6
P erfo rmance Measures P erfo rmance gap, � � ( C ) = V ( C ) V ( C ) � � R B Bandwidth gap, � Ho w much additional bandwidth must b e � added to a b est-e�o rt net w o rk to achieve the same utilit y as a reservation net w o rk? ( C ) = ( C + �( C )) V V � R B 7
Utilit y F unctions { ( b ) � Rigid 1 0.8 0.6 Utility 0.4 0.2 0 0 1 2 3 4 5 Bandwidth � ( b ) = 0 fo r � b < b � ( b ) = 1 fo r � b b � 8
Utilit y F unctions { ( b ) (cont.) � Adaptive 1 0.8 0.6 Utility 0.4 0.2 0 0 1 2 3 4 5 Bandwidth Minimum bandwidth requirement Signi�cant ma rginal utilit y over a wide range of b able to adjust to di�erent levels of net w o rk � service still b ene�t from reservations � 9
Load Mo dels { ( k ) P 3 distributions k � � � e P oisson: P ( k ) = � ! k � � � � k Exp onential: ( k ) = (1 ) e P e � � � Algeb raic: ( k ) = P � z � + k Rep resent a range of load mo dels, no claim ab out their validit y 10
Results { P oisson Adaptive P erfo rmance 1 Reservations Best Effort 0.8 0.6 Utility 0.4 0.2 0 0 200 400 600 800 1000 Capacity Bandwidth Gap 10 8 Incremental Capacity 6 4 2 0 0 200 400 600 800 1000 Capacity 11
Results { Algeb raic Rigid P erfo rmance 1 0.8 Reservations Best Effort 0.6 Utility 0.4 0.2 0 0 200 400 600 800 1000 Capacity Bandwidth Gap 500 400 Incremental Capacity 300 200 100 0 100 200 300 400 500 Capacity 12
Summa ry of Results P erfo rmance Gap, � Signi�cant fo r small (i.e., L ) but C C < � quickly converges to zero (except in the algeb raic case) Bandwidth Gap, � P oisson: � 0 � ! Exp onential/Adaptive: � 0 � ! Exp onential/Rigid: � ln C � � Algeb raic: � C � / Conjecture: �( C ) = ( e 1) C is maximum bandwidth � � gap 13
V a riable Capacit y Given a p rice p er unit bandwidth p , p rovision net w o rk to maximize total w elfa re: ( C ) V pC � Compute capacit y as a function of p rice: ( p ) C T otal w elfa re: ( p ) = ( C ( p )) ( p ) W V pC � � B B B B ( p ) = ( C ( p )) ( p ) W V pC � � R R R R Price ratio to equalize w elfa re: ~ p ( p ) = where ( ~ ) = ( p ) � � W p W R B p 14
V a riable Capacit y { Results As 0: p ! P oisson: ( p ) 1 � � ! Exp onential: ( p ) 1 � � ! Algeb raic: ( p ) � , with 1 � � > � ! F o r algeb raic distribution, no matter ho w cheap bandwidth b ecomes, reservation-based net w o rk retains an advantage over b est-e�o rt Conjecture: lim ( p ) fo r all distribu- � e � + p ! 0 tions 15
Extensions Sampling P erfo rmance va ries over time � Utilit y ma y b e a function of the maximum � load exp erienced F o r each �o w, assume utilit y is the mini- � mum value tak en over samples S Retry Rejected �o ws can request service later and � receive non-zero utilit y But some p enalt y fo r dela y � Mo del rejected �o ws retrying as additional � load 16
Extensions { Results P oisson { no e�ect Exp onential { little e�ect, except with C L � in sampling extension Algeb raic { signi�cant change b oth with C L � and in asymptotic b ehavio r �( C ) and ( p ) no longer b ounded � � C 17
Conclusions No simple answ er to our o riginal question Over-p rovisioning app ea rs su�cient with P ois- son and Exp onential load mo dels Reservations a re useful with Algeb raic distribu- tion What is the nature of future Internet load? 18
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