USC Computer Science Technical Reports, no. 656 (1997)

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Content Timer Adjustmen t in SRM
ChingGung Liu USC
Deb orah Estrin USCISI
Scott Shenk er Xero x
Lixia Zhang UCLAXero x
Abstract
SRM is a generic framew ork for reliable m ulticast data deliv ery The re
transmission requests and replies used in SRM error reco v ery are m ulticast to
the en tire group SRM uses random timers to a v oid the message implosion prob
lem and the eectiv eness of SRMs duplicate suppression dep ends critically on
the design of these random timers
This pap er in v estigates through analysis and sim ulation the relationship
bet w een the timer setting parameters and error reco v ery p erformance in SRM
The p erformance metrics are error reco v ery dela y and duplicates p er loss W e
prop ose an algorithm where the w aiting p erio d is prop ortional to a mem
b ers neigh b orho o d size and where a mem b ers estimate of neigh borhood size
based on the observ ations of curren t p erformance W e nd that this algorithm
ac hiev es nearoptimal duplicate suppression Moreo v er as the size of the global
group gro ws the reco v ery dela y and duplicates p er loss remain b ounded
In tro duction
Sc alable R eliable Multic ast SRM is one of the man y prop osed approac hes to
supp ort reliable m ulticast data deliv ery The main fo cus of SRM is to ac hiev e scala
bilit y dened as ecien t error reco v ery lo w error reco v ery dela y and few duplicate
messages p er loss across full range of group sizes and underlying net w ork top ologies
As w e explain later in Section of this pap er a k ey comp onen t of SRM is the use of
random timers when sending retransmission requests and replies In this pap er w e
in v estigate the relationship b et w een the timer setting parameters and error reco v ery
p erformance
The original see SRM timer algorithm incorp orated both a deterministic
and a probabilistic w aiting p erio d ie the timer w as selected in an in terv al b ounded
a w a y from zero Using both analysis and sim ulation w e nd that remo ving the
deterministic w ait in timer setting from the random timer reduces reco v ery dela y
This researchw as supp orted in part b y the Adv anced Researc h Pro jects Agency monitored
byF ort Huac h uca under con tracts D ABTC And b y the National Science F oundation
under granta w ard No NCR The views expressed here do not reect the p osition or
p olicy of the US go v ernmen t

signican tly without degrading duplicate suppression Moreo v er w e nd that near
optimal duplicate suppression can be ac hiev ed if the probabilistic w aiting period
is prop ortional to the mem b ers neigh b orho o d size The neigh b orho o d size refers
to the n um ber of mem bers who are comp eting to send retransmission requests or
replies regarding the same loss These ndings lead us to prop ose a new SRM timer
sc heduling sc heme that pro duces a nearconstan t reco v ery dela y
and duplicates
p er loss regardless ho w large the size of the m ulticast group
The pap er is organized as follo ws Section giv es a brief description of the
SRM framew ork as describ ed in and the problems that w e address in this pap er
Section lo oks in to the relationship b et w een the timer setting parameters and error
reco v ery p erformance Section prop oses a revised timer sc heduling sc heme Section
in tro duces our dynamic mec hanisms to measure the neigh b orho o d size and adjust
the timer setting parameters Section presen ts the sim ulation mo dels and analyzes
the sim ulation results and Section reviews related w orks W e conclude in Section
with a short summary Basic Approac h of SRM
In this section w e giv e an o v erview of SRM as describ ed in emphasizing the
features relev an t to our w ork here W e use the term session to mean a m ulticast
application that uses SRM as its underlying reliable m ulticast service SRM pro vides
only basic reliabilit y supp ort it guaran tees the ev en tual deliv ery of data to all
mem b ers in the m ulticast session More stringen t reliabilit y functionalities suc has
total ordering and fate sharing
if desired are left to the application itself Toa v oid message implosion at the source in the error reco v ery pro cess SRM is
receiv erinitiated with eac h receiv er b eing resp onsible for detecting data losses
and requesting retransmissions SRM also adopts the approac h of m ulticasting
ev erything to maximize the collab oration among mem bers in the pro cess of error
reco v ery Requests and replies are m ulticast to all mem bers in the session Multi
casting a request allo ws the nearest mem b er with the requested data to send a reply
rst it also suppresses other mem b ers from sending duplicate requests for the same
data Similarly m ulticasting a reply suppresses duplicate replies and also deliv ers
the reply to all mem b ers who suer the loss without requiring the replier to kno w
their individual iden tities or lo cations
The SRM mec hanisms can be decomp osed in to t w o parts group state syn
c hronization and receiv erinitiated error reco v ery Mem bers p erio dically exc hange
session messages to rep ort curren t group state eg the highest receiv ed sequence
n um ber from eac h source and to determine the propagation dela ys bet w een eac h
pair of mem bers
Mem b ers use group state information to detect data losses This
The reco v ery dela y is measured in terms of the onew a y propagation dela y from the data
source In other w ords it is the in terv al b et weenamem b ers detection of a loss and reception of a
retransmission divided b y the onew a y propagation dela y from the data source to the mem ber F ate sharing is when a m ulticast session terminates if a single mem b er or a sp ecic subset of
mem b ers in the session fail dep ending on the seman tics of the application
There is a seman tic dierence b et w een the dela y from a mem b er and the dela y to a mem ber W e

is critical for the receiv erinitiated error reco v ery approac h b ecause mem b ers do not
otherwise kno w what has been sen t to the session group Eac h mem ber uses the
propagation dela y information when sc heduling its request or reply timers
When a pac k et is lost eac h mem b er detecting the loss w aits a random time p erio d
b efore sending its retransmission request The random timer is sc heduled in the time
in terv al A T A B T where T is the propagation delaybet w een the requester
and the data source and A and B are constan ts
When the timer expires the
sc heduled request is m ulticast to the session group If a duplicate request is receiv ed
or the curren tly sc heduled request is sen t the requester exp onen tially bac ks o its
request timer to ensure retransmission reliabilit y If a reply is receiv ed the sc heduled
request is canceled A mem b er with the requested data
resp onds to the request b y
sc heduling a reply in the time in terv al a t a b t where t is the propagation
dela y bet w een the replier and the requester and a and b are constan ts When the
timer expires the sc heduled reply is m ulticast to the session The sc heduled reply
is canceled if a duplicate reply is receiv ed while w aiting
The randomization of request and reply timers in SRM giv es mem bers an op
p ortunit y to suppress one another and th us a v oid the request and reply message
implosion problem The p erio d of the SRM request timer consists of both a
deterministic w ait ie no messages are sen t b efore A T and a probabilistic w ait
the p erio d b et w een A T and A B T Both p ortions of the w ait are prop or
tional to the propagation dela y from a source Th us requesters far from a source
ha v e longer deterministic w aiting p erio ds than requesters near to the source W e
call it deterministic suppression if a request sen t at the maximal w ait A B T b y a closetothesource mem ber arriv es b efore the deterministic w ait of a farther
fromthesource mem ber has expired sc heduled requests for messages from this
particular source at the distan t requester will alw a ys be suppressed b y requests
from the nearer requester
Deterministic suppression can only o ccur if the dierence bet w een the deter
ministic w aiting p erio ds of t w o mem bers is large relativ e to the propagation dela y
bet w een them and th us deterministic suppression is comparativ ely rare Usually mem bers ha v e to rely on the randomization of their probabilistic w aiting p erio ds to
suppress one another W e call this probabilistic suppression
The same concepts of deterministic and probabilistic suppression can b e applied
to the reply timers A reply from a replier far from the requester is deterministically
suppressed b y a replier near the requester if the dierence b et w een their determin
istic w aiting p erio ds is sucien tly large Otherwise they rely on the probabilistic
w ait to suppress one another
In this pap er w ein v estigate the relationship b et w een the timer setting parame
will distinguish one from the other in our later discussion Ho w ev er in SRM a mem b er determines
its onew a y propagation delaytoanother mem ber b y taking half of its measured roundtrip dela y Therefore SRM assumes the paths b et weenapairofmem b ers are symmetric
In addition to the basic timer sc heduling sc heme also pro vides a probing mec hanism for
random timer adaptation W e discuss it further in Section SRM assumes all session mem b ers not only the data source ma ysa v e all the application data
If some mem b ers do not sa v e the data requested they simply do not participate in the error reco v ery
pro cess

ters and error reco v ery p erformance W e prop ose a dynamic adjustmentmec hanism
that mak es the timer parameters adaptiv e to the dynamic c hanges of the net w ork
en vironmen t One crucial facet of our prop osal is in making B and b prop ortional
to the n um ber of neighb ors
in the session and so the bulk of our sim ulations are
dev oted to comparing t w o approac hes to estimating the size of the neigh b orho o d Note that our goal is to optimize the o v erall p erformance and w e do not try to
guaran tee optimal results for the reco v ery of eac h individual loss
Timer Setting P arameters and P erformance
The error reco v ery p erformance in SRM dep ends hea vily on the sc heduling of the
request and reply timers Therefore the selection of the timer setting parameters is
essen tial In the follo wing sections w e will discuss the relationship b et w een timer
setting parameters and error reco v ery p erformance in terms of deterministic sup
pression probabilistic suppression and reco v ery dela y T o simplify the description
our discussion will fo cus on the request parameters A and B The same analysis
and conclusion can b e applied to reply parameters a and bas w ell
Deterministic Suppression
source s
requester p
q
u
v
a
b
tpr
A
B
tsp
tsp
replier r
tpq
tpr
Figure Radix dening the b oundary of deterministic suppression and probabilistic
suppression
Consider the scenario sho wn in Figure A data pac k et sen t b y source s is lost
bet w een mem ber r and mem ber p Mem ber p detects the loss at time and sc hedules
a request b efore A B t
sp
where t
sp
is the propagation dela y from s to p Mem ber
q also detects the loss no later than time t
pq
and sc hedules a request after t
pq
A t
sq
F or ps request to deterministically suppress q s request the latest time of ps
request arriving at q has to be so oner than q s earliest request sending time ie
Mem ber p is a neigh b or of mem ber q if p comp etes with q in sending requests or replies for a
loss

A B t
sp
t
pq
t
pq
A t
sq
Wekno w t
sq
t
sp
t
pq
b ecause q is farther from
s than pso w e get
A B t
sp
t
pq
t
pq
A t
sq
t
sq
t
sp
t
pq
t
pq
B
A
t
sp
The sc heduled requests at mem ber q will b e suppressed b y ps request determin
istically if q is farther from the source and its propagation dela y from p is greater
than
B
A
t
sp
If ps requests arriv eat q correctly it is guaran teed that ps requests will
alw a ys suppress q s requests Mem bers who share the same losses and are within
the radius of
B
A
t
sp
constitute the r e quester neighb orho o d of p with resp ect to source
s b ecause they comp ete with one another to send requests There is no guaran tee
that ps requests will alw a ys suppress others in its neigh borhood By applying the
same analysis the radius without deterministic reply suppression is
b
a
t
pr
for a
mem ber r with resp ect to a requester p Mem b ers within the radius constitute the
r eplier neighb orho o d of r with resp ect to source s Probabilistic Suppression
If requesters ha v e dieren t propagation dela ys from a source a nonzero A amplies
their dela y dierence and pro duces b etter suppression result On the other hand
a nonzero A do es not facilitate request suppression if all requesters ha v e the same
propagation dela y from a source The p erformance of request suppression dep ends
on the randomization of their probabilistic w aiting periods ie the v alue of B Figure illustrates this scenario
source s
tN
ts
requester p
tp
tn
requester neighborhood
replier neighborhood
replier q
Figure Mem bers rely on probabilistic suppression within their requester and
replier neigh borhoods
In Figure there are N mem bers lo cated within ps requester neigh b orho o d with resp ect to losses from source s Their propagation dela ys from s are all equal to
t
s
and the propagation dela ys b et w een eac h pair of them are roughly t
N
Assuming a
uniformly distributed random function is used to sc hedule requests the probabilit y

that ps request is not suppressed b yanymem b er within the neigh borhood is
P R
t
N
dx R
B t s
t
N
B t s x t
N
B t s
N dx
B t
s
t
N
B t
s
N
t
N
B t
s
N
t
N
B t
s
N
Since there are N mem b ers within ps requester neigh b orho o d the exp ected n um ber
of requests regarding a loss from source s is
E P N N
B
t
N
t
s

Similarly for a replier neigh b orho o d with n mem b ers whose propagation dela ys
from a requester p are t
p
and the propagation dela ys bet w een eac h pair of them
are roughly t
n
the exp ected n um ber of replies regarding a request from p is E
n
b
t n
t p
Reco v ery Dela y
Giv en A B and the propagation dela y from the source if the n um b er of requesters
in a neigh b orho o d comp eting to request retransmission is large the a v erage delayof
the rst expired request timer is shorter F or example consider the case as sho wn
in Figure where there are N requesters in a requester neigh borhood and their
propagation dela ys from a source s are roughly t
s
Assuming a uniformly distributed
random function is used to sc hedule requests the exp ected w aiting period of the
rst expired request timer within the neigh borhood is
D A t
s
N R
B t s
x B t s x
B t s
N dx
B t
s
A t
s
B
N
t
s
The same analysis can b e applied to the delayof the reply timers If there are
n mem b ers within a replier neigh borhood and their dela ys from a requester p are
roughly t
p
the exp ected w aiting period of the rst expired reply timer within the
neigh borhood is D
a t
p
b
n t
p
The reco v ery dela y is the sum of the request
dela y the reply dela y and the roundtrip propagation dela y bet w een the requester
and the replier In the w orst case where the source is the replier an estimate of the
reco v ery dela y is giv en b y D D
t
s
Discussion
In Section w e found that A con tributes the ma jorit y of request dela y when there
are man y mem b ers Th us it is desirable to mak e A as small as p ossible Ho w ev er
a small A increases the radius of the requester neigh b orho o d and th us decreases
the eectiv eness of deterministic suppression F ortunately the n um b er of duplicate
requests can still be reduced b y probabilistic suppression As w e argue b elo w if
B is selected prop erly the n um b er of duplicate requests and the reco v ery dela y can
b oth b e prop erly con trolled
Consequen tly w e c ho ose A a to minimize the reco v ery dela y and rely
on probabilistic suppression to minimize the n um ber of duplicates Since there is

no deterministic suppression all mem bers that share the same loss are all in the
requester neigh b orho o d for that loss ie they comp ete with one another to request
retransmission The remaining group mem bers are in the replier neigh borho od to
comp ete for retransmission
If A the exp ected n um b er of requests and the reco v ery delayforaloss from
a source s can b e rewritten as
E N
B
t
N
t
s
D B
N
t
s
Therefore if w ec ho ose B as a linear function of the requester neigh b orho o d size ie
B C N where C is a constan t the factor N in b oth equations will b e neutralized
As a result the exp ected n um b er of duplicate requests is roughly prop ortional to
t
N
t s
and the request dela y is constan t in terms of the onew a y propagation dela y from the
data source In other w ords the n um b er of requests p er loss and reco v ery dela y are
constan t as functions of the session size Similarlyif w ec ho ose a and b c n where c is a constantand n is the size of the replier neigh b orho o d w eget E
t n
c t p
and D
c t
p
If the replier is the source in the w orst case the reply dela yis c t
s
Therefore the reco v ery delayisequal to C c t
s
on the a v erage
Generally sp eaking the linear functions dene the tradeo bet w een the n um
ber of duplicates per loss and reco v ery dela y Note that C and c are univ ersally
iden tical ie all mem bers use the same linear functions in a session Ho w ev er C
and c can b e dieren t iethe linear function for the request parameter can b e dif
feren t from the linear function for the reply parameter The neigh b orho o d sizes of
mem b ers are dieren t b ecause they do not share exactly the same losses Since the
timer parameters are functions of the neigh b orho o d sizes they are also dieren t for
individual mem b ers
A Revised SRM Timer Sc heduling Sc heme
P erfect request and reply suppression do es not guaran tee the absence of duplicate
requests and replies other factors ma y cause duplicates F or example a requester
ma y send a premature second request b efore the reply arriv es A premature request
is not only a duplicate request but also a trigger for duplicate replies F urthermore
if duplicate requests are sen t a replier ma y issue a duplicate reply if a second request
arriv es after the rst reply has b een sen t In this section based on the conclusion
in Section w e will discuss mec hanisms that prev en t premature requests and
ignore unsuppressed requests and prop ose a revised v ersion of SRM timer sc heduling
sc heme
Prev en ting Premature Requests
After sending a request the requester bac ks o its request timer and sc hedules a
second request to ensure retransmission reliabilit y If the bac k o timer expires b efore

the reply to the rst request has arriv ed w esa y the second request is premature T o
prev en t premature requests the bac k o request timer should b e sucien tly large to
allo w the reception of a reply By setting A w eha v e increased the p ossibilityof
premature requests and w e therefore in tro duce another parameter I to comp ensate
Consider the replier neigh b orho o d in Figure There are n repliers in the replier
neigh borhood and their propagation dela ys from the requester p are t
p
When a
request from p arriv es at the neigh b orho o d all repliers in the neigh borhood will
sc hedule replies b et w een b t
p
The probabilit y that the rst expired reply times
out after t
p
is b
n
where b Wew an t to compute the v alue of for
whic h this probabilit y is sucien tly small for example In other w ords of
the rst expired replies will time out b efore t
p
lim
n
b
n
lim
n
c n
n
e
c
c
The prop er bac k o period for p to constrain the probabilityof premature requests
under is calculated b y taking in to accoun t
source s
requester p
replier q
tsp
tpq request
reply
premature
request
time
Itsp
3 c tpq
Figure Scenario of premature requests
In Figure requester p sends its rst request at time Replier q receiv es the
rst request at t
pq
and sc hedules a reply bet w een t
pq
t
pq
b t
pq
If q s reply
timer expires rst the w aiting p erio d of its sc heduled reply is less than c t
pq
with
a probabilit y of The arriv al time of a reply at p should be smaller than the
earliest sending time of the second request W e assume p bac ks o it request timer
for a p erio d of I t
sp
t
pq
c t
pq
I t
sp
c t
pq
t
sp
I I c
Note that
t pq
t sp
b ecause a lost pac k et is reco v ered b y the source in the w orst case
Th us w e conclude that after sending the rst request mem ber p has to bac k
o its request timer at least for a period of c t
sp
where c is the constan t
parameter used in the linear function to determine the reply parameter eg b and
is univ ersally iden tical for all mem b ers in a session
Ignoring Unsuppressed Requests
Request suppression and premature request prev en tion reduce the c hance of du
plicate requests Ho w ev er the p erformance dep ends hea vily on net w ork top ology
mem b ership distribution and other dynamic factors in the net w ork and the m ulti
cast session en vironmen t If duplicate requests do o ccur a mec hanism to prev en t
resp onse to unsuppressed requests is required
The reason a mem ber resp onds to an unsuppressed request is that it forgets a
reply has b een sen t for the same loss triggered b y a previous request It is imp ortan t
for a mem ber to remem b er the replies and ignore further requests regarding the same
loss Amem b er should hold the records of its sc heduled replies for a p erio d of time
to c hec k whether a request has b een replied and ignore other unsuppressed requests
It should not ignore them forev er since a reply ma y also b e lost
source s
requester p
replier r
tsp
tpr
request
reply
unsuppressed
time
H tsp
requester q
tpq
request
Figure Scenario of unsuppressed requests
Figure sho ws the scenario of an unsuppressed request Mem ber p sends a
request asking for retransmission The request do es not suppress the sc heduled
request in mem ber q Therefore q sends its o wn request for the same loss and this
request should be ignored b y replier r The hold period of r s sc heduled replies
should not be greater than the second request from p b ecause the previous reply
ma y b e lost and the replier should b e able to resp ond to the second request to ensure
transmission reliabilit y W e assume the hold p erio d for r is H t
sp
where t
sp
is the
propagation dela y from source s to the requester p who sen t the rst request If
p sen t its rst request at time the earliest sending time of its second request is
I t
sp
Therefore
t
pr
H t
sp
I t
sp
t
pr
H I H c
After sc heduling a reply triggered b y the rst request from p r should ignore
further requests of the same loss for a p erio d of c t
sp
Mem ber p should
include its propagation dela y from source s t
sp
in its request in order for r to
compute the prop er hold p erio d
Revised Error Reco v ery Sc heme
In this section w e will describ e the revised timer sc heduling sc heme from SRM
based on the conclusion from the previous sections
Before a session is activ ated t w o linear functions are selected These linear
functions are used to compute the timer setting parameters from the neigh b orho o d

sizes F or example the request timer parameter B is dened as B C N where C is
a constantand N is the requester neigh b orho o d size And the reply timer parameter
b is dened as b c n where c is a constantand n is the replier neigh b orho o d size
Since mem bers ha v e dieren t neigh b orho o d sizes in the follo wing sections w e will
use the notation of N
s
p
and B
s
p
to refer to mem ber ps requester neigh b orho o d size
and request timer parameter with resp ect to the losses from source srespectiv ely The notation of n
p
q
and b
p
q
are used to refer to mem ber q s replier neigh b orho o d size
and reply parameter with resp ect to the requests from requester p resp ectiv ely Mem b ers in a session exc hange session messages to determine propagation dela ys
bet w een eac h pair of mem b ers and to detect data losses When mem ber p detects a
loss from source sit sc hedules a request timer b et w een B
s
p
t
sp
where t
sp
is the
propagation dela y from source s to p When the timer expires p m ulticasts it request
to the session group and sc hedules a bac k o request b et w een I t
sp
I B
s
p
t
sp
to ensure retransmission reliabilit y If p receiv es a request of the same loss b efore
its o wn request timer expires it bac ks o its timer b y resc heduling a second request
bet w een I t
sp
I B
s
p
t
sp
F rom Section w e kno w I c Amem ber q with the requested data resp onds to the request from p bysc hedul
ing a reply bet w een b
p
q
t
pq
where t
pq
is the propagation dela y from p to q F urthermore q ignores further requests for the same loss for a p erio d of H t
sp
F rom Section w e kno w H c If q receiv es a reply of the same loss b efore
its reply timer expires q simply cancels its reply Otherwise q m ulticasts its reply
when its reply timer expires
Dynamic Timer Adjustmen t
F rom the previous section w e conclude that selecting timer parameters based on
the neigh b orho o d size pro duces optimal results in terms of the reco v ery dela y and
the n um b er of duplicates Unfortunatelymem b ers do not kno w their neigh b orho o d
sizes b eforehand F urthermore there are other dynamic factors whic hma y aect the
error reco v ery p erformance F or example net w ork trac load aects the propaga
tion dela y dynamic mem bership c hange aects the neigh b orho o d size and net w ork
top ology c hange aects the losssharing c haracteristic among mem b ers Mem bers
need to adapt their requester and replier neigh b orho o d sizes ie the timer setting
parameters to these dynamic factors b y learning from net w ork feedbac k
Figure sho ws the detailed con trol lo op of our dynamic adjustmen t mec ha
nism Eac h mem b ers feedbac k in terpreter observ es net w ork feedbac k to estimate
neigh b orho o d size A parameter adjuster calculates the timer parameters from the
estimated neigh borhood size And a timer sc heduler sc hedules requests and replies
with the new timer parameters W e already discussed the pro cedure to sc hedule
request and reply timers in Section W e will concen trate on the pro cedures of
feedbackin terpretation and parameter adjustmen t in the follo wing sections
T o b e sp ecic the requester neigh b orho o d sizes of mem ber p are dieren t for losses at individual
lossy links from a source Ho w ev er it is imp ossible for a mem b er to iden tify the p ointofloss w e
use the lo cation of the data source as an appro ximation

Feedback
network
Interpreter
Parameter
Adjuster
feedback
Timer
Scheduler
timer
parameter
neighborhood
size
Figure Con trol lo op of dynamic timer adjustmen t
In terpreting Neigh borhood Size from Duplicates
A feedbac k in terpreter observ es net w ork feedbac k to adjust the estimated neigh
b orho o d sizes There are t w o kinds of feedbac k that can be observ ed b y mem bers
for individual losses the reco v ery dela y and the n um ber of requests and replies
An in terpreter can estimate the neigh b orho o d sizes based on either of them F or
example the requester neigh b orho o d size can be in terpreted based on the n um ber
of requests p er loss b y the relationship illustrated in Equation on P age F rom Equation w e kno w the a v erage n um ber of requests in a neigh b orho o d
with N mem bers is roughly E N t
N
B t s
Therefore eac h request with resp ect
to the same loss represen ts
N
E
neigh bors That is a request from a mem b er that is
t
N
a w a y represen ts
B t s
t
N
C t s
neigh bors F or example if requester q sends a request
regarding a loss from source s its request represen ts
B
s
q
t sq
t pq C t sq
neigh b ors to mem ber
p Mem ber q should supply B
s
q
and t
sq
in its request for p to calculate the prop er
n um ber of neigh b ors represen ted b y the request Note that q s request represen ts
N
s
q
neigh b ors to itself since the dela y from q to itself is Since w e prefer a mem b er near the source to send requests rst w ew antmem bers
near the source to pro duce smaller neigh b orho o d size estimates than mem b ers far
from the source F or example if b oth mem ber p and r receiv e a request from
q w e w ould lik e q s request to represen t more neigh b ors to r if r is farther from
the source than is p One simple w a y to ac hiev e this is to w eigh t the n um ber of
neigh b ors represen ted b y q s requests b y the dela ys from source s In other w ords
the n um ber of neigh bors represen ted b y q s request is w eigh ted b y a factor of
t sp
t sq
at mem ber p and it is w eigh ted b y a factor of
t sr
t sq
at mem ber r As a result ps
estimated neigh b orho o d size is smaller than q s neigh borhood size b y a factor of
t sp
t sr
Note that the estimated neigh borhood size no longer represen ts the actual
n um b er of neigh b ors Instead it com bines b oth the n um ber of mem b ers comp eting
to request retransmission in a requester neigh borhood and their relativ e distance
from the source
A mem ber adds up all the n um bers of neigh b ors represen ted b y requests it re
ceiv ed for the same loss The new requester neigh borhood size is calculated b y

using an exp onen tialw eigh ted mo ving a v erage with a w eigh t bet w een the pre
vious neigh borhood size and the new estimation The requester neigh b orho o d size
is adjusted for individual sources
If mem b ers only receiv e one request for a loss they ac hiev e the p erfect suppres
sion result This could result from the case in whichmem b ers neigh b orho o d sizes
are o v erestimated so they ha v e a b etter c hance to hear from one another or from
one mem b er sending its request fast enough to suppress others F or the former case
mem bers should reduce their estimated neigh borhood sizes to prob e for the mini
m um reco v ery dela y Ho w ev er for the later case there is no connection with whether
the neigh b orho o d size is o v erestimated Therefore in this second case reducing the
estimated neigh b orho o d size do es not necessarily impro v e the p erformance Unfor
tunatelymem b ers can not distinguish one case from the other b ecause of the lackof
feedbac k eg duplicate requests In our approac h w e assume the neigh b orho o d
size is o v erestimated if there is only one request per loss and reduce a mem bers
neigh b orho o d size b y a factor of The v alue of determines the aggressiv eness of
the probing pro cess If is small the accurate neigh b orho o d size can be reac hed
quic klyho w ev er it is also more lik ely to underestimate the neigh b orho o d size and
cause duplicates On the other hand a close to one slo ws do wn the probing pro
cess during the probing p erio d the neigh b orho o d size is o v erestimated and results
in long reco v ery dela y In other w ords is a tuning knob of the tradeo bet w een
reco v ery dela y and duplicates p er loss
Since the mem b er who sen t the only request for a loss is most lik ely the closest
mem ber to the lossy link one could reduce the neigh b orho o d size of the mem ber
who sen t the request and k eep other mem b ers neigh b orho o d sizes unc hanged Ho w
ev er the h yp othesis of adaptiv e adjustmen t is that the past exp erience is a good
prediction of the future If there are m ultiple lossy links along a path mem bers
face dieren t neigh b orho o ds for losses at dieren t lossy links and the adaptiv e ad
justmen t mec hanism should b e less aggressiv e so the estimation from the past can
predict the a v erage b eha vior of the future F or example reducing ps neigh b orho o d
size b y a factor of increases the c hance that p will suppress other requests for the
next loss As a result p will k eep reducing its neigh borhood size un til duplicate
requests are observ ed Reducing ps neigh b orho o d size aggressiv ely based on the
losses at one lossy link ma y aect the error reco v ery p erformance of losses at an
other lossy link Therefore w e think it is prefered for all mem bers who share the
same loss with p to decrease their neigh b orho o d sizes b y a factor of as w ell
The follo wing algorithm is dev elop ed to adapt the requester neigh b orho o d size
to the dynamic c hanges in a m ulticast session The neigh b orho o d size is measured
for individual losses A measuremen t period starts when a loss is detected and it
ends when a reply is receiv ed
for eachsc heduled request in p for source s
Wec ho ose in our sim ulations
F rom F o otnote w ekno w that the requester neigh b orho o d size should b e adjusted on a p er
lossy link p er source basis It is an appro ximation to adjust requester neighborhoodsizeon a per
source basis If there are m ultiple lossy links b et w een source s and mem ber p N
s
p
is the a v erage of
the neigh b orho o d sizes of all lossy links

for eac h request receiv ed from q including p itself
B
s
q
t sq
t pq C t sq
t sp
t sq
if p only receiv es one request then N
s
p
N
s
p
W e can apply the same mec hanism to estimate the size of a replier neigh b orho o d The measuremen t p erio d of the replier neigh b orho o d size is equal to the hold time
of a sc heduled reply discussed in Section It starts when a request is receiv ed
and it ends when the sc heduled reply is cleared Note that if a replier receiv es
m ultiple requests for the same loss the estimation is for the requester whose request
is receiv ed rst
for eachsc heduled reply in p for requester r

for eac h reply receiv ed from q including p itself
b
r
q
t rq
t pq c t rq
t rp
t rq
if p only receiv es one reply then n
r
p
n
r
p
In terpreting Neigh borhood Size from Reco v ery Dela y
The requester neigh b orho o d size can also b e in terpreted from the reco v ery delayb y
using Equation on P age The dela y of the rst expired request timer that is
within a requester neigh b orho o d of N mem b ers is
B
N t
s
on the a v erage If the rst
expired request timer has the v alue B t
s
then w e can treat this as an estimate
of n N Th us a mem b er can in terpret its requester neigh b orho o d size from reco v ery dela y
if it iden ties the rst expired request and kno ws ho w long the rst expired request
hasbeensc heduled T o solv e this problem mem b ers put the original v alue of their
request timers in their outgoing requests and a requester can simply collect these
v alues in the incoming requests and iden tify the smallest one as the rst expired
request
T o be sp ecic mem ber q puts q
in its outgoing request if q sc hedules the
request regarding a loss from source s for a period of q
B
s
q
t
sq
If mem ber p
iden ties q
is the smallest one that has ev er b een observ ed it uses q
to estimate
its requester neigh borhood size Similarly other mem b ers who share the same loss
w ould iden tify q
as the smallest feedbac k In order to facilitate mem b ers near the
source to request retransmission rst q
is w eigh ted b y their dela ys from source s for
example p w eigh ts q
b y the ratio of
t sq
t sp
The exp onen tialw eigh ted mo ving a v erage
is also adopted Note that since the feedbac k from the net w ork is a mem ber
should p erform the exp onen tialw eigh ted mo ving a v erage on b efore con v erting to the estimated neigh borhood size N Otherwise if is con v erted to N and then
the exp onen tialw eigh ted mo ving a v erage is p erformed the result is div ergen t The
algorithm is sho wn b elo w

for eachsc heduled request in p for source s

for eac h request receiv ed from q including p itself min f q
t sq
t sp
g
s
p
s
p
N
s
p
s
p
One adv an tage of in terpreting neigh b orho o d size from reco v ery dela y is the abil
it y to distinguish whether a mem b ers neigh b orho o d size is o v erestimated or whether
it is sending requests fast enough to suppress others based on the feedbac k of its o wn
requests If a mem b ers neigh borhood size is o v erestimated the new neigh b orho o d
size in terpreted from its o wn should b e smaller than its original estimated neigh
b orho o d size on the a v erage Whereas if a mem b er sends its request fast enough to
suppress others its new estimation should b e greater than its original estimation
F or example if mem ber p is the only mem b er b ehind a lossy link p
is equal to
on the a v erage and its new estimated neigh b orho o d size is Therefore a mem ber
can still estimate its requester neigh b orho o d size correctly ev en if it only receiv es
the requests from itself
The same mec hanism discussed ab o v e can be applied to estimate the size of a
replier neigh b orho o d the algorithm is sho wn b elo w
for eachsc heduled reply in p for requester r

for eac h reply receiv ed from q including p itself min f q
t rq
t rp
g
r
p
r
p
n
r
p
r
p
Commen ts
Ab o v e w e ha v e describ ed t w o dieren t metho ds for estimating the neigh b orho o d
size After making this estimation a mem ber adjusts its timer parameter using a
predened linear function F or example if the estimated requester neigh b orho o d
size is Na mem ber w ould adjust its request timer parameter as B C N where
C is the constan t of the linear function In the next section w e compare these
t w o metho ds of estimation One migh t consider com bining b oth neigh b orho o d size
in terpretation mec hanisms F or example a mem ber migh t tak e both estimates of
neigh borhood size and then use the a v erage as the new estimated neigh b orho o d
size Ho w ev er since one in terpreter do es not rev eal more information than the other
com bining these t woin terpretation mec hanisms do es not mak e the neigh b orho o d size
estimation more accurate Moreo v er our results suggest that one need not resort to
the additional complexit y of com bining the estimation algorithms to ac hiev e good
p erformance
Before turning to the our sim ulation results w e wish to return to the issue
of setting A b y reconsidering what happ ens with nonzero A As w e ha v e

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1.2
1.6
2.0
2.4
2.8

A = 0 A = 1 A = 3 A = 2
Figure Lo cal minim um solution for a nonzero A in dynamic timer parameter
adjustmen t
men tioned in Section one ma jor disadv an tage with nonzero A is that it pro duces
longer reco v ery dela y than with A F or example Figure a sho ws the reco v ery
dela y on a tree top ology with a single lossy link near the source The deterministic
w ait dominates the reco v ery dela y F urthermore from Section the requester neigh b orho o d is prop ortional to
B
A
so the eectiv eness of deterministic suppression is prop ortional to
A
B
as w ell On the
other hand from Section the n um ber of duplicate requests within a requester
neigh b orho o d is prop ortional to
B
so the eectiv eness of probabilistic suppression
is prop ortional to B Therefore the eectiv eness of request suppression is not a
monotonic function of either A or B In other w ords increasing B to facilitate
request suppression ma y include more mem b ers within the requester neigh b orho o d whic h could in tro duce more duplicates F or example Figure b sho ws the the results
of the n um b er of requests p er loss on the same tree top ology F or a nonzero A the
p erformance in terms of the n um ber of requests per loss could be sub optimal due
to the existence of lo cal minima
Since our revised timer sc heduling sc heme c ho ose A a the eectiv eness of
request suppression is prop ortional to B In other w ords giv en the net w ork top ology
and mem b ership distribution the n um b er of requests p er loss is a monotonic func
tion of B Therefore the complexit y of the timer parameter adjustmen t is simplied
signican tly Sim ulation Results and Discussion
As in the b eha vior of our prop osed mec hanisms can b e most easily understo o d
b y rst testing a v ariet y of extreme scenarios b efore mo ving on to more complicated
scenarios Consequen tly w e initially explored our revised timer sc heduling sc heme
and dynamic timer parameter adjustmen t in three extreme but simple top ologies
star string and binary tree eac h with a single data source The star top ology
represen ts a session where all mem bers ha v e equal distance to the source and are
siblings of one another The string top ology represen ts a session where all mem bers
ha v e upstreamdo wnstream relationship and share the data deliv ery paths with their
upstream mem b ers The binary tree top ology represen ts a mixture of b oth
Eac h top ology is p opulated with v e dieren t session sizes and

to examine scaling beha vior Three dieren t linear functions for adjusting
the timer setting parameters eg B and b based on estimated neigh b orho o d size
are tested ie C c and W e sim ulate the p erformance of our revised
sc heme with b oth neigh borhood size in terpretation mec hanisms ie the duplicate
in terpreter and the dela y in terpreter Sim ulations using the session size as an ap
pro ximation of the the neigh borhood size are also run for comparison Eac h sim u
lation co v ers the error reco v ery activities of losses The losses are generated
b y assigning an error rate on eac h link of the sim ulated top ologies and these error
rates are xed throughout a single sim ulation
T op ologies with a Single Lossy Link
The rst set of sim ulations examines the p erformance of top ologies with a single
lossy link near the data source That is all mem bers except the source share
iden tical losses and comp ete to request retransmission Therefore the size of the
session is the actual requester neigh b orho o d size W e did not plot the results of the
a v erage n um ber of replies per loss because the source is the only replier and the
a v erage n umberof replies perloss isv ery close to one
Note that the analysis in
the follo wing sections from the single replier scenario can be applied to the single
requester scenario That is if only the leaf mem ber loses pac k ets the a v erage
beha vior of the repliers is similar to the a v erage beha vior of the requesters in the
single replier scenario
In the sim ulations w e c ho ose I H c and for
the duplicate in terpreter The reco v ery dela y is measured in terms of the onew a y
propagation dela y from the data source more precisely the reco v ery dela y is the
in terv al bet w een a mem bers detection of a loss and reception of a retransmission
divided b y the onew a y propagation dela y from the data source to the mem ber Star T op ology
Figure sho ws the sim ulation results in the star top ology The dash curv es rep
resen t the results from sim ulations of the duplicate in terpreter the solid curv es
represen t the results from sim ulations of the delayin terpreter and the graycurv es
represen t the results from sim ulations that use session size as an appro ximation of
the neigh b orho o d size The a v erage n um ber of requests per loss and the reco v ery
dela y measured in sim ulations that use b oth feedbackin terpreters are v ery close to
the results from sim ulations that use the session size as an appro ximation whic h
suggests that the estimated neigh b orho o d sizes from b oth in terpreters are v ery sim
ilar to the actual neigh b orho o d size ie the session size Consequen tly b oth the
a v erage n um ber of requests and reco v ery dela y remain constan t regardless of the
session size Note thatthe a v erage requests p er loss from sim ulations with small C
is greater than the a v erage requests p er loss from sim ulations with large C On the

The mec hanism to ignore unsuppressed requests reduces the c hance of resp onse to a replied
request Ho w ev er in some rare pathological cases there are m ultiple replies sentb y the source As
weha v e discussed in Section the probabilit y of premature requests is b elowb yc ho osing
I c therefore the c hance of duplicate replies is also b elo w
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session size
recovery delay
(b)

size interpreted from recovery delay,ω=1/8, I=H=2+3c C = c = 1/2
for example,
size interpreted from duplicates,ω=1/8, I=H=2+3c,δ=0.9
using session size as the neighborhood size
C = c = 1
C = c = 2
means the neighborhood size is interpreted from the number of
requests per loss andω = 1/8 ,δ = 0.9 , C = c = 1/2 , I = H = 2 + 3 c
Figure Sim ulation results in the star top ology all mem b ers share iden tical losses
other hand the a v erage reco v ery dela y from sim ulations with small C is less than
the a v erage reco v ery delayfromsim ulations with large C If w e tak e a close lo ok of Figure w e nd that the sim ulations of the duplicate
in terpreter generate a higher n um b er of requests p er loss and smaller reco v ery dela y
than the other t w o mec hanisms In the sim ulations of the duplicate in terpreter
mem bers reduce their estimated neigh b orho o d sizes b y a factor of if there is
no duplicate request Ho w ev er reducing the neigh borhood size ma y not be the
correct decision in the absence of duplicates and this b eha vior ma y cause mem bers
to underestimate their neigh b orho o d sizes As a result mem bers send requests
more aggressiv ely and the a v erage n um ber of requests increases while the a v erage
reco v ery dela y decreases
In the sim ulations using session size as an appro ximation the replier neigh b or
ho o d size of the source is set to one These sim ulations generate smaller reply dela ys
than the sim ulations of the delayin terpreter Therefore the reco v ery dela y that re
sults from using the delayin terpreter is sligh tly greater than the reco v ery dela y that
results from using session size as an appro ximation
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requester neighborhood size
(b) size interpreted from delay
estimated neighborhood size of a specific member
estimated neighborhood size of other members
Figure Neigh b orho o d size distribution in the no de star top ology all mem bers
share iden tical losses

The distribution of the estimated requester neigh b orho o d sizes is sho wn in Figure
In the sim ulations of the duplicate in terpreter mem bers ha v e dieren t estimated
neigh borhood sizes Since a measuremen t p erio d ends when a reply is receiv ed a
mem b er will not coun t a duplicate request for a loss if the request arriv es after the
reply Ho w ev er a late request is less lik ely to b e the rst expired request for a loss
so mem bers estimated neigh borhood sizes are iden tical in the sim ulations of the
delayin terpreter
String T op ology
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size interpreted from recovery delay,ω=1/8, I=H=2+3c C = c = 1/2
for example,
size interpreted from duplicates,ω=1/8, I=H=2+3c,δ=0.9
using session size as the neighborhood size
C = c = 1
C = c = 2
means the neighborhood size is interpreted from the number of
requests per loss andω = 1/8 ,δ = 0.9 , C = c = 1/2 , I = H = 2 + 3 c
Figure Sim ulation results in the string top ology all mem bers share iden tical
losses
Figure sho ws the sim ulation results in the string top ology In Figure a the
n um b er of requests p er loss asymptotes to a constan t

except for the sim ulations of
the duplicate in terpreter As sho wn in Figure the neigh b orho o d sizes in terpreted
from duplicates are distributed in a narro w er range than the estimated neigh b orho o d
sizes in terpreted from dela y Hence mem b ers are less lik ely to hear from one another
and as a result they generate more duplicate requests
F urthermore since mem bers w eigh t their estimated neigh borhood sizes b y their
relativ e distance from the source mem b ers near the source ha v e smaller estimated
neigh b orho o d sizes than mem b ers far from the source The estimated neigh b orho o d
sizes for the mem b er closest to the source are plotted in blo c k dot in Figure The reco v ery dela y in Figure b decreases with the session size b ecause the
reco v ery dela y is measured in terms of the onew a y propagation dela y from the
source Mem b ers far from the source rely on the requests from mem bers near the
source for retransmission without sending their o wn requests Consequen tly the
a v erage reco v ery dela y is reduced when the length of the string top ology increases
If a feedbackin terpreter is adopted the estimated requester neigh borhood size is a

The n um b er of requests is prop ortional to the ratio of the propagation dela ys among mem b ers
and the propagation dela y from the source ie E N
B
t
N
t s
When the length of the string
top ology increases the ratio of propagation dela ys ie
t
N
t s
also increases Ho w ev er the increased
amoun t is negligible and the n um b er of requests p er loss still remains constan t

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requester neighborhood size
(b) size interpreted from delay
estimated neighborhood size of the member closest to the source
estimated neighborhood size of the member farthest from the source
estimated neighborhood size of other members
Figure Neigh b orho o d size distribution in the no de string top ology all mem
b ers share iden tical losses
com bination of b oth the n um ber of mem b ers comp eting to request retransmission
and their relativ e distance from the source The mem ber closest to the source
pro duces the smallest estimated neigh b orho o d size as sho wn in Figure and sends
requests for the ma jorit y of the losses Th us the reco v ery dela y in the sim ulations
of b oth feedbac k in terpreters decreases faster with the session size than it do es in
the sim ulations that use session size as an appro ximation
T ree T op ology
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(b)
size interpreted from recovery delay,ω=1/8, I=H=2+3c C = c = 1/2
for example,
size interpreted from duplicates,ω=1/8, I=H=2+3c,δ=0.9
using session size as the neighborhood size
C = c = 1
C = c = 2
means the neighborhood size is interpreted from the number of
requests per loss andω = 1/8 ,δ = 0.9 , C = c = 1/2 , I = H = 2 + 3 c
Figure Sim ulation results in the tree top ology all mem bers share iden tical
losses
Figure sho ws the sim ulation results in the tree top ology Unlik e the results in the
star and string top ologies the n um b er of requests p er loss increases with the session
size As weha vemen tioned in Section the exp ected n um b er of requests p er loss
is
t
N
t s
where t
N
is the propagation dela ys among mem bers and t
s
is the propagation
dela y from the source to mem b ers F or the tree top ology t
s
is analogous to the

depth of the tree and t
N
is analogous to the width of the tree When the session
size increases the width of the tree increases exp onen tially with the depth of the
tree Therefore
t
N
t s
increases signican tly with the session size whic h explains wh y
the a v erage n um ber of requests per loss is no longer constan t with the session size
in the tree top ology The reco v ery dela y do es not decrease with the session size as w e exp ected The
n um ber of mem bers that are i hops a w a y from the source is t wice as large as the
n um ber of mem bers that are i hops a w a y from the source Ev en though a
mem ber near the source sends more requests than a distan t mem ber the total
n um b er of requests sentbymem b ers that are i hops a w a y from the source do es
not necessarily exceed the n um ber of requests sen t b y mem bers that are i hops
a w a y from the source Consequen tly the reco v ery dela y do es not decrease with the
session size as w e sa w in the string top ology F urthermore as sho wn in Figure the estimated neigh borhood sizes are more closely distributed among mem bers It
is more lik ely a mem b er far from the source sends requests for retransmission Since
the reply timer is based on the propagation dela y from the requester to the replier
a request from a distan t requester results in longer reply dela y |
0
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20
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40
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60
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80
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100
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0
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4
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8
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12
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16
time %
requester neighborhood size
(a) size interpreted from duplicates
|
0
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20
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40
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60
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80
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100
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0
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4
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8
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16
time %
requester neighborhood size
(b) size interpreted from delay
estimated neighborhood size of the member closest to the source
estimated neighborhood size of the member farthest from the source
estimated neighborhood size of other members
Figure Neigh b orho o d size distribution in the no de tree top ology all mem bers
share iden tical losses
Comparison among Dieren t T op ologies
Figure sho ws the request distribution among mem b ers in the no de top ologies
Data source is lab eled as sr c and other mem bers are lab eled as m
through m
according to their distance from the source Requests are ev enly distributed among
mem bers in the star top ology b ecause all mem bers ha v e equal distance from the
source Ho w ev er in the string and tree top ologies mem bers near the source send
more requests than mem b ers far from the source The dierence is more ob vious if
a feedbackin terpreter is adopted Note that m
and m
in the tree top ology ha v e
similar distributions b ecause their distances from sr c are iden tical
Figure sho ws the request and reco v ery dela y distribution of individual losses

| |
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0
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20
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40
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60
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80
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100
| |
||||||
session member
request percentage %
star string tree
src src src
topology topology topology
m
1
m
2
m
3
m
4
m
5
m
6
m
7
m
1
m
2
m
3
m
4
m
5
m
6
m
7
m
1
m
2
m
3
m
4
m
5
m
6
m
7
interpreting the neighborhood size from recovery delay
interpreting the neighborhood size from duplicates
Using session size as an approximation of the neighborhood size
Figure Distributions of the requests among mem b ers in no de top ologies all
mem b ers share iden tical losses
||
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10
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30
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requests per loss
percentage %
(a)
star string tree
1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6
topology topology topology
||
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0
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10
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20
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30
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40
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50
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60
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70
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||||||||
recovery delay
percentage %
(b)
star string tree
1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6
topology topology topology
interpreting the neighborhood size from recovery delay
interpreting the neighborhood size from duplicates
Using session size as an approximation of the neighborhood size
Figure Distributions of the n um ber of requests per loss and reco v ery dela y in
no de top ologies all mem b ers share iden tical losses
in the no de top ologies Since mem bers ha v e the same distance from the source in
the star top ology one mem b ers requests do not ha v e a b etter c hance to suppress
others So the n um ber of losses triggering one request is similar to the n um ber of
losses triggering t w o requests In other w ords more duplicate requests are generated
in the star top ology On the other hand in the string top ology the mem ber closest
to the source has the b est opp ortunit y to request retransmission and other mem bers
can tak e adv an tage in terms of the reco v ery dela y Therefore most of the losses are
reco v ered within the roundtrip time
As w e ha v e men tioned in Section is another parameter to con trol the
tradeo b et w een the n um b er of requests p er loss and the reco v ery dela y Ho w ev er
the eectiv eness of is minor W e sim ulated our mec hanism with four dieren t
v alues of and and the dierence of their p erformance is not
signican t The sim ulation results are sho wn in T able
requests
per loss
recovery
delay
816 32 64
size
128 816 32 64 128
δ
1.781 1.761
star topology string topology tree topology
816 32 64 128
2.070 2.140 2.161 2.179 2.030 2.180 2.322 2.435 1.905 2.088 2.271 2.483 1.975 0.50
0.67
0.75
0.90
0.50
0.67
0.75
0.90
2.017
1.985
1.933
3.12
3.16
3.21
3.26
1.906
1.879
1.807
3.17
3.23
3.25
3.31
2.071
2.039
1.985
3.13
3.19
3.23
3.23
2.100
2.069
2.024
3.12
3.21
3.20
3.23
2.123
2.039
2.036
3.12
3.15
3.17
3.20
1.680
1.630
1.520
1.93
2.07
2.27
2.54
1.896
1.850
1.749
1.32
1.43
1.49
1.68
2.071
2.012
1.907
0.85
0.92
0.95
1.06
2.245
2.171
2.040
0.53
0.56
0.59
0.65
2.342
2.270
2.167
0.32
0.34
0.37
0.39
1.679
1.645
1.564
2.71
2.78
2.88
2.94
1.853
1.811
1.733
2.69
2.71
2.71
2.89
2.014
1.991
1.913
2.63
2.73
2.74
2.86
2.213
2.180
2.080
2.67
2.71
2.74
2.78
2.410
2.397
2.299
2.62
2.69
2.74
2.75
T able Sim ulation results of in terpreting neigh borhood size from duplicates with
dieren tv alue of all mem b ers share iden tical losses
T op ologies with Multiple Lossy Links
Figures and sho w sim ulation results when all links ha v e uniformly
distributed error rates and their error rates are xed throughout the sim ulation
Generally sp eaking the results are consisten t with the conclusions dra wn from the
sim ulations with a single lossy link Note that as w eha v e iden tied in F ootnote if there are m ultiple lossy links along the path from a mem ber to the source the
mem bers estimated neigh b orho o d size is the a v erage of the neigh b orho o d sizes of
all lossy links
|
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35
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140
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0.8
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0.9
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1.1
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1.2
| | | | |
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session size
requests per loss
(a)
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session size
requests per loss
(a)
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8
| | | | | | | |
|||||
session size
recovery delay
(b)

size interpreted from recovery delay,ω=1/8, I=H=2+3c
C = c = 1/2
for example,
size interpreted from duplicates,ω=1/8, I=H=2+3c,δ=0.9
C = c = 1
C = c = 2
means the neighborhood size is interpreted from the number of
requests per loss andω = 1/8 ,δ = 0.9 , C = c = 1/2 , I = H = 2 + 3 c
Figure Sim ulation results in the star top ology all links with uniformly
distributed error rates
In the star top ology mem bers ha v e indep enden t losses so the n um b er of requests
per loss is close to one The n um ber of replies per loss and reco v ery dela y are
constan t regardless of the size of the session In the string top ology since mem bers estimated neigh b orho o d sizes are more closely distributed in the sim ulations of the
duplicate in terpreter they send requests and replies more aggressiv ely As a result
the n um b er of request and replies p er loss is higher and the reco v ery dela y is smaller
than the sim ulations of the delayin terpreter
In the tree top ology w e notice that the n um ber of requests decreases with the
session size and the the n um ber of replies increases with the session size Since
the width increases exp onen tially with depth in the tree top ology more losses are

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session size
requests per loss
(a)
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| | | | |
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session size
replies per loss
(b)
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||||||
session size
recovery delay
(c)
size interpreted from recovery delay,ω=1/8, I=H=2+3c
C = c = 1/2
for example,
size interpreted from duplicates,ω=1/8, I=H=2+3c,δ=0.9
C = c = 1
C = c = 2
means the neighborhood size is interpreted from the number of
requests per loss andω = 1/8 ,δ = 0.9 , C = c = 1/2 , I = H = 2 + 3 c
Figure Sim ulation results in the string top ology all links with uniformly
distributed error rates
|
0
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35
|
70
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140
|
1.0
|
1.2
|
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|
2.0
| | | | |
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session size
requests per loss
(a)
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70
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|
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session size
replies per loss
(b)
|
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| | | | |
||||||
session size
recovery delay
(c)
size interpreted from recovery delay,ω=1/8, I=H=2+3c
C = c = 1/2
for example,
size interpreted from duplicates,ω=1/8, I=H=2+3c,δ=0.9
C = c = 1
C = c = 2
means the neighborhood size is interpreted from the number of
requests per loss andω = 1/8 ,δ = 0.9 , C = c = 1/2 , I = H = 2 + 3 c
Figure Sim ulation results in the tree top ology all links with uniformly
distributed error rates
distributed to w ards the leaf mem bers when the session size increases Therefore
few er losses are shared b y a ma jorit y of the mem bers and the n um ber of requests
p er loss decreases On the other hand since more losses are distributed to w ards the
leaf mem b ers more requests can be replied b y a ma jorit y of the mem b ers Th us
the beha vior of the repliers is v ery similar to the beha vior of the requesters in the
single lossy link case W e found Figure b is v ery similar to Figure a
It is the w orst case scenario that all links in a top ology are lossy T o understand
the a v erage b eha vior of our dynamic timer sc heduling mec hanisms w e randomly
select
of the links in a top ology to be with uniformlydistributed error rates In
other w ords there one lossy link in the no de top ologies t w o lossy links in the
no de top ologies and so on The sim ulation results are sho wn in T able and
they are consisten t with the results and analysis from top ologies that all links are
lossy
The n um b er of requests p er loss in the top ologies with one lossy link is less than one b ecause
some of the requests are queued in the net w ork when the sim ulation terminates

star topology string topology tree topology topology
session size
requests
replies
recovery
1.015
816 32 64 128 816 32 64 128 816 32 64 128
0.998 0.999
A
B
neighborhood size interpreted from duplicates :ω=1/8, C=c=1, I=H=2+3c,δ=0.9
neighborhood size interpreted from recovery delay :ω=1/8, C=c=1, I=H=2+3c
per loss per loss delay
A
B
A
B
A
B
1.022
2.051
1.866
3.42
3.44
1.018 1.022 1.019 1.025
1.022
2.006
1.919
3.49
3.43
1.025
1.995
1.953
3.53
3.48
1.019
1.937
1.969
3.53
3.41
1.026
1.961
1.968
3.54
3.47
1.267 1.344 1.259 1.266
0.999
1.546
1.585
1.26
1.47
1.352
1.518
1.524
1.86
1.83
1.357
1.526
1.641
1.74
1.69
1.390
1.562
1.801
1.74
1.25
1.440
1.532
1.854
1.86
0.97
1.140 1.201 1.202 1.185
0.999
1.707
1.679
1.90
2.17
1.147
1.812
1.781
2.32
2.58
1.158
1.909
1.935
2.67
2.96
1.137
2.020
2.049
2.90
3.39
1.091
2.128
2.193
3.02
4.12
T able Sim ulation results of the randomlyselected links are with uniformly
distributed error rate
Discussion
Based on the sim ulation results the dela yin terpreter app ears to b e a b etter c hoice
for our dynamic timer adjustmentmec hanism than the duplicate in terpreter First
of all the duplicate in terpreter prob es for the optimal neigh b orho o d size if there is
no duplicate Reducing the estimated neigh b orho o d size b y a factor of maynot be
the righ t decision in some cases As w e ha v e seen in the sim ulations reducing the
estimated neigh borhood size causes aggressiv e action in sending the requests and
replies Secondly with the duplicate in terpreter the tradeo bet w een the n um ber
of duplicates p er loss and the reco v ery dela y is dened b y the linear functions pa
rameter C and cand the v alue of whic hmak es the tuning more complicated and
the p erformance less predictable
Finallyas w eha v e iden tied in Equation the n um b er of duplicates p er loss is
aected b y not only the neigh b orho o d size N but also the neigh b orho o d radius
t
N
In other w ords the distribution of neigh b ors Our revised timer sc heduling
mec hanism can eliminate the inuence of the neigh b orho o d size but it is unable to
con trol for the neigh b orho o d radius One could prop ose the use of a nonzero A and
a to con trol the neigh b orho o d radius F or example from Section the ratio of
B
A
has to b e xed in order to con trol the requester neigh b orho o d radius Ho w ev er
it is impractical to adjust A and B at the same pace in terms of the reco v ery dela y W e think the b est solution to con trol for the neigh b orho o d radius is to lo calize the
error reco v ery scop e Th us the neigh borhood radius is constrained b y the
scop e of requests or replies More researc h is required
Related W ork
Most of the error reco v ery mec hanisms in the prop osed reliable m ulticast proto cols
fo cus on the a v oidance of message implosion Generally sp eaking they can b e cate
gorized in to structurebased and timerbased approac hes In the structurebased
approac h a subset of mem bers are selected either to organize the error reco v ery
activities or to pro cess error reco v ery messages In the timerbased approac h all
mem bers sun the error reco v ery algorithm and they rely on the randomization of

timers to suppress duplicate error reco v ery messages A few examples are discussed
b elo w
StructureBased Approac hes
RBP is a tok enbased reliable m ulticast proto col Atok en circulates among mem
bers in a roundrobin fashion to distribute the w orkload The mem ber p ossessing
the tok en b ecomes the currenttok en site RBP adopts a senderbased error con trol
mec hanism b et w een senders and tok en sites and a receiv erinitiated error reco v ery
mec hanism b et w een tok en sites and receiv ers The currenttok en site is resp onsible
for ac kno wledging eac h data reception It is also resp onsible for reco v ering losses
for other mem b ers and replies to the retransmission requests
In MTP time is divided in to slots called heartb eats for data transmission
A xed n um ber of messages are sen t in eac h time slot including both the new
data and the replies A master is elected from among all sources for the purp ose
of gran ting tok ens A mem ber m ust obtain the tok en to b ecome the sender of
the curren t slot A t an y poin t in time only one data source can send data The
retransmission requests are unicast to sources and the replies are m ulticast to the
whole group
Holbro ok et al suggested a hierarc hic logging serv er structure to distribute
the error reco v ery w orkload Logging serv ers ac kno wledge eac h data reception from
the source and they are resp onsible for reco v ering losses for other receiv ers Receiv ers
con tact their lo cal secondary serv er for retransmission instead of the remote primary
serv ers to a v oid NAK implosion and to minimize reco v ery latency and bandwidth
A serv er either unicasts or m ulticasts a reply based on the n um ber of requests it
receiv es
In RMTP data are explicitly ac kno wledged b y the receiv ers T o a v oid
A CK implosion mem b ers are group ed in to lo cal regions and lo cal regions are con
structed in to a tree hierarc h y A designated receiv er DR is selected in eac h region
it is resp onsible for pro cessing A CKs from its lo cal region and ac kno wledging the
data reception to its paren t DR DRs cac he receiv ed data and resp ond to retrans
mission requests in their lo cal regions A reply is either unicast or m ulticast based
on the n um b er of requests p er loss
TMTP has a similar a v or to RMTP in terms of the hierarc hic error reco v ery
structure It groups mem b ers in to domains and organizes domains in to a hierarc hic
con trol tree Mem b ers in a domain request the domain manager for retransmission
A domain manager is also resp onsible for error reco v ery of its c hildren managers in
the con trol tree The scop e of retransmission is restricted b y limiting the TTL
TimerBased Approac hes
Grossglauser presen ts DTRM to compute deterministic timer v alues based on
the m ulticast tree top ology and sourcetoreceiv er propagation dela ys F or a single
loss the deterministic timers ensure that one mem b er sends a request fast enough so
the reply triggered b y the request will arriv e at other mem b ers b efore their request
timers expire

Flo yd et al prop osed an adaptiv e adjustmen t mec hanism of the random
timer A threshold of the n um ber of duplicates p er loss and a threshold of the re
co v ery dela y are predened Timer parameters are increased if the a v erage n um ber
of duplicates p er loss is greater than the duplicate threshold Otherwise the param
eters are decreased if the a v erage reco v ery dela y is greater than the dela y threshold
Therefore the mec hanism satises the duplicate threshold rst and then the dela y
threshold
Conclusion
W e in v estigated the relationship bet w een the timer setting parameters and error
reco v ery p erformance in SRM Both analysis and sim ulations suggest that the de
terministic w ait from the random timer can b e remo v ed to reduce the reco v ery dela y
and the probabilistic w aiting p erio d should b e prop ortional to the mem b ers neigh
borhood size to facilitate duplicate suppression In fact b y computing the timer
parameters using linear functions from the neigh b orho o d sizes the n um ber of re
quests and replies p er loss and the reco v ery dela y are not signican tly aected b y
the session size
W e revised the curren t timer sc heduling sc heme in SRM whic h eliminates the de
terministic w aiting p erio ds of the request and reply timers minimizes the o v erhead
of premature requests and prev en ts duplicate replies in resp onse to unsuppressed
requests W e also compared t w o feedbac k in terpretation mec hanisms in our dy
namic timer parameter adjustmen t Mem bers estimate their requester and replier
neigh b orho o d sizes from the net w ork feedbac k indep enden tly to adjust their timer
parameters F rom the sim ulation results w e found that the mec hanism of in terpret
ing neigh borhood size from reco v ery dela y p erforms b etter than the mec hanism of
in terpreting neigh b orho o d size from duplicates
References
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S Deering Host extensions for IP m ulticasting Internet Dr aft RF C August ChingGung Liu A Scalable Reliable Multicast Proto col PhD Dissertation
Pr op osal University of Southern California No v em ber ChingGung Liu Deb orah Estrin Scott Shenk er and Lixia Zhang Lo cal Error
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for In teractiv e Collab orativ e Applications Pr o c e e dings of A CM Multime dia
M Grossglauser Optimal Deterministic Timeouts for Reliable Scalable Mul
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