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USC Computer Science Technical Reports, no. 586 (1994)

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USC Computer Science Technical Reports, no. 586 (1994)

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Content Asymptotic Resource Consumption in Multicast
Reserv ation St yles
USCCS
Dann y J Mitzel Scott Shenk er
mitzelcatarin aus ced u shenk erparcxer o x com
Computer Science Departmen t XeroxP AR C
Univ ersit y of Southern California Co y ote Hill Road
Los Angeles CA P alo Alto CA and
Hughes Aircraft Compan y
P O Bo x Los Angeles CA Septem b er COMPUTER SCIENCE DEP AR TMENT
UNIVERSITY OF SOUTHERN CALIF ORNIA
LOS ANGELES CALIF ORNIA
T e chnic al R ep ort USCCS
Asymptotic Resource Consumption in
Multicast Reserv ation St yles
Dann y J Mitzel Scott Shenk er
mitzelcatarina usc ed u shenk erparc xer o x com
Computer Science Departmen t XeroxP AR C
Univ ersit y of Southern California Co y ote Hill Road
Los Angeles CA P alo Alto CA and
Hughes Aircraft Compan y
P O Bo x Los Angeles CA Abstract
The goal of net w ork design is to meet the needs of resi
den t applications in an ecien t manner Adding realtime
service and p oin ttom ultip ointm ulticast routing to the In
ternets traditional p oin ttop oin t b est eort service mo del
will greatly increase the In ternets eciency in handling
p oin ttom ultip oin t realtime applications Recen tlythe
RSVP resource reserv ation proto col has in tro duced the con
cept of reserv ation st yles whic h con trol ho w reserv ations
are aggregated in m ultip oin ttom ultip oin t realtime appli
cations In this pap er whic h is an extension of w ean alytically ev aluate the eciency gains oered b ythis new
paradigm on three simple net w ork top ologies linear mtree
and star W e compare the resource utilization of more tradi
tional reserv ation approac hes to the RSVP reserv ation st yles
in the asymptotic limit of large m ultip oin t applications W e
nd that in sev eral cases the eciency impro v emen ts scale
linearly in the n um b er of hosts
Intro duction
The goal of net w ork design in its most concise form ulation
is to meet the needs of residen t applications
in an ecien t
manner The k ey concept here is eciency Most application
needs can b e met merely b y pro viding sucien t bandwidth
Ho w ev er bandwidth is not free and so net w orks should b e
designed to meet application p erformance goals while using
bandwidth ecien tly The In ternet and other similar pac k etswitc hed net w ork
arc hitectures oer p oin ttop oin t b esteort service The
net w ork tak es pac k ets from a single source and deliv ers them
to a single destination Eac hpac k et is giv en b esteort ser
By residen t applications w e mean those applications using the
net w ork not those applications residing in the net w ork
vice whic h means that no guaran tees are made as to when
and whether it will b e deliv ered Op erationally b esteort
service is t ypically implemen ted using FIF O service at net
w ork switc hes with no admission con trol or resource reser
v ation that is sources need not notify the net w ork b efore
transmitting data and no resources are set aside for an y
particular o w
This arc hitecture with its p oin ttop oin t b esteort ser
vice mo del has supp orted a wide v ariet y of data applications
in an extremely ecien t manner Applications lik e remote
login eg T elnet le transfer eg FTP and electronic
mail are handled m uc h more ecien tly in this arc hitecture
than they are in sa y X or in the telephone net w ork
Ho w ev er there are application requiremen ts that this
service mo del do es not handle ecien tlyF or instance ap
plications likein teractiv e video and v oice often ha v e strin
gen t realtime requiremen ts on the deliveryofpac k ets T obe
useful to these application pac k ets m ust arriv e within some
dela y b ound see for a fuller discussion of these require
men ts There has b een signican t recentw ork sho wing that b y carefully sc heduling pac k ets and
utilizing admission con trol to prev en t net w ork o v erload one
can ac hievesuc h realtime dela y b ounds in a pac k etswitc hed
en vironmen t It is widely b eliev ed that pro viding suchde la y b ounds only to those o ws whic h need them b yusing
resource reserv ation and non trivial sc heduling algorithms is
m uc h more ecien t than con tin uing to use FIFOsc heduling
and merely adding enough bandwidth to pro vide lo w dela y
service to all o ws
Notice that reserv ations c hange the concept of resource
consumption in the net w ork Without reserv ations the us
age of resources in these net w orks is tied directly to send
ing pac k ets ie if y ou ha v ent sen tanypac k ets y ou ha v ent
consumed an y resources since y ou ha v ent denied or aected
an yb o dy elses service With reserv ations admission con trol
will den y access if there are not sucien t unreserv ed re
sources a v ailable reserv ations ev en if un used can therefore
prev en t other o ws from reserving resources Th us reserv a
tions themselv es can b e seen as consuming resources some
what indep enden tly
from the actual usage of those reser
The degree of indep endence dep ends on the nature of realtime
service pro vided Service whichpro vides w orstcase dela y b ounds
m ust base all admission con trol decisions on the reserv ation parame

T e chnic al R ep ort USCCS
v ations In this pap er w e will fo cus on the reserv ation of
resources rather than their actual use Although audio and
video applications often do not ha v e a xed qualit yof ser vice requiremen t ie they can op erate o v er a broad range
of data rates pro viding v arying degrees of p erceiv ed qual
it y w e assume that a reserv ation mec hanism is required to
ensure minimal signal qualitylev els
Another class of applications whose requiremen ts are not
handled ecien tly bythe In ternets p oin ttop oin t b estef
fort service are those that require the same data to b e sen t
to sev eral receiv ers This o ccurs in teleconferences and re
mote lectures where v oice and video from one individual go
to man y other participan ts Using the traditional p oin tto
p oin t service a separate pac k et is sentto eac h receiv er w e
call this sim ultaneous unicasts m ultiple copies of pac k ets
are sento v er the o v erlapping p ortions of the routes to indi
vidual receiv ers Multicast routing solv es this prob
lem byha ving the net w ork whenev er the routes div erge
send a single cop y along eac h path As w equan tify later
this leads to tremendous eciency gains In fact m ulticast
as em b o died in the Mb one has b een crucial in enabling
the widespread distribution of video and v oice in broadcast
ing In ternet Engineering T ask F orce meetings Broadcasting
these meetings whic hattimesha vesev eral h undred listen
ers w ould simply ha v e b een imp ossible without m ulticast
giv en the curren t limited bandwidth on manyIn ternet links
Adding m ulticast and realtime service will transform the
In ternet from a p oin ttop oin t b est eort net w ork in to one
that also oers p oin ttom ultip oin t realtime service This
will greatly expand the range of applications whose needs
can b e ecien tly met bythe In ternet W e should note ho w
ev er that there are some realtime applications that are b est
describ ed as m ultip oin ttom ultip oin t an example of this is
an nw a y teleconference where ev ery participan t needs to
see and hear ev ery other participan t Suc h applications can
b e dealt with as a set of indep enden t p oin ttom ultip oin t
applications when the paths from t wodieren t sources to
the same receiv er o v erlap resources are reserv ed for b oth
sources indep enden tly This approac his t ypically sucien t
when the trac from these sources and the receiv ers de
sire to see that trac
is relativ ely indep enden t Ho w ev er
as rst recognized in when the sources are not inde
p enden t this approac h leads to ineciencies The RSVP
resource reserv ation proto col in tro duced the concept of
reserv ation st yles Reserv ation st yles are dieren tw a ys of
aggregating the resource requiremen ts for eac h source on a
single link T able summarizes the reserv ation st yles in v es
tigated in this study The detailed denition of these reser
v ation st yles and the mec hanisms that implemen t them
ha v e b een describ ed elsewhere Our purp ose in this pap er is to ev aluate the extentto
whic h these reserv ation st yles increase eciency in particu
lar w e fo cus on asymptotic resource usage as n the n um ber
of participan ts in the m ultip oin t application gets large An
earlier w ork discussed these issues in a more informal
manner the presen tw ork is an attempt to quan tify these
sa vings in a more systematic and rigorous fashion W end
that the RSVP reserv ation st yles ac hievev ery signican t
sa vings for large nTh us if m ultip oin ttom ultip ointap plications represen t a sizable p ortion of the future net w ork
load then it will b e imp ortan t to include these reserv ation
ters without regard for the actual usage Service whic h pro vides lo w er
qualit y assurances lik e the predictiv e service in can base ad
mission con trol decisions at least in part on actual usage
By this w e mean that m y desire to see source A is indep enden t
of m y desire to see source B
st yles in the basic In ternet service mo del
Welook att w o cases where these reserv ation st yles are
useful The rst case is selflimiting trac where the v ery
nature of the application leads to correlations in the trac
patterns from the dieren t sources An example of this is an
audio conference when the so cial prohibition of sim ultane
ously sp eaking means that rarely will more than one or p er
haps a few sp eak ers b e activeat an y one time The second
case is c hannel selection where receiv ers w an t the option
of receiving data from anyofthe a v ailable sources but will
nev er w an t to receiv e data from more than one or a few at
a time Eac h of these cases violate the indep endence as
sumption and th us the reserv ations for trac from separate
senders should not necessarily b e treated indep enden tly Wein v estigate the asymptotic resource sa vings ac hiev ed
b y these RSVP reserv ation st yles in three simple net w ork
top ologies see Figure linear mtree and star These
top ologies are not mean t of course to b e realistic Rather
b y restricting ourselv es to simple and tractable top ologies
our in tentistopro vide a more rigorous and systematic anal
ysis of resource consumption in large m ultip oin ttom ulti
poin t applications Most of our results are analytical al
though w e do rely on sim ulations for some quan tities whic h
ha v e so far deed direct calculation
This pap er has sections W e rst in Section de
ne the basic resource consumption mo del and describ e the
three simple top ologies W e then in Sections and de
scrib e the t w o reserv ation st yles and analyze through b oth
calculations and sim ulations their asymptotic resource con
sumption W e conclude with a summary of our results in
Section Net w o rk Mo del
W e consider m ultip oin ttom ultip oin t applications running
onaset of n net w ork hosts Eac h host is b oth a sender
of data and a receiv er of data Eac h host generates an
equiv alen t trac stream whic h consumes or at least re
quires the reserv ation of some giv en amoun t of bandwidth
The quan tityof in terest is the total reserv ed bandwidth
needed to supp ort a giv en size application W e will set the
amoun t of bandwidth reserv ed to b e the unit of bandwidth
so that ev ery indep enden t reserv ation consumes one unit of
bandwidth
All reserv ations are unidirectional in nature
W e consider the three net w ork top ologies depicted in Fig
ure linear mtree and star While none of these top olo
gies are particularly go o d mo dels for a real net worktheydo
represen t a wide sp ectrum of p ossibilities Man y of our re
sults are relativ ely indep enden t of top ology whic h suggests
that p erhaps our results are relev an t to more general net
w orks Eac h link is bidirectional with separate reserv ations
for bandwidth in eac h direction W e consider the capacit y
of eac h link to b e unlimited
Eac h source sends its data to all other hosts Routing is
done via m ulticast Since these are acyclic top ologies there
is no am biguit y in the routes There is a m ulticast distribu
tion tree from eac h source to all other hosts Similarly there
isarev erse tree going from eac h receiv er to all other hosts
this describ es the paths tak en b y data arriving at that host
In our top ologies the distribution tree and the rev erse tree
are alw a ys iden tical In fact for all hosts they b oth are the
en tire net w ork in all of our top ologies although links ma ybe
tra v ersed in dieren t directions in dieren t trees eac hlink
Note that w e are using a rather primitiv e mo del of reserv ations
using only bandwidth to describ e the reserv ation In practice the
o w sp ecication will lik ely b e somewhat more complex

T e chnic al R ep ort USCCS
Reserv ation St yle Description
Indep endentT ree A separate and indep enden t reserv ation is allo cated for eac h source distribution
tree P erlink reserv ation is based on the n um b er of upstream senders N up sr c Shared T ree A shared reserv ation is allo cated on eac h link in the distribution mesh for use
byan y source P erlink reserv ation is based on the n um b er of upstream senders
limited b y the n um ber of sim ultaneous sources that will transmit at an y one time
MI N N up sr c N sim sr c
Chosen Source A separate and indep enden t reserv ation is allo cated along the distribution tree
from eac h source to only the set of receiv ers that are curren tly tuned in to that
source P erlink reserv ation is based on the n um b er of upstream senders that
ha v e b een selected b y at least one do wnstream receiv er N up sel sr c Dynamic Filter A set of shared resources is allo cated on eac h link to accommo date the maximal
do wnstream resource demand Eac h reserv ation has a receiv ercon trolled lter
allo wing dynamic selection among sources P erlink reserv ation is based on the
n um b er of upstream senders limited b y the n um b er of indep enden t reserv ations
required to allo w all do wnstream receiv ers to mak e indep enden t source selections
MI N N up sr c N dow n rcvr N sim chan T able Summary of Reserv ation St yles
= Host = Router = Link Legend:
Linear m-tree (m=2) Star
Figure Net w ork T op ologies
is tra v ersed exactly once in eac h tree A distribution mesh
is the union of the distribution trees F or our net w orks the
distribution mesh is alw a ys the en tire net w ork with ev ery
link tra v ersed in b oth directions
F or eachnet w ork top ologyw e consider a net w ork with
n end hosts and let the net w ork growas the n um b er of hosts
do es There are sev eral quan tities that will b e relev an t to our
later analysis F or a giv en size net w ork nw e can consider
T otal Links L The total n um b er of links in the top ology Diameter D The maxim um hosthost distance in n um
b ers of hops
Av erage P ath A The a v erage hosthost distance in n um
b ers of hops This do es not coun t a host connecting
to itself
Let us no w briey discuss the three top ologies The
linear top ology has n links with eac h connecting t w o
hosts Clearly D L n A sligh tly more non trivial
calculation
rev eals that A n Here as elsewhere in the pap er w e will spare the reader the
deriv ation of these essen tially com binatoric form ulae Also all of
In the mtree top ology the hosts are at the lea v es of the
tree and the tree has a constan t branc hing ratio of mHere n m
d
where d is the depth of the tree The longest path
is one that tra v erses to and from the ro ot of the tree so
D d log
m
nW e also ha v e L m
m n and
A m n log
m
n n n m The star conguration has a cen tral h ub and there is a
link connecting eac h host to this h ub Here D A and
L n Notice that the star top ology is merely the limiting
case of the mtree top ology with d and m n These results are summarized in T able F or later com
parisons weno w compute the resource usages of m ulti
cast and sim ultaneous unicasts The quan tityof in terest
is the total n um b er link tra v ersals whic h coun ts eac h time
apac k et tra v erses a link as a separate use of the link T odo
this computation and later computations w e dene t w o
quan tities for a giv en direction along a giv en link
these form ulae are only v alid for n and for v alues of n that
represen t a complete top ology This is not an issue for the linear or
star top ologies but is relev an t for the mtree where n m
d
are the
only v alid v alues for n Ev en though links are bidirectional when referring to the reser
v ations along a link wet ypically are referring to a single direction

T e chnic al R ep ort USCCS
T op ology L D A
Linear n n n
mT ree
m
m n log
m
n
m n log
m
n n n m
Star n T able T op ological Prop erties
N up sr c is the n um b er of upstream sources that include the
link in their m ulticast distribution tree
N dow n rcvr is the n um ber of do wnstream hosts that receiv e
data along this link
F or the top ologies w e consider these t won um b ers m ust
alw a ys sum to n N up sr c N dow n rcvr n since ev ery
link is on ev ery distribution tree F urthermore considering
the rev erse direction of the link merely rev erses these t w o
n um bers When using sim ultaneous unicasts the total n um ber of
pac k ets tra v ersing a particular link is giv en b y N up sr c N dow n rcvr When using m ulticasts the total n um ber of
pac k ets tra v ersing a particular link is giv en b y N up sr cbe cause duplication for dieren t receiv ers is eliminated
Sending a pac k et from eac h source to eac h destination
without using m ulticast in v olv es n n A link tra v ersals
the data from a single source tra v els o v er n paths of a v er
age length A and there are n suc h sources Using m ulticast
in v olv es merely nL link tra v ersals since no link is tra v ersed
more than once byan y pac k et and all links are tra v ersed in
exactly one direction in eachm ulticast tree Th us the ratio
of n A to L is an estimate of resource sa vings due to
m ulticast F or the linear net w ork these sa vings are O n for mtrees the sa vings are O log
m
n and for a star the
sa vings are O W e should note that these sa vings are calculated for link
tra v ersals of data In the rest of the pap er w e are in terested
in sa vings in terms of reserv ed resources Reserv ation st yles
do not aect the actual n um b er of link tra v ersals only the
resources reserv ed
SelfLimiting Applications
Weno w consider selflimiting applications These are m ul
tip oin ttom ultip oin t applications whichha v e application
lev el constrain ts that inhibit data sources from transmitting
sim ultaneouslyAs w e men tioned b efore an audio confer
ence is one example of this where the so cial inhibitions tend
to discourage sim ultaneous sp eaking
Another rather dif
feren t example is satellite trac king Here there are a n um
b er of large an tennae and when the satellite is within their
range the data is do wnloaded and then sen t to the other
sites If the ranges of the an tennae do not o v erlap so the
satellite is only within range of a single an tenna at anyone
time then the trac is selflimiting b ecause t w o sources
are nev er activ e sim ultaneously More generally w e can de
scrib e a selflimiting application b y the maximal n um ber of
sources that will transmit at an y one time w e will denote
this quan tityb y N sim sr c The traditional approachis tomak e separate and inde
p enden t reserv ations for eac h distribution tree W e will call
Note that a vido conference is not selflimiting since video is in
dep enden t of what other participan ts are doing
this the Indep ende nt T r e e approac h On ev ery link the n um
b er of units of bandwidth reserv ed is giv en b y N up sr cThe
total bandwidth reserv ed o v er the whole net w ork is giv en b y
nL n n A since there is an indep enden tly reserv ed
path from ev ery sender to its n receiv ers and there are
n senders
Ho w ev er as w as noted in the application require
men ts are en tirely met if on ev ery link there are merely
sucien t reserv ed resources to accommo date the maxim um
n um b er of upstream sources that will sim ultaneously trans
mit Th us on eac h individual link w e need only reserv e
MI N N up sr c N sim sr c whic his incon trast to the N up sr c
units reserv ed b y the Indep endentT ree approac h RSVP has
dened a reserv ation st yle whichw e call
Shar e d in whic h
only this necessary reserv ation of MI N N up sr c N sim sr c is made these resources are shared b et w een the upstream
sources in the sense that trac from an yofthemcan use
this reserv ed bandwidth
F or simplicit yw e fo cus on the case where N sim sr c so in the Shared reserv ation st yle eachlinkhas either or
units of bandwidth reserv ed The dierence in reserv a
tion st yles can then b e concisely captured b y noting that
the Indep enden t reserv ations are based up on the sum of all
links in all distribution trees while the Shared reserv ations
are based up on the union of the links across the distribu
tion mesh In all of our top ologies the mesh consists of all
the links tra v ersed in b oth directions whereas eac h distribu
tion tree consists of all links tra v ersed in only one direction
Th us the ratio of bandwidth consumed b et w een these t w o
approac hes is alw a ys
n
in our three top ologies Weha v e
summarized these results in T able In fact whenev er the distribution mesh is acyclic the ra
tio of Indep enden t to Shared resource usage is exactly
n
Consider the distribution tree from source A and assume
that it do es not touc h some link in either direction in the
distribution mesh Since this link is in the distribution mesh
it m ust lie on the path b et w een t w o sources assume that this
link is on the path from B to C Then the path from A to
Bto C toA con tains a cycle since it can only tra v erse the
missing link once going from B to C Th us if the distri
bution mesh is acyclic then ev ery distribution tree touc hes
ev ery link once and only once It then directly follo ws that
the distribution mesh touc hes ev ery link in b oth directions
Therefore whenev er the distribution mesh is acyclic the ra
tio of resource usage is exactly
n
Note that in cyclic net
w orks this result need not hold F or instance in a fully con
nected net w ork the Indep enden t and the Shared resource
demands are exactly the same
F or purp oses of comparison it is in teresting to note that
m ulticasts adv an tage o v er sim ultaneous unicasts ranged from
O n in linear net w orks to O log
m
n in mtree net w orks
The terminology of the reserv ation st yles in RSVP is somewhat in
ux so here w e adopt a somewhat indep enden t terminology to a v oid
direct inconsistencies The shared reserv ation st yle is curren tly called
wildcardlter in
T e chnic al R ep ort USCCS
T op ology Num b er of Reserv ations Ratio
Indep enden t Shared
Linear n n n n
T ree
nm n
m m n m n
Star n
n
n
T able Resource Allo cation for SelfLimiting Applications with N sim sr c to O in star net w orks In con trast the shared reserv a
tion st yle has an adv an tage of
n
in all net w orks with acyclic
distribution meshes Observ e also that the results for the
Shared and Indep enden t reserv ation st yles are consisten t
with the in tuition that the resource requiremen ts of Inde
p enden t scale as O nL whereas those of Shared scale as
O L Channel Selection
Denition of Reservation St yles
The other class of applications w e consider are c hannel se
lection applications These are applications in whic h
the trac from eac h sender is indep enden t but the receiv er
only wishes to receiv e data from a limited n um b er of senders
at an y one time The ep on ymous example is that of tele
vision where one w an ts access to manyc hannels but only
w an ts to receiv e one at a time Similarly large m ultipart y
video conferences are sometimes an example of this in that a
receiv er ma y b e unable to accommo date data streams from
all activ e participan ts sim ultaneously but desires the abil
it y to dynamically select a subset of the sources to receiv e
at an y time This restriction on the n um ber of sim ultane
ous sources ma y b e due to bandwidth limitations displa y
or co dec hardw are or the inabilit y of the user to assimilate
information from all sources concurren tly In general w e
can c haracterize a c hannel selection application b y the max
im um n um ber of c hannels N sim chan it wishes to receiveat
an y one time
F rom the users p ersp ectiv e there are t w o alternativ e
service mo dels assured c hannel selection and nonassured
c hannel selection In assured c hannel selection the user is
guaran teed that the resources will b e a v ailable to view the
selected c hannel Th us assured c hannel selection in v olv es
prereserving resources for all of the c hannels Assured c han
nel selection is the service that is appropriate for the exam
ples cited ab o v e In nonassured c hannel selection no suc h
guaran tee is made and the request can b e denied b y admis
sion con trol W e consider this case only b ecause it pro vides a
con v enientlo w er b ound to the resources required for assured
c hannel selection There is a tradeo b et w een the extra as
surance of the assured service mo del and its presumably
higher cost due to extra resource consumption one of the
goals in this section is to examine quan titativelythisextra
resource consumption Weno w describ e the reserv ations
required to supp ort these assured and nonassured services
The most direct w a y to supp ort this nonassured service
is to mak e a new reserv ation ev ery time a new c hannel is
selected and then to tear do wn the old reserv ation W e
will call this the Chosen Sour c e reserv ation st yle since it
only reserv es for the curren tly c hosen sources Resources are
reserv ed along the distribution subtree from eachsourceto
the set of receiv ers that are curren tly tuned in to that source
The trees from dieren t sources are indep enden t Th us the
reserv ed amountonalink isgiv en b y N up sel sr c whichis
the n um b er of senders upstream that ha v e b een selected
byatleast one do wnstream receiv er The Chosen Source
reserv ation st yle b ecause it only reserv es for the curren tly
selected sources pro videsalo w er b ound for the resource
consumption required b y assured service W e can pro vide
assured service using t w o dieren t reserv ation st yles
The traditional w ayto pro vide assured c hannel selec
tion is to reserv e indep enden t trees for eac h source whic h
is just the Indep enden t reserv ation st yle discussed in Sec
tion This pro vides sucien t resources for all sources to
sim ultaneously arriv e at the receiv er The receiv er can then
switchbet w een c hannels b y selecting the desired incoming
stream The c hannel selecting or ltering of incoming data
is done en tirely at the receiv er m uchlik e the signals for all
TV c hannels arriv e at the cable settop b o x and the tuner
selects one
RSVP in tro duced the idea inspired b y a commen t
from Jon Cro w croft that this selecting or ltering pro
cess can o ccur within the net w ork rather than just at the
receiv er Eac h reserv ation on a link is accompanied bya l
ter that determines whic h pac k ets get to use the reserv ed re
sources One of the no v el asp ects of RSVP is that ev en while
the reserv ation is xed this lter can c hange dynamically in
resp onse to signals from the receiv ers RSVP oers a Dy
namic Filter reserv ation st yle whic h reserv es enough band
width on eac h link so that the receiv er can alw a ys select
without failure an y set of N sim chan sources RSVP pro
vides a mec hanism whereb y receiv ers inform their upstream
routers whic h sources they wish to receiv e and the lters are
then set to only allo w pac k ets from those sources to pass
The resource requiremen ts can b e expressed as follo ws on
ev ery link the amoun t reserv ed is giv en b y MI N N up sr c N dow n rcvr N sim chan recalling that N dow n rcvr is the
n um ber of do wnstream hosts that receiv e data from an y
source along the link ie the n um b er of receiv ers for whic h
this link is in the rev erse tree and N up sr c is the n um ber
of upstream sources that include the link in their m ulticast
distribution tree
This form ula merely expresses the insigh t that one need
not reservemorec hannels than the n um b er of upstream
sources nor more than the maximal n um ber of do wnstream
requests As one can see directly from the expression for
p erlink reserv ations on ev ery link the resources required
for Dynamic Filter reserv ations is b ounded ab o vebythe
Indep enden t reserv ation and b elowb y the Chosen Source
reserv ation
Weno w pro ceed to analyze the asymptotic resource con
sumptions of these v arious reserv ation st yles F or simplic
it yw ec ho ose N sim chan so ev ery receiv er receiv es only
one c hannel at a time With this c hoice the reserv ation
in the t w o directions on a link are iden tical since rev ers
ing directions merely rev erses the meanings of N up sr c and

T e chnic al R ep ort USCCS
N dow n rcvr Assured Channel Selection Alternatives
Weno w compare the t w o assured c hannel switc hing reser
v ation st yles The Indep enden t reserv ation case w as already
considered in Section recall that the total resource con
sumption is giv en b y nL The Dynamic Filter reserv ation
st yle requires a reserv ation of MI N N up sr c N dow n rcvron
ev ery link the presence of the MI N function mak es this
st yle somewhat harder to c haracterize and compute
In the linear case the reserv ation needed on a link in the
ith p osition is MI N i n i F or n o dd this sums to
n
and for n ev en it sums to
n
in T able w eonlyshowthe
result for n ev en
F or the mtree top ology the expression MI N N up sr c N dow n rcvr reduces to the n um b er of hosts b elo w the link
on the tree assuming the ro ot of the tree is up There
are m
i
links at depth i in the tree and there are m
d i
no des
b elo w the links at depth iTh us the resource consumption
at ev ery lev el is just m
d
the factor of is b ecause eac h
link has t w o directions Since there are d lev els the to
tal resource consumption is just dm
d
In terms of nthis
b ecomes n log
m
n The star top ology result can b e calculated b y merely
setting m n in the mtree result yielding a resource con
sumption of n These results are summarized in T able They are con
sisten t with the in tuition that the w orst case of Chosen
Source and hence Dynamic Filter scales as O nD in con
trast to Indep enden t scaling as O nL Dynamic Filter vs Nonassured Selection Overhead
As men tioned earlier our in terest in the Chosen Source
reserv ation st yle is primarily b ecause it represen ts the mini
mal resources needed to supp ort the curren tly selected sources
Th us w e can use this reserv ation st yle to quan tify the o v er
head incurred in pro viding the extra assurance in the assured
selection service as opp osed to the nonassured service pro
vided b y the Chosen Source st yle Ho w ev er the total re
source requiremen ts for Chosen Source dep end not only on
net w ork top ology and participan t distribution

but also on
the set of sources selected b y eac h receiv er When describing
the resource consumption of Chosen Source w e therefore
need to c haracterize the set of source selections Conse
quen tlyw e dene three classes of Chosen Source b eha vior
worst c ase CS worst o ccurs when all receiv ers correlate their
source selections to maximize the total resource consump
tion aver age c ase CS av gis the a v erage result when eac h
receiv er p erforms an indep enden t and random source selec
tion and b est c ase CS bestisac hiev ed when receiv ers cor
relate their source selections to minimize the total resource
consumption F or eac h of these Chosen Source b eha viors w e
compute either through analysis or sim ulation the total re
source consumption and compare these asymptotic resource
requiremen ts with those of the Dynamic Filter reserv ation
st yle
While w e exp ect that the w orst case of Chosen Source will scale
as O nD in more general top ologies w e doubt that Dynamic Filter
will con tin ue to b e equal to the w orst case of Chosen Source in more
general top ologies
These completely determine the resource requiremen ts for the In
dep enden t and Dynamic Filter reserv ation st yles
Chosen Source W o rst Case CS worst The w orst case for Chosen Source results when eac h receiv er
selects a distinct source resulting in no o v erlap in distribu
tion trees suc h that the set of selections maximizes the to
tal p oin ttop oin t distance F or the linear top ology CS worst
is obtained when eac h receiv er selects the host
n
distance
a w a y assuming for con v enience that n is ev en The total
resource requiremen ts for this case can b e easily calculated
to b e
n
F or mtree CS worst is obtained when eachre ceiv er selects a host that requires tra v ersal of the ro ot no de
this results in D link reserv ations p er source giving a to
tal requirementof nD n log
m
nF or the star top ology CS worst is obtained whenev er eac h receiv er selects a distinct
source resulting in n reserv ations
These results are repro duced in T able Surprisingly for all the top ologies studied the ratio of CS worst to Dy
namic Filter is alw a ys exactly That is in these top olo
gies pro viding assured c hannel selection requires absolutely
no additional resources when compared to the w orst case of
the nonassured c hannel selection W e do not y et knowho w
fully general this result is Wedokno w that it do es not
hold for the fully connected net w ork where Dynamic Filter
requires n n reserv ations and CS worst requires only n
Chosen Source Average Case CS av g Weno w consider the a v erage case p erformance of the Chosen
Source reserv ation st yle when all receiv ers mak e an indep en
den t and random source selection W eha v e b een unable to
solv e this case exactly and so instead w e use sim ulation to
compute CS av g Our exp erimen tal metho dology w as to sim ulate eachof
the three net w ork top ologies for v arious v alues of nF or
eachv alue of n w e p erformed random source selection for
eac h receiv er selecting a Chosen Source from among the
n other participan ts with uniform probabilit yThen w e
calculated the exact n um b er of link reserv ations required
b y the Chosen Source reserv ation st yle W e rep eated this
pro cess m ultiple times and used the sample mean to predict
CS av gEv en though the total n um b er of p erm utations for
sourcereceiv er selection gro ws as n n
w e found that
rep eating the random source selection pro cess just times
for eac h n resulted in an estimate of CS av g with less than
relativ e error at a condence lev el
Rather than displa ying CS av g s absolute p erformance
w e showho w CS worst compares to CS av g
In Figure w e
plot the ratio of the sim ulated CS av g resource requiremen ts
against those of CS worst for the linear mtree with m
and m and star top ologies Note that the ratio ap
p ears to asymptotically approac h a nonzero constan t for all
top ologies in v estigated the constan t dep ends on the top ol
ogy but in eac h top ology the ratio app ears to asymptote
to a constan t This implies that Dynamic Filter o v erallo
cates only a xed p ercen tage of resources when compared
to Chosen Source a v erage case Th us not only do es the
assured service of Dynamic Filter not require anyo v erallo
cation when compared to the w orst case of the nonassured
service of Chosen Source but it also only requires a xed
p ercen tage of o v erallo cation when compared to the a v erage
case of the nonassured service of Chosen Source Again w e
do not knowho w general these results are but they do hold
in eac h of our three top ologies

Note that CS worst is equiv alen t to Dynamic Filter th us this
also represen ts the ratio in p erformance of Dynamic Filter assured
c hannel selection to a v erage case Chosen Source nonassured c hannel

T e chnic al R ep ort USCCS
T op ology Num b er of Reserv ations Ratio
Indep enden t Dyn Filter
Linear n n n
n n
T ree
mn n m n log
m
n
m n m log
m
n
Star n
n
n
T able Resource Allo cation for Assured Channel Selection with N sim chan T op ology Num b er of Reserv ations Ratio
CS worst CS av g CS best CS av g C S worst CS best C S worst
Linear
n
O n
sim ulation n sim ulation
n
T ree n log
m
n O n log
m
n sim ulation
m n m sim ulation
m n n m log
m
n
Star n O nsim ulation n sim ulation
n n
T able Resource Allo cation for NonAssured Channel Selection with N sim chan
0
0.2
0.4
0.6
0.8
1
100 200 300 400 500 600 700 800 900 1000
Resource Allocation Ratio
Number of Hosts (n)
Linear Topology
M-tree Topology (m=2)
M-tree Topology (m=4)
Star Topology
Figure Ratio of Chosen Source Av erage and W orst Case
for Selected T op ologies
Chosen Source Best Case CS best Chosen Source b est case is when the source selections min
imize the total resources required This o ccurs when all
receiv ers but one select the same source a receiv er cannot
select itself as its source and the exceptional receiv er selects
a nearest source This results in a single m ulticast distribu
tion tree from the source to all but one of the receiv ers plus
the path from the exceptional receiv er to its nearest neigh
b or Th us the total resources required are L for the
linear top ology and L for the mtree and star top ologies
F or eac h top ology CS best scales as O n In con trast
Dynamic Filter scales as O n
in the linear top ology and
as O n log
m
n in the tree top ology and as O ninthe
star top ology Therefore only when comparing Dynamic
Filter to the b est case of Chosen Source in the linear and
tree top ologies do w e nd an asymptotic scaling adv an tage
for Chosen Source The exten t of this adv an tage scales as
O D since Dynamic Filter scales as O nD and Chosen
Source b est case scales as O n selection
Summa ry
In this pap er w e studied the asymptotic resource consump
tion of v arious RSVP reserv ation st yles in three simple to
p ologies T o our kno wledge this is the rst analytic com
parison of the relativ e merits of these approac hes F or self
limiting applications the Shared reserv ation st yle ac hiev es
sa vings of
n
o v er the traditional Indep enden t reserv ation
st yle in an y top ology with an acyclic distribution mesh F or
c hannel selection applications the Dynamic Filter reserv a
tion st yle ac hiev es substan tial sa vings o v er the Indep enden t
reserv ation st yle in the mtree and star top ologies More
surprisingly the Dynamic Filter reserv ation st yle uses ex
actly the same resources as the w orst case of the Chosen
Source reserv ation st yle and app ears to b e only a constan t
factor w orse than the a v erage case of the Chosen Source
reserv ation st yle These results suggest that at least for
large m ultip oin t applications the RSVP reserv ation st yles
of Shared and Dynamic Filter oer substan tial sa vings in re
source consumption o v er the traditional Indep enden t reser
v ation st yle and that the assured c hannel selection service
do es not incur asymptotically div erging o v erallo cation when
compared to the nonassured service
These results of course relied on man y simplications
W e hop e in future w ork to explore v ariations on the v arious
mo dels suc h as considering N sim chan and N sim sr c
and allo wing the n um b er of senders and receiv ers to b e dif
feren t More imp ortan tly these results w ere deriv ed on o v er
simplied top ologies It is imp ortan t to explore to what
exten t they apply to real net w orks This question is more
subtle than it rst app ears since our results describ e the
large n limit of a net w ork where b oth the net w ork and the
n um b er of residen t hosts are gro wing Tw o questions m ust
b e addressed Ho w can one c haracterize real net w orks
Certainly randomly generated net w orks are no more real
than the simple top ologies considered here T o some exten t
real net w orks are the pro duct of c haotic gro wth at the edges
and planned gro wth in the in terior Assuming one can c har
acterize more realistic net w orks ho w can one explore the
asymptotic limit Should one hold the densit y xed or the
ratio of the diameter to n um b er of hosts or is there some
other criterion In these simple top ologies the answ er w as
clear but in more general net w orks this is a completely un

T e chnic al R ep ort USCCS
explored issue These are issues w e hop e to return to in
future w ork they are relev an t not just to the presen t study
but to anyin v estigation whic h dep ends on net w ork top ology Ackno wledgments
W e wish to thank Deb orah Estrin for her helpful commen ts
on this pap er and to gratefully ac kno wledge b oth her and
Lixia Zhang for collab orating with us on an earlier v ersion
of this w ork
References
Casner S Deering S First IETF In ternet Audio
cast A CM SIGCOMM Computer Communic ation R e
viewv ol no July D Clark S Shenk er and L Zhang Supp orting R e al
Time Applic ation s in an Inte gr ate d Servic es Packet
Network A r chite ctur e and Me chanism In Pro ceedings
of SIGCOMM pp J Cro w croft p ersonal comm unication
Deering S Multicast Routing in a Datagram In ter
net w ork T ec hnical Rep ort ST ANCS Stan
ford Univ ersit y Decem b er D F errari and D V erma A Scheme for R e alTime
Channel Establishment in WideA r e a Networks In
IEEE JSA CV ol No pp April S J Golestani A Stop and Go Queueing F r amework
for Congestion ManagementIn Pro ceedings of SIG
COMM pp J Hyman A Lazar and G P acici R e alTime
Sche dulin g with Quality of Servic e Constr aints In
IEEE JSA CV ol No pp Septem ber
C Kalmanek H Kanakia and S Kesha v R ate Con
tr ol le d Servers for V ery HighSp e e d NetworksIn Pro
ceedings of Glob eCom pp Mitzel D Estrin D Shenk er S Zhang L An Ar
c hitectural Comparison of STI I and RSVP to app ear
in Pr o c e e dings of IEEE Info c om June A P arekh A Gener alizedPr o c essor Sharing Appr o ach
to Flow Contr ol in Inte gr ate d Servic es Networks In
T ec hnical Rep ort LIDSTR Lab oratory for In
formation and Decision Systems Massac h usetts Insti
tute of T ec hnology P artridge C A Prop osed Flo w Sp ecication Inter
net R e quest for CommentsRF C Septem b er S Shenk er D Clark and L Zhang A Sc heduling Ser
vice Mo del and a Sc heduling Arc hitecture for an In te
grated Services P ac k et Net w ork preprin t T op olcic C Exp erimen tal In ternet Stream Proto col
V ersion STI I Internet R e quest for Comments RF C Octob er D V erma H Zhang and D F errari Delay Jitter Con
tr ol for R e alTime Communic ation in a Packet Switch
ing NetworkIn Pro ceedings of T riCom pp Zhang L Deering S Estrin D Shenk er S and Zap
pala D RSVP A New Resource ReSerV ation Proto
col IEEE Network Magazine Septem b er
Zhang L Braden R Estrin D Herzog S and S Jamin R esour ceR eSerV ation Pr oto c ol RSVP V er
sion F unctional Sp e cic at ionRF C in preparation

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Description

Danny J. Mitzel and Scott Shenker. "Asymptotic resource consumption in multicast reservation styles." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 586 (1994).

Asset Metadata

Creator Mitzel, Danny J. (author), Shenker, Scott (author)

Core Title USC Computer Science Technical Reports, no. 586 (1994)

Alternative Title Asymptotic resource consumption in multicast reservation styles (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 9 pages (extent), technical reports (aat)

Language English

Unique identifier UC16270841

Identifier 94-586 Asymptotic Resource Consumption in Multicast Reservation Styles (filename)

Legacy Identifier usc-cstr-94-586

Format 9 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)

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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)