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USC Computer Science Technical Reports, no. 613 (1995)

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USC Computer Science Technical Reports, no. 613 (1995)

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Content Multicast Routing in Dense and Sparse Mo des Sim ulation Study of
T radeos and Dynamics
Liming W ei Deb orah Estrin
Computer Science Departmen t Computer Science departmen t ISI
Univ ersit y of Southern California Univ ersit y of Southern California
Los Angeles CA Los Angeles CA lweic atarinausce du estrinusce du
Abstract
PIM Proto col Indep enden t Multicast is capable of sup
p orting sparse mo de SM and dense mo de DM op
erations In sparse mo de PIM can use shared trees
RPT or shortest path trees SPT to deliv er data pac k
ets One frequen tly ask ed questions w as ho w to decide
when to use sparse mo de and when to use dense mo de
What is the criteria Another unansw ered question w as
whether pac k ets can b e lost when receiv ers switc h from
RPT to SPT This pap er rep orts a study of the
o v erhead tradeos b et w een dense mo de op erations and
sparse mo de op erations the b eha viors of PIM when
receiv ers transitioning from RPT to SPT
One imp ortan t result presen ted is the crosso v er p oin t
of sparse mo de and dense mo de o v erheads whic hgiv es a
hin t for selecting proto col mo des according to the group
densit y metric
Keyw ords Multicast Routing Sparse mo de Dense
mo de Ov erhead
In tro duction
PIM has b een in tro duced as a scalable m ulticast arc hi
tecture that can optimaly supp ort m ulticast groups that
are either sparsely distributed or densely distributed
The dense mo de PIM op eration is c haracterized b y p eri
o dic broadcasts and prunes As in D VMRP a sources
data pac k ets are broadcast deliv ered to net w ork no des
that are absen t of state for that source and m ulticast
group then the few leaf subnet w orks that dont ha v e
group mem b ers will set up negativ e state and prune
the un w an ted branc hes from the tree The negativ estate
will time out after a certain p erio d of time resulting
in the broadcasting of data pac k ets and pruning of un
w an ted branc hes again In sparse mo de op eration data
This w ork has b een supp orted b y NSF under con tract n um ber
CD A Sun microsystem Inc and Cisco systems Inc
pac k ets are not broadcasted and only routers on the m ul
ticast tree need to k eep state information for a group
The state of a m ulticast tree is set up when receiv ers des
ignated routers send join messages to w ard a Rendezv ous
P oin t RP or a source In sparse mo de receiv ers ma y
sta y on the RPro oted shared tree abbreviated as RP
tree or RPT for lo w rate sources while for high sp eed
sources the receiv ers can c ho ose to switc h to the source
ro oted shortest path trees SPT F or more detailed pro
to col descriptions please see In this pap er w ein v estigate the tradeos of dieren t
op erating mo des and the b oundary conditions for some
transien t pro cesses W e will analyze the phenomena and
pro vide form ulae for some situations When the com
plexit y of the situation mak es analytical metho ds inade
quate w e use sim ulation to conduct exp erimen ts closely
reecting the w a y the proto col op erates in a real net
w ork
Ov erhead tradeos of sparse mo de
and dense mo de
Weev aluate the o v erhead of sparse mo de and dense
mo de op erations in terms of con trol bandwidth consump
tion and state storage requiremen ts in all routers
In terms of con trol trac the broadcast and prune
in dense mo de is a global b eha vior while in sparse mo de
con trol trac is constrained to b e along m ulticast tree
branc hes In b oth mo des con trol trac is sen t p erio di
cally normally with dieren t frequencies The curren tly
suggested dense mo de SPT en try timer is times the
sparse mo de p erio dic refresh timer In dense mo de
the n um b er of broadcast pac k ets can b e reduced byusing
av ery long timer v alue for the negativ e state at the cost
of k eeping state for extinct groups for longer times and
not b eing able to adapt to routing c hanges as quic kly as
needed
In terms of storage o v erhead groups op erating in
PIM dense mo de will main tain state either p ositiv eor

negativ e in all routers Groups in sparse mo de ho w ev er
only main tain state in routers on pac k et deliv ery trees
When ev aluating b oth of the criteria w em ust con
sider group mem b ership distributions There are ob vi
ously t w o extreme cases of group mem b ership distribu
tions one extreme is a v ery large group for whichev ery
router either is needed to forw ard pac k ets for some do wn
stream mem b ers or the router itself has group mem b ers
attac hed the other extreme is a v ery small group whic h
only requires a small n um b er of ontree routers to de
liv er pac k ets to all mem b ers Scenarios b et w een these
extreme cases will b e ev aluated in detail in section Another factor that can aect an applications pref
erence for dense mo de or sparse mo de is join latency Are join latencies dieren t in the t womodes The join latency is incurred in t w o cases
A new receiv er joining a group In dense mo de
the receiv ers designated router will send a graft
message to w ard existing sources according to the
routers negativ e cac he state When a graft mes
sage reac hes a router already on a m ulticast tree
attac hmen t p oin t data pac k ets will b e able to
o wdo wnstream to the new receiv er This pro cess
tak es a round trip time b et w een the new receiv er
and the attac hmentpoin t In sparse mo de a new
receiv er joins a group b y sending a join message
to w ard the Rendezv ous P oin t RP When the join
message reac hes a router that is already on the RP
tree data pac k ets from all existing sources will b e
able to o wdo wnstream to w ard the new receiv er
This also tak es a round trip time b et w een the new
receiv er and the attac hmentpoin t on the RP tree
The dierence in join latency is negligible in this
case
A new source app ears and an existing receiv er
needs to join it In dense mo de the rst or a
few pac k et is broadcast deliv ered to all routers
An existing receiv er receiv es the rst pac k et after
a onew a y dela y time b et w een the source and the
receiv er In sparse mo de the new source sends the
rst few data pac k ets encapsulated in RPregister
messages to w ard the RP The RP will decapsu
late the RPregister pac k ets and forw ard the data
pac k ets do wn the RP tree The receiv ers will re
ceiv e the data pac k ets after a onew aydelaybe t w een the source and the receiv er along the RP
tree The dierence in join latency is the dier
ence b et w een the RP tree dela y and the SPT dela y The dierence in join latency can b e in fact around a few
millisecond s But since the new receiv er joins in the middle of the
transmission s and all pac k ets sen t in past history w ere gone for
the new receiv er suc h minor dierence in joining time should b e
negligible in general
j
j j j
j
j
j j
D
B R E
C
A S
RPT
SPT
Receiv er
RP
Source
Figure The receiv er lea v es RPT and joins SPT
Again this is negligible in general
It is our opinion that join latencies will not b e an issue
when c ho osing b et w een dense mo de and sparse mo de
op erations In the rest of the pap er w e will not b e con
cerned with the join latency issues
Sparse Mo de Dynamics the transi
tion from RPT to SPT
In sparse mo de PIM all receiv ers join the RP tree rst
then the receiv ers switc h to sourcero oted shortest path
trees when needed W e will asses the p ossibilityofpac k et
losses when switc hing from the RP tree to the SPT W e
call a time in terv al a blackout p erio d if during that in
terv al a receiv er can not receivean y data pac k ets from
a source due to the lac k of forw arding state inside the
net w ork
Blac k out p erio ds during RPT to SPT
transitions
Here w e briey review the PIM proto col actions when
receiv ers switc h from a RP tree to a source ro oted short
est path tree See the example in gure the receiv er R
already on the RP tree receiv es a series of data pac k ets
from source S and decides to switchto S ro oted short
est path tree Rs designated router initiates a SPTjoin
to w ard the source whic h will set up the SPT state from
S to R B con tin ues to accept pac k ets from the RP tree
b efore the upstream SPT state is fully set up When a
data pac k et from S arriv es at B along the SPT branc h
B kno ws that the upstream SPT state has b een com
pletely setup b ecause the incoming in terface for SPT is
dieren t from that of the RPTs and will prune itself
o the RP tree for source S
A ag SPTbit is set in
B to signal the completion of this transition In gure once the transition from RPT to SPT
is completed router B will reject all S s data pac k ets
coming do wn the path RP D B and will only
accept data pac k ets from S that come do wn the SPT
path Assume pac k ets sentb y S are n um b ered n according to the order of departure times at S and the
Suc h prunes will set up negativecac he state along the RP tree
so that pac k ets from S will not b e forw arded along the RP tree
an y more

path A RP D B is longer than the path A C B After router A has established SPT routing
state assume the rst data pac k et A forw ards do wn the
SPT path is pac k et iWhen pac k et i arriv es at B B will set its SPTbit indicating the completion of RPT
to SPT switc h If b y this time pac k et i is still in
the transmission path RP D B it will b e rejected
b y B when it ev en tually arriv es at B Section will giv e
a quan titativ e analysis of suc h blac k out p erio ds when
they do exist
Are there duplicate pac k ets during the
transiti ons
Can there b e duplicates when con trol messages are lost
during the switc h from RPT to SPT One p ossibilit y
is to ha v e the negativecac he state along the RPT b e
mistak enly deleted so that receiv ers will receiv e pac k
ets coming do wn b oth SPT and RPT But in PIM ev en
if con trol messages are lost suc h mistak es can not o c cur This can b e sho wn in gure if b oth the SPT and
RPT paths are forw arding data pac k ets from S to B B
with its SPTbit set will do an incoming in terface c hec k
and only accept pac k ets from the SPT path and drop
all pac k ets coming from the RPT path ie no duplicate
pac k ets Ho w ev er when B s incoming in terface is a m ul
tiaccess LAN ie the incoming in terfaces for the RPT
and the SPT are the same the incoming in terface c hec k
will not b e able to distinguish pac k ets forw arded b y SPT
from those forw arded b y the RPT In this situation the
assert mec hanism will b e activ ated so that the router
that forw ards pac k ets from the RPT on to the m ultiaccess
LAN is pruned o Therefore in the rest of this pap er
w e will not b e concerned with duplicate pac k ets
Design of PIMSIM a PIM sim ulator
A pac k et lev el sim ulator PIMSIM has b een dev elop ed
to exercise PIM mec hanisms The goal of suc h a sim u
lator is to capture the details of the dynamic b eha viors
of basic PIM mec hanisms W ec hose MaRS Maryland
Routing Sim ulator as the basis of the sim ulator
and utilized or adapted MaRSs ev en t managemen t rou
tines basic net w ork construction mo dels and X windo w
user in terface routines The new sim ulator has PIM sp e cic routing mo dules m ulticast trac mo dules m ulti
cast capable no de mo dules and m ultiaccess LANs
Before applying the sim ulator to real sim ulations w e
tested the sim ulator o v er a n um b er of top ologies and
with v arious kinds of m ulticast groups W ev eried that
the correct con trol messages w ere sen t and correct state
information w as established in the net w ork F or more
details ab out PIMSIM design and usage please see T radeo of o v erheads in
sparse mo de and dense mo de
In this section w e dene basic metrics and form ulate
the o v erheads of sparse mo de and dense mo de op era
tions W e will also presen t sim ulation results sho wing
the temp oral dynamics of bandwidth o v erhead in a real
net w ork
Metrics and F orm ulae
The o v erhead comparisons of dieren t mo des are based
on t w o measures the total state stor age required net
w ork wide and the total c ontr ol b andwidth consumed to
main tain certain m ulticast groups inside the net w ork
Storage Ov erhead
Let v
v
v
n
b e the no des inside the net w ork C
i
g S
j
b e the storage cost on no de i for group g source S
j
or
RP The o v erall storage cost under a certain mo de is
dened as assume there are n no des in the net w ork and
m sources for g Cost
stor ag e
mode
n
X
i m
X
j C
i
g S
j
Since the dierence in dense mo de and sparse mo de
routing en tries is rather small it is sucien tto
compare the total n um ber of en tries under dieren top erating mo des in the storage comparisons In the rest
of this section w e assume dense mo de and sparse mo de
en tries are of the same size
Let the cost of eac h routing en try b e In dense
mo de eac h router m ust main tain a routing en try for eac h
source group pair either p ositiv eornegativ e The
total storage cost of dense mo de m ulticast routing en tries
in the net w ork will b e Cost
stor ag e
dense mode G n m In sparse mo de the storage cost consists of the costs
of the SPT en tries RPT G en tries and the negativ e
cac he SGRPbit en tries Let N
g G b e the n um ber
of RPT en tries for group set G N
sg G b e the n um ber
of SPT en tries for group set G and N
sg RP bit Gbe
the n um b er of negativ e cac he en tries
If ev ery m ulticast group in G uses shar edtr e e in
sparse mo de the storage cost will b e
Cost
stor ag e
rpt mode G N
g G N
sg G Note that if due to lo w data rate all RPs do not establish
SPT state and receiv e all data pac k ets encapsulated in
register messages N
sg G in the ab o v e form ula will

b e zero This mo de is also represen tativ e of CBT as w ell
If mem b ers switchto SPT the storage cost will b e C ost
stor ag e
spt mode G N
g G N
sg G N
sg RP bit Bandwidth con trol Ov erhead
F or a m ulticast group g let P t l g b e the n um ber of
tree main tenance pac k ets sen t on link l from time ! to
time t The total n um b er of tree main tenance pac k ets in
the net w ork is
Cost
ctr l band
t g
k
X
l P t l g The lo cal IGMP or PIM query and rep ort messages
ha v e no global eects and are the same for dense mo de
and sparse mo de Suc h lo cal messages will b e ignored in
the denitions and exp erimen tal measuremen ts in this
pap er
Since dieren t proto col mo des use dieren t kinds of
tree main tenance pac k ets dense mo de and sparse mo de
bandwidth o v erheads need to b e measured in dieren t
w a ys In dense mo de data pac k ets are broadcast deliv
ered to propagate routing information A prune pac k et is
triggered byanun w an ted data pac k et whic h will delete
an outgoing in terface in a routing en try The band
width o v erhead of dense mo de op eration is th us dened
as the total n um b er or b ytes of un w an ted data pac k ets
transmitted o v er all net w ork links plus the total n um
ber b ytes of p erio dic prune messages In the follo wing
discussions bandwidth o v erhead is measured in unit of
pac k et coun t The bandwidth o v erhead in b ytes can b e
estimated based on o v erhead pac k et coun t and applica
tion pac k et sizes
Let D
unw anted pk t
t b e the total n um ber of un w an ted
data pac k ets from time ! to tand D
pr une
t b e the to
tal n um b er of prunes sen t during the same p erio d then
dense mo de bandwidth o v erhead can b e dened as
C ost DM
ctr l band
t G D
unw anted pk t
t G D
pr une
t G In sparse mo de the bandwidth o v erhead can b e dened
as the total n um b er of PIM con trol messages D
pim msg
sen t ie SG join"prune G join SG RPbit prune
C ost SM
ctr l band
t G D
pim msg
t G Densit y of a Multicast Group
The density of a m ulticast group reects the p ercen tage
of ontree links vs the total n um b er of links in the
net w ork
nd1
nd2
nd3
nd4
nd5
nd6
nd7
nd8
nd9
nd10
nd11
nd12
nd13
nd14
nd15
nd16
nd17
nd18 nd19
nd20
nd21
nd22
nd23
nd24
nd25
nd26
nd27
nd28
nd29
nd30
nd31
nd32
nd33
nd34
nd35
nd36
nd37
nd38
nd39 nd40
nd41
nd42
nd43
nd44 nd45 nd46
nd47
Figure Arpanet top ology used in dense mo de and
sparse mo de sim ulations
Let g b e a globalscop e m ulticast group with only
one sender s let l b e the total n um b er of links on the
tree ro oted at s using a shortest path tree algorithm to
calculate the m ulticast tree
Let L b e the total n um ber
of links within the net w ork The follo wing measure is
called the density of g with r esp e ct to source s D ensity s g
l
L

If g has more than one sender the densit y metric
for the whole group is dened as the a v erage of densities
o v er all sources Let s
s
s
m
b e the sources of group
g where m is the n um b er of sources Let l
i
i m b e the n um b er of links on the shortest path tree ro oted
at source s
i
The densit yofgroup gtak en in to accoun t
all sources is dened as
D ensity g
P
m
i l
i
m L
#
F or a group with kno wn densit y metrics the follo wing
pro vides a lo w er b ound for the dense mo de c ontr ol b and
width c ost form ula where the equalit y holds when
there is only one copyof eachun w an ted data pac k et tra v
eling on eac h link during eac h broadcast and prune cycle
assume negativ ecac he timeout in terv al is T
DM

C ost DM
ctr l band
t g D ensity g L m t
T
DM
!
If there is more than one shortest path tree c ho ose the one
with the least n um b er of ontree links
The sp arseness of g with r esp e ct to source s is dened as the
recipro cal of D ensity s g
The corresp ondin g sp arseness metric considering all sources is
dened as the recipro cal of Densityg
0.0 0.2 0.4 0.6
Density (l / L)
0
200
400
600
800
Number of entries
(a) State Storage Overhead
Dense Mode
Sparse Mode, Lower Bound
Sparse Mode, Upper Bound
0.0 0.2 0.4 0.6
Density (l / L)
0
1000
2000
3000
4000
Number of Packets
(b) Control Bandwidth Overhead
Dense Mode, Lower Bound
Sparse Mode, Upper Bound
Figure T radeos of Sparse mo de SPT and Dense mo de in arpanet no de for sender m ulticast groups
When all receiv ers use SPTs in sparse mo de op era
tion if the RP is placed at a receiv er
con trol messages
will only tra v el through links that are on at least one
of the source ro oted shortest path trees When dier
en t shortest path trees and the RP tree o v erlap con trol
messages are aggregated in to one con trol pac k et The fol
lo wing giv es an upp erb ound to the sp arse mo de c ontr ol
message overhe ad in terms of n um b er of con trol pac k
ets cf form ula Assume the sparse mo de refresh
in terv al is T
SM
C ost SM
ctr l band
t g D ensity g L m t
T
SM
If the RP is placed at mem ber s
i
whic h is also a sender
the n um ber of SPT en tries will b e D ensity g L mthe
n um b er of RPT g en tries will b e D ensity s
i
g L The sp arse mo de stor age c ost represen ted b y form ula can b e rewritten as
C ost
stor ag e
spt mode g D ensity g L m D ensity s
i
g L N
sg RP bit Since the n um b er of negativecac he en tries is smaller than
the total n umberofSPT en tries when the RP is placed at
a mem b er"sender the follo wing inequalities pro vide an
upp er and a lo w er b ound for C ost
storage
spt mode g
D ensity g L m D ensity s
i
g L
C ost
stor ag e
spt mode g D ensity g L m D ensity s
i
g L Figure sho ws the memory and bandwidth o v erhead
curv es of the ab o veform ulae for the arpanet top ology
or the receiv ers rst hop router
e
e e
e
e e
e
e e
e
R r
l L Densit y r
Group Size Group Size r
r
r
S
S
l L Densit y r
Figure Example of t wom ulticast groups ha ving the
same densit y
g with an audio conference of senders Fig a
sho ws the dense mo de vs sparse mo de memory tr ade o the dense mo de storage cost represen ted byform ula and the upp er"lo w er b ounds of the sparse mo de SPT op
eration inequalit y Figure b sho ws the sparse
mo de and dense mo de c ontr ol b andwidth tradeo the
lo w er b ound of dense mo de bandwidth cost represen ted
b y inequalit y ! and the sparse mo de bandwidth o v er
head upp er b ound from inequalit y The tradeos
of dense mo de and sparse mo de under dieren tgroup
densities are v ery ob vious in these t w o graphs
The group size and the densit y of a tree are related
but there is no onetoone corresp ondence F or a certain
net w ork and a giv en source there can exist a n um ber
of groups with dier ent sizes but with the same density Fig sho ws an example of t wom ulticast groups ha ving
the same densit y In the top ology sho wn the maxim um
size of a group with densit y ! is the minim um size
of a group with the same densityis Note that in gure the densit y axis do esnt extend to this
is b ecause none of the m ulticast trees can include all net w ork links

0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Group Size (Percentage of total number of nodes)
Density (l / L)
Group size vs Multicast tree density (arpanet (47-node))
Maximum Group Size
Minimum Group Size
Size of Random Groups
Figure Maxim um and Minim um group size vs densit y
It is easy to sho w that the maxim um group size under
a certain densityis density L
The minim um group
size under a certain densit yho w ev er is dep enden ton
the top ology and can not b e expressed in a simple for
m ula W e constructed an exp erimento v er the arpanet
top ology and t w o !!no de random top ologies measured
the corresp onding minim um group sizes for eac h den
sityv alue Figure sho ws three curv es of the maxim um
group size minim um group size and the a v erage size of
random groups o v er the arpanet top ology The error bars
for random groups represen t the standard deviations there are ab out ! !! random groups for eac h densit y
v alue
Note that all curv es terminate at the densityof about
! at densit y of ! there is no w a y to increase the
densit y of the tree further all leaf domains are mem b ers
of the group and all net w ork no des are on tree In fact
the maxim um group size is n in a nno de Llink strongly
connected net w ork Only n out of the L links are
used to construct a tree with n no des in this case the
maxim um densit y of a group in a nno de net w ork is
n L
Therefore for net w orks of dieren t sizes if they ha vethe
same no de degree the maxim um group size curv e in
units of p er c entage of no des should remain the same
W e sp eculate that under the same no de degree their
minim um group size curv es and their random group size
curv es should also ha v e little dierence
W e can pro veb y construction that if the size of a group is
incremen tedb y adding new no des as mem b ers in the same order a
breadthr stse arc h algorithm starting from the source w ould visit
the no des the size of the group is k ept maxim um for the densit y
of the tree constructed
W e ran exp erimen ts on t w o no de random top ologies one
with a v erage no de degree of the other with no de degree of The result from the net w ork with no de degree of is v ery close to
that sho wn in g The result from the other no de top ology
has similar shap es except that ev ery curv e is compressed in the
0
500
1000
1500
2000
2500
3000
0 100 200 300 400 500 600
# of ’control’ pkts
Time (Seconds)
SM/DM Bandwidth Tradeoff in ’arpanet’, 5-member group
"Dense Mode"
"Sparse Mode"
Figure SM"DM con trol bandwidth o v erhead supp ort
ing a sparse group in arpanet
SMDM tradeo exp erimen ts
The gure upp erb ound and lo w erb ound o v erhead
curv es for groups with certain densities are useful for
estimating the ranges of o v erhead Whereas sim ulations
on a sp ecic m ulticast group inside a particular top ol
ogy can mak e it p ossible to measure precisely howthe
o v erhead is incurred o v er time
In the subsequen t sim ulation exp erimen ts sparse
mo de groups and dense mo de groups are put in the same
net w ork separately in dieren t runs Rep orted here are
sim ulations o v er the Arpanet top ology sho wn in gure The group in v olv ed in the sim ulation is assumed to
ha v e global scop e All sources share the same sending
b eha vior The sim ulated scenario is a participan tau dio conference The participan ts are lo cated at no des
and # of the arpanet top ology g In
sparse mo de op eration no de is c hosen as the RP for
the group In the rst run the group is started in dense
mo de and all sources start sending at ! seconds oset
from the net w ork startup time In the second run the
group is started in sparse mo de and the same exp eri
men t rep eated
T o log parameters as the exp erimen ts progress a sp e cial monitor comp onen t is created in the sim ulator to
p erio dically collect the storage usage and v arious pac k et
coun ts at dieren t no des and links The sampling times
t
t
t
i
t
i t
n
can b e congured in to the monitor
comp onen t F or this particular exp erimen t all measure
men t p erio ds are set to the same small constant!! ms
horizon tal direction to the left b y ab out
The storage o v erhead for dense mo de can b e treated as a con
stan t g a The storage o v erhead for sparse mo de dep ends
on the n um b er of on tree no des It can b e deriv ed from the tree
costs as rep orted in Therefore w ew ont replicate the exp eri
men ts already done in and only presen t the results for con trol
bandwidth o v erhead here

Figure sho ws the bandwidth o v erhead when sup
p orting this group with dense mo de thin solid line
sparse mo de with SPT thic k line The step function
of the dense mo de measuremen t reects the dense mo de
p erio dic broadcast and prune b eha vior In this exp eri
men t all timers are set to the default v alue suggested in
the PIM sp ecication do cumen t In a real net w ork
the timers can b e set dieren tly in order to ac hievea
more suitable bandwidth"adaptabilit y tradeo In gen
eral a longer negativecac he timer will result in less p eri
o dic broadcast and prune trac and will also result in
slo w er adaptation to routing c hanges The small steps
in the sparse mo de measuremen t reects the artifacts of
the w a y the sim ulator is initialized all PIM routing
mo dules are started at the same time The group densit y
for this conference is ! It can b e seen that for this sender"receiv er group
the n um b er of dense mo de con trol pac k ets increases
m uc h faster than the sparse mo de con trol pac k ets The
adv an tage of sparse mo de for small groups is ob vious in
terms of the con trol o v erhead
Blac k out p erio d when switc h
ing from RPT to SPT
If a m ulticast group op erates in sparse mo de all receiv ers
will join the RP tree rst When a sources pac k et rate
is high enough the receiv ers will switc h to the source
ro oted shortest path tree As describ ed in subsection
there ma y exist a blac k out p erio d during the switc h
from RPT to SPT
The length of the blac k out p erio d is dep endenton
the dierence b et w een relev an t sections along the RPT
and the SPT paths The n um ber of pac k ets lost is pro
p ortional to the length of the blac k out p erio d and the
sources rate
First w e formally dene the relev an t parameters and
metrics
Let s b e a source and r b e a receiv er D
spt
s r be the
propagation dela y for pac k ets from source s to receiv er
r along the shortest path Let D
rpt
s r b e the onew a y
dela y along the RP tree path from s to rLet R sbe
ss sending rate in unit of pack etssecond The bandwidth o v erhead of a net w ork supp orting mixed sparse
mo de and dense mo de groups has an additive pr op erty the total
bandwidth o v erhead is equal to the sum of the bandwidth o v erhead
when the net w ork has only sparse mo de groups and the bandwidth
o v erhead when the net w ork has only dense mo de groups This is
b ecause dense mo de con trol messages and sparse mo de messages
are alw a ys sen t in separate pac k ets Storage o v erhead also has the
additive pr op erty Exp erimen ta l results gained from net w orks with
only sparse mo de groups and results with only dense mo de groups
can b e com bined to predict net w ork o v erhead with mixed sparse
and dense mo de groups
The n um ber of pac k ets in igh t along the shortest
path tree from s to r at stable state is F
spt
F
spt
s r D
spt
s r R s The n um b er of pac k ets in igh t along the RP tree from
s to r at stable state F
rpt
is
F
rpt
s r D
rpt
s r R s When a receiv er switc hes from RPT to SPT the n um ber
of pac k ets lost during the transition L
rpt spt
is appro x
imately
L
rpt spt
s r F
rpt
s r F
spt
s r In the most fa v orable situation RPT to SPT switchcan
b e free of pac k et loss if
The path from the source to the receiv er along the
RP tree is exactly the same as the path along the
SPT ro oted at the source Ie the ph ysical pac k et
deliv ery path do es not c hange during the RPT to
SPT transition
The dierence in dela ybet w een the RPT path and
the SPT path is smaller than the time in terv al b e t w een consecutivepac k ets
When loss do es happ en the w orst case is that the
in terpac k et in terv als are m uc h smaller than the dela y
dierence b et w een the RPT path and SPT path This
w orst case scenario ma y happ en resulting from the selec
tion of an extremely nonfa v orable router as an RP for
a widely disp ersed m ulticast group
Note that when the source rate is xed pac k et loss
during the RPT to SPT transition is directly related to
the data pac k et size the larger the pac k et size the
longer the in terpac k et in terv al the few er the n um ber of
pac k ets lost F or example a v at

p cm source Kb"s
!ms frames with a ! ms SPT path to a receiv er and a
!! ms RPT path the maxim um n um b er of pac k et loss
can b e t w o b yte pac k ets But if the v at uses p cm
enco ding Kb"s !ms frames no pac k et will b e lost
duing the RPT to SPT switc h$
T o fully understand the transitioning pro cess it is
ideal if one simple exp erimen t setup can co v er all p ossible
scenarios The follo wing statemen t eectiv ely reduces
the exp erimen t space without sacricing the generalit y
of our sim ulation results
Statement In PIM sp arse mo de when a r e c eiver
switches fr om RPT mo de to SPT mo de the numb er of
p ackets dr opp e d during the black out p eriodisonly de p endent on two factors
V at is an audio terminal to ol dev elop ed byV an Jacobson and
Stev e McCanne at LBL

-1
0
1
2
3
4
5
6
0 500 1000 1500 2000 2500
# packets lost
Packet size (Bytes)
RPT/SPT path differenec: 50 ms, Source rate: 71 Kbps (PCM2 audio)

Figure P ac k et loss as a function of pac k et size source
rate xed
the delay dier enceb etwe en the RPT p ath and SPT
p ath fr om the sour c e to the r e c eiver and
the sour c es sending b ehavior r ate p acket size
Other factors such as top olo gic al fe atur es in a p articu
lar network ar e irr elevant to the p acket loss during this
p erio d
Hence it suces to sim ulate the top ology sho wn in
gure with ranges of dieren t link and source parame
ters The results will hold in other top ologies and group
mem b ership distributions if the RPT path and SPT path
dela y dierence and the sources sending b eha vior are the
same
Figure sho ws sim ulated pac k et loss as a function
of pac k et size in the net w ork of gure The source
rate is xed at K bps The dierence in dela yalong
the RPT path and SPT path is ! ms roughly the
w orst case scenario for arbitrary RP placemen t inside
the con tinen tal United States One useful fact in this
picture is that for a PCM enco ded audio source there
is no pac k et loss when the pac k et size is larger than !!
b ytes
Figure sho ws pac k et loss as a function of b oth
source rate and pac k et size in the net w ork of gure for a PCM enco ded audio source when the RPT"SPT
path length dierence is ! ms The con tour lines on
the base plain sho w the b oundaries of regions ha ving the
same drop rates
Conclusion
The tradeos b et w een sparse mo de and dense mo de PIM
op erations are ev aluated via t w o measures the state
storage o v erhead and the con trol bandwidth o v erhead
With kno wn measures of group density the state stor
age and the con trol bandwidth o v erheads can b e calcu
lated for dense mo de op erations The b ounds for suc h
Pkt loss during RPT/SPT switch (RPT/SPT difference: 50 Milliseconds)
"rptspt3D.dat"
36
27
18
9
3
1
500
1000
1500
2000
500
1000
1500
0
10
20
30
40
50
60
Packet size (Bytes)
Source rate (Kbps)
Packets lost
Figure P ac k et loss as as function of source rate and
pac k et size
o v erheads can b e estimated for sparse mo de op erations
Sim ulations w ere run o v er the arpanet top ology and re
sults presen ted The arpanet exp erimen ts sho w ed that
for groups with densities of less than ! sparse mo de op
eration has less storage and bandwidth o v erhead in gen
eral A densit yv alue of ! in the arpanet corresp onds to
groups with !% to !% of the total n um ber of net w ork
no des W e sp eculated and v eried with random top olo
gies that the results from the arpanet top ology can b e
generalized to net w orks of dieren t sizes with the same
a v erage no de degree T o estimate the o v erhead tradeo
in net w orks with dieren t no de degrees the results need
to b e factored along the densit y axis b y the ratio of the
t wonet w orks no de degrees
The n umberofpac k ets lost during the transition from
RPT to SPT is a function of the path length dierence
bet w een the RPT and SPT branc hes and the sources
in terpac k et in terv als or the sources rate and pac k et
sizes Slo w to mo derate rate applications suchasaudio
sources normally suer no or insignican tpac k et losses
in normal op erating enrironmen ts High sp eed sources
can incur higher pac k et loss rates esp ecially when the
dierence b et w een the RPT path and SPT path is signif
ican t Since suc h losses only o ccur when switc hing from
RPT to SPT it is advised to a v oid frequen tly switc hing
bet w een the t w o dieren ttreet yp es unnecessarily References
S Deering D Estrin D F arrinacci V Jacobson
C Liu and L W ei An arc hitecture for widearea
m ulticast routing In Pr o c e e dings of the SIGCOMM London ##

S Deering and D Cheriton Multicast routing in
datagram in ternet w orks and extended lans A CM
T r ansactions on Computer Systemspages & Ma y ##!
S Deering D Estrin D F arrinacci V Ja
cobson C Liu and L W ei Proto col inde
p endentm ulticast pim Proto col sp ecication
## ftp""catarinauscedu"pub"estrin"PIM"ietf
idmrpim! ps
L W ei The design of the usc pim sim ulator pim
sim T ec hnical Rep ort TR #! Computer Science
Departmen t USC feb ##
Cengiz Alaettinoglu A Uda y a Shank aar Klaudia
DussaZieger and Ibrahim Matta Design and im
plemen tation of mars A routing testb ed T ec hnical
Rep ort CSTR# Computer Science Departmen t
Univ ersit y of Maryland sep ##
Cengiz Alaettinoglu A Uda y a Shank aar Klaudia
DussaZieger and Ibrahim Matta Mars maryland
routing sim ulator v ersion ! users man ual T ec h
nical Rep ort CSTR Computer Science Depart
men t Univ ersit y of Maryland jun ##
Dino F arrinacci and Puneet Sharma Priv ate com
m unications ##
A J Ballardie P FF rancis and J Cro w croft Core
based trees In Pr o c e e dings of the A CM SIGCOMM San F rancisco ##
# L W ei and D Estrin The tradeos of m ulticast trees
and algorithms In Pr o c e e dings of the Interna
tional c onfer enceon c omputer c ommunic ations and
networks San F rancisco Septem b er ##
#

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Description

Liming Wei, Deborah Estrin. "Multicast routing in dense and sparse modes: simulation study of tradeoffs and dynamics." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 613 (1995).

Asset Metadata

Creator Estrin, Deborah (author), Wei, Liming (author)

Core Title USC Computer Science Technical Reports, no. 613 (1995)

Alternative Title Multicast routing in dense and sparse modes: simulation study of tradeoffs and dynamics (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 UC16270546

Identifier 95-613 Multicast Routing in Dense and Sparse Modes Simulation Study of Tradeoffs and Dynamics (filename)

Legacy Identifier usc-cstr-95-613

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)

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

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)