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USC Computer Science Technical Reports, no. 696 (1999)

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USC Computer Science Technical Reports, no. 696 (1999)

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Content T est Syn thesis Applied to P erformance Ev aluation of Multip oin t Proto cols
Ahmed Helm y Deb orah Estrin Sandeep Gupta
Univ ersit y of Southern California
Los Angeles CA
email fahelm y estrin guscedu sandeepp oissonuscedu
A bstr act The adv entofm ultip ointm ulticastbased applica
tions and the gro wth and complexityof the In ternet
has complicated net w ork proto col design and testing
In this pap er w e presen t a metho d for automatic
syn thesis of w orst and b est case scenarios for m ul
tip oin t proto col p erformance ev aluation As a case
study w e analyze v arian ts of the timer suppression
mec hanism used in m ultip oin t proto cols in the In ter
net W e use our metho d to ev aluate the mec hanism
with resp ect to t w o p erformance criteria n um ber of
resp onses p er request and resp onse time The results
are applied to examples in reliable m ulticast proto cols
The metho d uses a faultorien ted test generation
F OTG algorithm for searc hing the proto col and sys
tem state space to syn thesize the scenarios The algo
rithm is based on a global nite state mac hine GFSM
mo del W e ha v e extended the algorithm with tim
ing seman tics to handle endtoend dela ys and address
p erformance criteria W e in tro duce the notion of a
virtual LAN to represen t the underlying m ulticast dis
tribution tree
W e hop e this metho d can serv e as a mo del for apply
ing more systematic test generation to other net w ork
proto cols as w ell
I Intr oduction
The longevit y and po w er of In ternet tec hnologies
deriv es from its abilit y to op erate under a wide range
of op erating conditions underlying top ologies and
transmission c haracteristics as w ell as heterogeneous
applications generating v aried trac inputs P er
haps more than an y other tec hnology the range of
op erating conditions is enormous it is the cross pro d uct of the top and b ottom of the IP hourglass
P erhaps it is this enormous set of conditions that
has inhibited the dev elopmen t of systematic ap
proac hes to analyzing In ternet proto col designs Ho w
can one ev en hop e to test for correctness or c harac
terize p erformance of a proto col when the set of in
puts is in tractable Nev ertheless net w orking infras
tructure is increasingly critical and there is enormous
need to increase the robustness and understanding of
net w ork proto cols It is time to dev elop tec hniques
for systematic testing of proto col b eha vior ev en in
the face of the ab o vec hallenges and obstacles
A t the same time weha v e no delusions that com
plex adaptiv e proto cols will b e automatically v eri
able under their full range of conditions Rather w e
are prop osing a framew ork in whic h a proto col de
signer can follo w a set of systematic steps assisted
b y automatoin where p ossible and co v er a sp ecic
part of the design and op erating space
The proto col designer will still need to create the
initial mec hanisms describ e it in the form of a nite
state mac hine and iden tify the p erformance crite
ria or correctness condition that they w anttoin v es
tigate Our automatable metho d pic ks up at that
poin t pro viding algorithms that ev en tually result in
scenarios or test suites that stress the proto col with
resp ect to the iden tied criteria
This pap er demonstrates some of our progress to
date in realizing this vision W e apply it to the p er
formance ev aluation of m ultip oin t proto cols
A Motivation
The recentgro wth of the In ternet and its increased
heterogeneit y due to dieren t switc hing tec hnologies
transmission media and applicatoins has in tro duced
new failure mo des and added complexitytoprotocol
design and testing In addition the adv entof m ul
tip oin t applications has in tro duced new c hallenges
of qualitativ ely dieren t nature than the traditional
poin ttop oin t proto cols Multip oin t applications in
v olv e a group of receiv ers and one or more senders
sim ultaneously As more complex m ultip oin t appli
cations and proto cols are coming to life the need
for systematic and automatic metho ds to study and
ev aluate suc h proto cols is b ecoming more apparen t
Suc h metho ds aim to exp edite the proto col dev elop
men t cycle and impro v e resulting proto col robustness
and p erformance
Through our prop osed metho dology for test syn
thesis w e hop e to address the follo wing k ey issues of
proto col design and ev aluation
A Scenario dep enden t ev aluation and the use of
v alidation test suites
Proto cols ma y be ev aluated for correctness and
p erformance
In manyev aluation studies of m ultip oin t proto cols
esp ecially sim ulation studies the results are dep en
den t up on sev eral factors suc h as mem b ership dis
tribution net w ork top ology and dela y parameters
Hence the conclusions dra wn from studies on suc h
proto cols dep end hea vily up on the sim ulation inputs
The proto col design pro cess usually passes through
iterativ e cycles of renemen t and mo dication Eac h
mo dication of the proto col requires revisiting the
ev aluation scenarios to ensure that no erroneous or
undesirable beha vior has b een in tro duced This
brings ab out the need for v alidation test suites Con
structing these test suites can be an onerous and
errorprone task if p erformed man ually Unfortu
nately little w ork has been done to automate the
generation of suc h tests for net w ork proto cols let
alone m ultip oin t proto cols
In w e prop osed a faultorien ted test generation
F OTG algorithm for syn thesizing test scenarios to
study the correctness of m ulticast routing proto cols
In this pap er w e extend the algorithm to deal with
a p erformance issues and b endtoend hostto
host m ultip oin t proto cols and applications
A New c hannel c haracteristics and the adv an tage
of w orst case analysis
Wireless mobile and satellite comm unication net
w orks ha v e proliferated in the In ternet Suc h net
w orks ha v e dieren t dela y and loss c haracteristics
than terrestrial net w orks Proto cols that w ere de
signed for terrestrial net w orks ma y fail or perform
p o orly in wireless en vironmen ts F or example re
searc hers ha v e observ ed that TCP ma y exp erience
undesirable in teraction with lossy c hannels and ha v e
striv ed to o v ercome this problem It is dicult to design a proto col that w ould p er
form w ell in all en vironmen ts But iden tifying break
ing poin ts that violate correctness or exhibit w orst
case p erformance b eha viors of a proto col ma y giv e
insigh t to proto col designers and help in ev aluating
the design tradeos In general it ma y b e desirable
to iden tify early on in the design cycle scenarios un
der whic h the proto col exhibits w orst or best case
beha vior
The metho d presen ted in this pap er automates the
generation of scenarios in whichm ultip oin t proto cols
exhibit w orst and b est case b eha viors
A Iden tifying commonalities and in teresting build
ing blo c ks
The design of m ultip oin t proto cols has in tro duced
new c hallenges and problems Some of the problems
are common to a wide range of proto cols and applica
tions One suc h problem is the multir esp onder prob
lem where m ultiple mem b ers of a group ma y resp ond
almost sim ultaneously to an ev en t whic h ma y
cause a ood of messages throughout the net w ork
and in turn ma y lead for example to unin tended
and coun terpro ductiv e sync hronized resp onses and
ma y cause additional o v erhead eg the w ellkno wn
A ck implosion problem leading to lo w p erformance
One common tec hnique to alleviate the ab o v e
problem is the multic ast damping tec hnique whic h
emplo ys a timer suppr ession mec hanism
This mec hanism is emplo y ed in a range of m ulti
poin t proto cols suc has m ulticast routing proto cols
eg PIMDM PIMSM and IGMP m ul
ticast transp ort proto cols eg SRM RRM
MFTP and R TPR TCP address allo cation
AAP SDR and MASC adaptiv ew eb
cac hing and other m ultip oin t applications me
dia gatew a y Section I I describ es the role of the
timer suppression mec hanism in some of these proto
cols
As a case studyw eiden tify primitiv es used in the
m ulticast timer suppression mec hanism and examine
its w orst and best case beha viors in a systematic
automatic fashion
The b eha vior is not proto col sp ecic and if a
proto col is comp osed of previously c hec k ed building
blo c ks these parts of the proto col need not b e rev ali
dated in full Ho w ev er in teraction b et w een the build
ing blo c ks still needs to b e v alidated
A P erformance b enc hmarking
F or p erformance ev aluation the metrics used are
based on the giv en proto col and function p erformed
Common metrics for ev aluation of reliable m ulticast
proto cols that employm ulticast damping for exam
ple include the a v erage resp onse dela y and n um ber
of requestsreplies incurred b y loss reco v ery
Prop osed proto cols ho w ev er ma y prop ose to re
ne a mec hanism with resp ect to a particular p er
formance metric using for ev aluation those scenar
ios that sho w p erformance impro v emen t Ho w ev er
without systematic ev aluation these same renemen t
studies mayunin ten tionally o v erlo ok other scenar
ios and p erformance criteria that ma y b e relev an t
The test scenarios eg the t yp e of top ologytraf c and failure mo dels mem b ership distribution and
dynamics ma y be in tegrated in to the p erformance
benc hmark
In summary w e in tend that our metho dology for
test generation w ould con tribute to the understand
ing of b etter p erformance b enc hmarking and the de
sign of more robust proto cols
B The Appr o ach
A proto col designer creates the initial mec hanism
design In order to use our metho d a designer needs
to sp ecify the system ie proto col and message se
man tics in a pro cessable form W e suggest an ex
tended FSM mo del in this pap er In addition the
ev aluation criteria be it related to p erformance or
correctness m ust be giv en as input to the metho d
in the appropriate form In this pap er ho w ev er w e
only address p erformance issues Weha v e addressed
correctness in previous studies The proto col and system description is then pro
cessed b y the test generation algorithms These al
gorithms use searchtec hniques to syn thesize the test
scenarios based on the ev aluation criterion
The output of this pro cess consists of tests whic h
are sequences of proto col actions top ology c haracter
istics and p ossibly net w ork failures that meet the
ev aluation criteria eg exhibit maxim um o v erhead
or dela y
The rest of the pap er is organized as follo ws Re
lated w ork is giv en in section II Section III in
tro duces the mo del used to represen t the proto col
and top ology Section IV describ es ho w to apply
the metho d and outlines the algorithm used The
timer suppression mec hanism and its mo del are pre
sen ted in section V Sections VIVI I I and VI I presen t
p erformance analyses for proto col o v erhead and re
sp onse time follo w ed b y illustrativ e examples and
case studies Issues and related w ork are discussed in
section IX while section X concludes Algorithmic
details on deriving w orst and b est case relations are
giv en in app endix A
II Rela ted w ork
The related w ork falls mainly in the areas of proto
col v erication test generation and m ultip oin t proto
cols esp ecially those related to the timer suppression
mec hanism used in this pap er
There is a large body of literature dealing with
v erication of proto cols V erication systems t ypi
cally address w elldened prop erties suc has safety liveness and r esp onsiveness and aim to detect
violations of these prop erties In general the t w o
main approac hes for proto col v erication are theo
rem pro ving and reac habilit y analysis Theo
rem pro ving systems dene a set of axioms and re
lations to pro v e prop erties and include mo delb ase d
and lo gicb ase d formalisms These systems
are useful in man y applications Ho w ev er they ma y
not b e suitable for complex m ultip ointIn ternet pro
to cols since the n umberofaxioms gro ws with proto
col complexit y Moreo v er these systems w ork with
abstract sp ecications and tend to abstract out some
net w ork dynamics that w e will study eg selectiv e
pac k et loss and they do not address p erformance
issues p er se
Reac habilit y analysis algorithms on the other
hand try to insp ect reac hable proto col states and
suer from the state space explosion problem T o
circum v entthis problem state reduction tec hniques
could b e used These algorithms ho w ev er do not
syn thesize net w ork top ologies Reduced reac habilit y
analysis has b een used in the v erication of cac he
coherence proto cols using a global FSM mo del
W e adopt a similar FSM mo del and extend it for our
approac h in this study Automatic test generation tec hniques ha v e been
used in sev eral elds VLSI c hip testing uses test
v ector generation to detect singlestuc k faults T est
v ectors ma y b e generated based on circuit and fault
mo dels using the faultorien ted pro cess that uti
lizes implic ation tec hniques These tec hniques w ere
adopted in todev elop faultorien ted test genera
tion F OTG for m ulticast routing In that pap er
F OTG w as used to study correctness of a m ulticast
routing proto col on a LAN W e extend F OTG to
study p erformance of endtoend m ultip oin t mec h
anisms Wein tro duce the concept of a virtual LAN
to represen t the underlying net w ork in tegrate timing
and dela y seman tics in to our mo del and use p erfor
mance criteria to driv e our syn thesis algorithm
In a sim ulationbased stress testing framew ork
based on heuristics w as prop osed Ho w ev er that
metho d did not pro vide automatic top ology gener
ation nor did it address p erformance issues The
VINT to ols pro vide a framew ork for In ternet pro
to col sim ulation Based on the NS sim ulation and
NAM animator this framew ork pro vides a library of
proto cols and a set of v alidation test suites Ho w ev er
VINT do es not pro vide a generic to ol for generating
these tests automatically W ork in this pap er ma y
complemen t suc h studies and ma ybe in tegrated with
these prop osed framew orks as part of their scenario
generation
A large n um ber of m ultip oin t proto cols has b een
recen tly prop osed for the In ternet W e only men tion
ones that use the mec hanism under study The timer
suppression mec hanism is used in sev eral m ultip oin t
proto cols
IPm ulticast proto cols suc h as PIM and
IGMP use the timer suppression mec hanism on
LANs to reduce the n um b er of con trol messages sen t
in the JoinPrune and Assert mec hanisms
F or reliable m ulticast sc hemes suc h as scalable re
liable m ulticast SRM the mec hanism is used
to alleviate the ac kimplosion problem or reduce
n um ber of resp onses on a LAN as in m ulticast ftp
MFTP V arian ts of the SRM timers are used in
registry replication eg RRM and adaptiv ew eb
cac hing In m ulticast address allo cation sc hemes suc hasthe
address allo cation proto col AAP and session
directory sdr the timer suppression mec hanism
is used in the requestresp onse proto col to a v oid an
implosion of resp onses during the collision detection
phase
In the con text of activ e services eg in a
service oered b y media gatew a y serv ers m ulticast
damping is used to launc h one service agen t serv en t
from a p o ol of serv ers
There are other applications of the timer suppres
sion mec hanism in areas of selforganizing hierarc hies
SCAN and transp ort proto cols eg XTP and R TP
III The model
The mo del is a pro cessable represen tation of the
system under study that enables automatoin of our
metho d The o v erall mo del consists of A the pro
to col mo del B the top ology mo del and C the fault
mo del
A The Pr oto c ol Mo del
W e represen t the proto col b y a nite state ma
c hine FSM and the o v erall system b y a global FSM
GFSM as follo ws
I FSM mo del Ev ery instance of the proto col run
ning on a single endsystem is mo deled b y a deter
ministic FSM consisting of i a set of states ii
a set of stim uli causing state transitions and iii
a state transition function or table describing the
state transition rules F or a system i this is repre
sen ted b y the mac hine M
i
S i

i
where S is
a nite set of state sym b ols i
is the set of stim uli
and i
is the state transition function S i
S II Glob al FSM mo del The global state is dened
as the comp osition of individual endsystem states
The beha vior of a system with n endsystems ma y
b e describ ed b y M
G
S
G
G

G
where S
G
S
S
S
n
is the global state space G
n
S
i i
is
the set of stim uli and G
is the global state transition
function S
G
G
S
G
B The T op olo gy Mo del
The top ology cannot be captured simply b y one
metric Indeed its dynamics ma y be complex to
mo del and sometimes in tractable W e prop ose to
capture the ma jor c haracteristics of the top ology the
dela ys and loss patterns see the fault mo del W e
use a virtual LAN VLAN mo del to represen t the
underlying net w ork top ology and m ulticast distribu
tion tree The VLAN captures dela y seman tics using
a dela y matrix D see Figure where d
ij
is the
dela y from system i to system j Q
V. LAN
1
2 3
0 dQ,1 dQ,2 dQ,3
d1,Q 0 d1,2 d1,3
d2,Q d2,1 0 d2,3
d3,Q d3,1 d3,2 0
D =
Fig The virtual LAN and the dela y matrix
C The F ault Mo del
A fault isalo w lev el eg ph ysical la y er anoma
lous b eha vior that ma y aect the proto col under test
F aults ma y include pac k et loss system crashes or
routing lo ops F or brevit y w e only consider pac k et
loss in this study Selectiv e loss is the typeofpac k et
loss that ma y b e exp erienced byam ultip oin t appli
cation where a m ulticast message ma y be receiv ed
b y some systems but not others The loss of a mes
sage b y a sp ecic system prev en ts its reception and
hence prev en ts the transition that it triggers at that
system
IV Appl ying The Method
T o apply the metho d the designer iden ties the
task at hand and then applies the algorithm to obtain
p ossible solutions
A T ask Denition
Weiden tify t w o kinds of tasks to whic h our metho d
ma y b e applied top ology syn thesis and timer
conguration
T op ology syn tehsis is p erformed when the timer
v alues are kno wn and required is the top ology ie
D matrix that pro duces the b est or w orst case b e
ha vior
Timer conguration is p erformed when the
top ology is giv en ie the D matrix is kno wn and
the timer v alues are b eing determined ie v ari
ables The solution in this case is the timer expi
ration v alues that cause b est or w orst case b eha vior
Note that for the rst task w e need to map the out
put dela y matrix on to a top ology The dela ys used in
the dela y matrix reect dela ys o v er the m ulticast dis
tribution tree In general these dela ys are aected b y
sev eral factors including the m ulticast routing proto
col tree t yp e and dynamics the unicast routing pro
to col and the propagation transmission and conges
tion dela ys F or example if branc hes of the underly
ing m ulticast distribution tree coincide with the hop
coun t based unicast routes then one p ossible top ol
ogy w ould b e the completely connected net w ork with
the dela ys represen ting the propagation and trans
mission dela ys
B A lgorithm Outline
This section outlines the sk eleton of the algorithm
used for test syn thesis The basic algorithm passes
through three main steps the target ev en t iden
tication the searc h and the task sp ecic
solution
The target ev en t The algorithm used in our
metho d starts from a giv en ev en t called the target
ev en t The ev en t eg sending a message is iden ti
ed b y the designer as one relev anttothe ev aluation
criteria eg the o v erhead of a giv en message
The searc h Three steps are tak en in the searc h
iden tifying conditions obtaining sequences and for
m ulating inequalities
a Identifying c onditions Using the transition
rules conditions and transitions necessary to trigger
the target ev en t are iden tied
b Obtaining se quenc es Once the previous transi
tions are iden tied the algorithm uses i bac kw ard
searc h and ii forw ard searchtec hniques to build se
quences of ev en ts leading to these transitions and cal
culates the duration of these sequences as follo ws
i Bac kw ard searc h is used to iden tify p ossible
previous ev en ts and uses implication rules that op
erate on the transition table of the mec hanism Some
implication rules include timing seman tics to accoun t
for net w ork dela ys or duration of timers Implica
tion rules include receptiontransmission pairing
where reception of a transmitted message is implied
after applying the net w ork dela y if the message is not
lost timer expiration where the ev en t of ring
the timer is implied after the expiration p erio d and
state creation where previous states are implied
byrev ersing the state transition rules
ii F orw ard searc h is used to v erify the bac k
w ard steps tak en and eliminate con tradictions Bac k
trac king is used to reco v er from con tradictions and
branc hing is used to explore optional steps
c F ormulating ine qualities Based on the condi
tions and transitions previously obtained along with
the timed sequences leading to the transitions the
algorithm form ulates timing constrain ts in the form
of inequalities that trigger an y w an ted transitions
and a v oids anyun w an ted transitions
T ask sp ecic solution The output of the searc h
ma y include a set of ev en t sequences and constrain ts
in the form of timing inequalit y relations bet w een
timers and net w ork dela ys that satisfy the giv en con
dition or ev aluation criterion
The output is then pro cessed to nd a solution de
p ending on the task denition whether it is top ology
syn thesis or timer conguration
V The Timer Suppression Mechanism
As explained earlier the timer suppression mec ha
nism is used in v arious m ultip oin t proto cols Webe liev e it is a go o d building blo c k to analyze as a rst
endtoend case study since it is ric hin m ulticast and
timing seman tics and can be ev aluated using stan
dard p erformance criteria In this section w e presen t
a simple description of the mec hanism then presen t
its mo del used thereafter in the analysis
The timer suppression mec hanism in v olv es a re
quest q and one or more resp onses p When a system
Q detects the loss of a data pac k et it sets a request
timer and m ulticasts a request q When a system
i receiv es q it sets a resp onse timer randomly or
as a function of some parameter the expiration of
whic h after duration Exp
i
triggers a resp onse p If
the system i receiv es a resp onse p from another sys
tem j b efore its timer expires it suppresses its o wn
resp onse
A Evaluation Criteria
Tw o criteria ma y be used to ev aluate the p erfor
mance of this mec hanism
The rst is the n um b er of resp onse messages p er
request In this case w e dene the w orst case be ha vior to b e one that pro duces the maxim um n um
ber of resp onses per request As an extreme case
this o ccurs when no suppression tak es place ie all
p oten tial resp onders that set their timers do indeed
resp ond
The second p erformance criterion is the resp onse
dela y ie the time tak en b y the requester to receiv e
a resp onse The w orst scenario in this case is one
that exp eriences maxim um resp onse dela y B Timer Suppr ession Mo del
F ollo wing is the mo del of the timer suppression
mec hanism w e use in the rest of the pap er
B Proto col states S State Meaning
D poten tial resp onder
D
T
resp onder with the resp onse timer set
R original state of the requester
R
T
requester with the request timer set
B Stim uli or Ev en ts
Sendingreceiving messages sending resp onse
p
t
and request q
t
receiving resp onse p
r
and re quest q
r
Timer and other ev en ts the ev en ts of ring the
request timer Req and resp onse timer Res L denotes
detecting pac k et loss
B Notation
An ev en t subscript denotes the system initiating the ev en t
eg p t
i
is resp onse sentb y system i while the subscript
m denotes m ulticast reception eg p r m
denotes receipt
of a message byall mem b ers of the group if no loss o ccurs
The state subscript T is used to denote the existence
of a timer and is used b y the algorithm to apply the timer
implication to re the timer ev en t after the expiration p erio d
A state transition has a start state and an end state and
is expressed in the form star tS tate endS tate
eg D D
T
It implies the existence of a system in the
star tS tate ie D as a condition for the completion of the
transition to the endS tate ie D
T
An ee ct in the transition table maycon tain a state transition
and a stim ulus in the form star tS tate endS tate stimul us whic h indicates the triggering of the stim ulus if the state
transition o ccurs An eect ma y con tain sev eral transitions
eg T rans T rans whic h indicates that out of these
transitions all transitions with satised conditions will o ccur
B T ransition T able The transition rules for the timer suppression
mec hanism are giv en bythe follo wing transition ta
ble
Sym bol Ev en t Eect Meaning
loss L R R
T
q t detecting loss of pac k et
causes request transmission
and setting of request timer
tx req q t q r m
transmission of q causes
m ulticast reception
of q after net w ork
dela y is applied
rcv req q r D D
T
reception of q causes a
system in P state
to set resp onse timer
res tmr Res D
T
D p t expiration of resp onse timer
causes transmission of p
and a c hange to P state
tx res p t p r m
transmission of p causes
m ulticast reception of
p after applying
net w ork dela y
rcv res p r R
T
R reception of p bya
D
T
D system with the timer
set causes suppression
req tmr Req q t expiration of request timer
causes transmission of q
The mo del con tains one requester Q and sev eral
p oten tial resp onders eg i and j Let t
be the
time at whic h Q sends the request q All the p oten
tial resp onders initially exist in state D The request
sen t b y Q is receiv ed b y i and j at times d
Qi
and
d
Qj
resp ectiv ely When the request q is sen t the
requester transitions in to state R
T
b y setting the re
quest timer Up on receiving a request a poten tial
resp onder in state D transitions in to state D
T
b y
setting the resp onse timer The time at whic h an
ev en t o ccurs is giv en b y t ev ent eg p
r j
o ccurs at
t p
r j

B Implication Rules
The bac kw ard searc h uses the follo wing implication
rules deriv ed from the transition table
T ransmissionReception Tx Rcv The recep
tion occurs after applying the net w ork dela ys An
example of this implication is p
r i
p
t j
where
The time of a state is when the state w as rst created so
t D
T
i
is the time at whic h i transited in to state D
T
t p
r i
t p
t j
d
ji
Timer Expiration Tmr Exp The expiration
o ccurs Exp units after the timer is set An example
of this implication is Res
i
D
i
D
T i
D
T i
where
t Res
i
t D
T i
Exp
i
and Exp
i
is the duration
of the resp onse timer Res
i
State Creation St Cr A state is created from
another b y rev ersing the transition rules and going
to w ards the star tS tate of the transition F or exam
ple D
T i
D
T i
D
i
In the follo wing sections w e use the ab o vemodel
and algorithm to syn thesize w orst and b est case b e ha vior scenarios according to the proto col o v erhead
and the resp onse time p erformance criteria
VI Pr otocol O verhead Anal ysis
In this section w e conduct w orst and b est case p er
formance analyses for the timer suppression mec ha
nism with resp ect to the n um ber of resp onses trig
gered per request F or brevit y w e assume no loss
of messages un til reco v eryand w e assume that the
request timer is high enough that the reco v ery will
o ccur in one round of request Other cases ma y be
dealt with similarly A Worstc ase analysis
A T arget ev en t and conditions
Since the o v erhead in this case is measured as the
n um b er of resp onse messages the designer iden ties
the ev en t of triggering a resp onse p
t
as the target
ev en t and the goal is to maximize the n um ber of
resp onse messages
A The searc h
As previously describ ed in section IVB there are
three main steps for the searc h algorithm
iden tifying the targets w an ted and un w an ted con
ditions and transitions
W e use the notation E v entE f f ect to represen t a transi
tion
obtaining sequences leading to the w an ted and
un w an ted transitions and calculating the times for
these sequences and
form ulating the inequalities that ac hievethe time
constrain ts required to in v okew an ted transitions and
a v oid un w an ted transitions
Iden tifying conditions
The algorithm searc hes for the transitions necessary
to trigger the target ev en t and their conditions re
cursiv ely These are called wante d tr ansitions and
wante d c onditions resp ectiv ely In addition the al
gorithm searc hes for transitions that n ullify the tar
get ev entor in v alidate an y of its conditions These
are called unwantedtr ansitions In our case the target ev en t is p
t
The algorithm
iden ties transition r es tmr Res D
T
D p
t
as a
wante d tr ansition and its condition D
T
as a wante d
c ondition T ransition r cv r e q q
r
D D
T
is also
iden tied as a wantedtr ansition since it is necessary
to create D
T
The unwante d tr ansition is iden tied as transition
r cv r es p
r
D
T
D since it alters the D
T
state with
out in v oking p
t
Obtaining sequences
Using bac kw ard searc h the algorithm obtains se
quences and calculates time v alues for the follo w
ing transitions the w an ted transition r es tmr the w an ted transition r cv r e q and the un
w an ted transition r cv r es as follo ws
T o obtain the sequence of ev en ts for transi
tion r es tmr the algorithm applies implication rules
Tmr Exp St Cr Tx Rcv in that order and w e get
Res
i
D
i
D
T i
p
t i
q
r i
D
T i
D
i
q
t Q
Hence the calculated time for t p
t i
b ecomes
t p
t i
t
d
Qi
Exp
i
T o obtain the sequence of ev en ts for transi
tion r cv r e q the algorithm applies implication rule
Tx Rcv and w e get
q
r i
D
T i
D
i
q
t Q
Hence the calculated time for t q
r i
b ecomes
t q
r i
t
d
Qi
T o obtain the sequence of ev en ts for transition
r cv r es for systems i and j the algorithm applies im
plication rules Tx RcvTmr Exp St Cr Tx Rcv in
that order and w eget
p
r i
D
i
D
T i
Res
j
D
j
D
T j
p
t j
q
r j
D
T j
D
j
q
t Q
Hence the calculated time for t p
r i
b ecomes
t p
r i
t
d
Qj
Exp
j
d
ji
F orm ulating Inequalities
Based on the ab o vew an ted and un w an ted transitions
the algorithm a v oids transition r cv r es while in v oking
transition r es tmr to transit out of D
T
T o ac hiev e
this the algorithm deriv es the follo wing inequalit y
see App endix A for more details
t p
t i
t p
r i
Substituting expressions for t p
t i
and t p
r i
previ
ously deriv ed w eget d
Qi
Exp
i
d
Qj
Exp
j
d
ji
In other w ords V
t i
V
t j
d
ji
where V
t i
d
Qi

Exp
i
V
t i
is the time required for system i to trigger
a resp onse transmission if an y
Alternativ ely the system m ust exist in a state dier
en t than D
T
to a v oid the un w an ted transition and
the algorithm deriv es the follo wing inequalit y see
App endix A for more details
t p
r i
t q
r i
Again substituting expressions deriv ed ab o v e w e
get
d
Qi
d
Qj
Exp
j
d
ji
Note that equations and are general for
anyn um b er of resp onders where i and j are anyt w o
resp onders in the system
Figure sho ws equations and in a and
b resp ectiv ely A T ask sp ecic solutions
T op ology syn thesis Giv en the v alues of Exp wew an t to nd a feasible solution for the w orstcase
dela ys A feasible solution in this con text means p os
time
Q
2
1
Exp 1
Exp 2
d 1,2
d Q,2
d Q,1
p
r2
p
t2
q
r2
p
t1
q
r1
q
t
q
t
Timer
suppression
Exp 1 d 1,2
d Q,2
d Q,1
p
r2
q
r2
p
t1
q
r1
Exp 2 Exp 2
p
t2
q
r2
Exp 1 d 1,2
d Q,2
d Q,1
p
r2
p
t1
q
r1
q
t
(a) (b) (c)
t(p
t2
) < t(p
r2
) t(p
r2
) < t(q
r2
) t(p
t2
) > t(p
r2
)
t(p
r2
) > t(q
r2
)
Fig Time lines sho wing p ossible ev en t sequencing a and
b sequences do not lead to suppression while c leads
to timer suppression
itivedela y assignmen ts
In equation ab o v e if w e tak e d
Qi
d
Qj
w e
get
Exp
i
Exp
j
d
ji
The inequalities put an upp er limit on the dela ys d
ji
hence w e can alw a ys nd a p ositiv e d
ji
to satisfy the
inequalities
Timer conguration Giv en the delayv alues or
b ounds w e w an t to obtain timer expiration v alues
that pro duce w orstcase b eha vior
W e can obtain a range for the relativ e timer settings
ie Exp
i
Exp
j
using equation ab o v e
Sev eral examples in the section VI I illustrate ho w
to apply the ab o v e solutions
Note ho w ev er that there ma y b e a practical upp er b ound
on the dela ys in the top ology Hence the solution that sat
ises the ab o v e inequalities ma y not necessarily satisfy the
constrain ts set forth for the dela ys In this case the problem
b ecomes one of maximization where the w orstcase top ology
is one that triggers maxim um n um b er of resp onses p er request
but that n um ber ma y b e less than the p oten tial resp onders
This is part of our future w ork
B Bestc ase analysis
B T arget ev en t and conditions
The p erformance criteria is c hanged to minimize
the n um ber of resp onses per request The designer
iden ties the ev en t q
t
as the target ev en t only this
time the condition is to a v oid ie minimize the tar
get ev en t Hence the algorithm iden ties transition
r es tmr as the un w an ted transition Alternativ ely the algorithm iden ties transition r cv r e q as the tar
get condition
B The searc h
The follo wing conditions are form ulated using
steps similar to those giv en in the w orstcase anal
ysis
t p
t i
t p
r i
and
t p
r i
t q
r i
These are complemen tary conditions to those giv en
in the w orst case analysis Figure sho ws equations
and in c Refer to the App endix A for
more details on the inequalit y deriv ation
B T ask sp ecic solutions
T op ology syn thesis
Giv en the expiration v alues Expw ew anttosyn the
size the b estcase dela y assignmen t for the top ology Using equation if w etak e d
Qi
d
Qj
w e get
Exp
i
Exp
j
d
ij
In this case the output top ology ma y not alw a ys b e
feasible eg if Exp
i
Exp
j
and problem b ecomes
that of minimization of the n um ber of responses Timer conguration
Giv en the dela y b ounds for the top ologyw ew antto
determine the timer expiration settings that pro duce
the b estcase b eha vior
F rom equation w e get
d
Qi
d
Qj
Exp
j
d
ji

This can b e rewritten as
Exp
j
d
Qi
d
Qj
d
ji
d
Qj
d
Qi
d
ji
F rom equation ab o v e w eget d
Qi
Exp
i
d
Qj
Exp
j
d
ji
whic h can b e rearranged in to
Exp
i
Exp
j
d
Qj
d
Qi
d
ji
If the dela ys are giv en for example in an in terv al
xy then using in terv al analysis d
Qj
d
Qi
d
ji
x y y x a b F rom equations and
w e get the t w o inequalities for the b est case
p erformance b ecome
Exp
j
aand
Exp
i
Exp
j
b These relations are used in sev eral examples in the
next section
VI I Example Case Studies
In this section w e presentsev eral case studies that
sho w ho w to apply the previous analysis results to
examples in reliable m ulticast and related proto col
design problems
A T op olo gy Synthesis
In this subsection w e apply the test syn thesis
metho d to the task where the timer v alues are kno wn
and the top ology ie D matrix is to b e syn thesized
according to the w orstcase beha vior W e explore
v arious timer settings W e use the virtual LAN in
Figure to lo ok at t w o examples of top ology syn
thesis one uses a timers with xed randomization
in terv als and the other uses timers that are function
of distance
Let Q b e the requester and and b e p oten tial
resp onders A t time t
Q sends the request
F or simplicityw e assume without loss of general
it y that the systems are ordered suc h that V
t i
V
t j
for i j eg system has the least d
Q Exp
then and then Th us the inequalities V
t i
F rom in terv al analysis x
y
x
y
x
x
y
y

x
y
x
y
x
y
y
x
z x y z y Q
V. LAN
1
2 3
Fig The virtual LAN with p oten tial resp onders
V
t j
d
ji
are readily satised for i j and weneed
only satisfy it for i j F rom equation for the w orstcase ab o v e w e
get
V
t V
t d
V
t V
t d
and
V
t V
t d
A Timers with xed randomization in terv als
Some m ulticast applications and proto cols suc h
as wb IGMP or PIM emplo y xed random
ization in terv als to set the suppression timers F or
instance for the shared white board wb the
resp onse timer is assigned a random v alue from the
uniformly distributed in terv al t!t where t msec for the source sr c and msec for other re
sp onders
Assume Q is a receiv er with alost pac k et Using
wb parameters w e get Exp
sr c
msec and
Exp
i
msec for all other no des
T o derivew orstcase top ologies from the inequali
ties w ema y use a standard mathematical to ol
Ho w ev er in the follo wing w e illustrate general tec h
niques that ma y b e used to obtain the solution
F rom the inequalities w eget d
Q Exp
V
t V
t d
d
Q Exp
d

This can b e rewritten as
d
Q d
Q d
Exp
Exp
dif f
where
dif f
if is src if is src Otherwise Q 1
2 3
d
Q,1
d
Q,2
d
Q,3
d
1,3
d
2,3
d
1,2
Fig The virtual LAN with dela y assignmen t and lab els
Similarlyw e deriv e the follo wing from inequalities
for V
t d
Q d
Q d
dif f
and
d
Q d
Q d
dif f
If w e assume system to b e the source and for a
conserv ativ e solution wec ho ose the minim um v alue
of dif fw e get
min dif f
min dif f
min dif f
W e then substitute these v alues in the ab o v e in
equalities and assign the v alues of some of the de
la ys to compute the others F or example if w e assign
d
Q d
Q d
Q msec w e get d
d
and d
Note that d
and d
can
eachtakean y p ositivev alue
Figure sho ws one p ossible top ology to whichthe
ab o v e assigned dela ys can b e applied These dela ys
exhibit w orstcase b eha vior for the timer suppr ession
me chanism A Timers as function of distance
In con trast to xed timers this section uses timers
that are function of an estimated distance
The expiration timer maybe set as a function of
the distance to the requester F or example system i
ma y set its timer to rep ond to a request from system
Q in the in terv al C
E
iQ
C
C
E
iQ

where E
iQ
is the estimated distancedela y from
i to Q whic h is calculated using message exc hange
eg SRM session messages and is equal to d
iQ

d
Qi
Note that this estimate assumes symmetry
whic h sometimes is not v alid
suggests v alues for C
and C
as or log
G where G is the n um b er of mem b ers in the group
WeT ak e C
C
to syn thesize the w orstcase
top ology W e get the expression
Exp
Exp
d
Q
d
Q d
Q
d
Q d
Q
d
Q d
Q
d
Q
If w e then assume for example that d
Q
d
Q d
Q
d
Q msec w e can rewrite the ab o v e
relation as
Exp
Exp
msec
Substituting in equation ab o v e w e get d
msec Under similar assumptions w e can obtain
d
msec and d
msec
T op ologies with the ab o v e dela y settings will exp e rience the w orst case o v erhead b eha vior as dened
ab o v e for the timer suppr ession mec hanism
B Timer c ongur ation
In this subsection wegiv e simple examples of the
timer conguration task solution where the dela y
b ounds ie D matrix are giv en and the timer v alues
are adjusted to ac hiev e the required b eha vior
In these examples the delayis giv en as an in terv al
xy msec W e sho w examples for w orstcase and
b estcase analysis
B W orstcase analysis
If the giv en ranges for the dela ys are msec
for all dela ys then the term d
Qj
d
Qi
d
ji
ev aluates
to F rom equation ab o v e w e get
Exp
i
Exp
j
to guaran tee that a resp onse
is triggered
If the dela ys are msec w eget Exp
i
Exp
j
ie is expiration timer m ust be less than j s b y
at least msecs
Note that w e ha v e an implied inequalit y that
Exp
i
for all i These timer expiration settings w ould exhibit
w orstcase b eha vior for the giv en delaybounds B Bestcase analysis
This case is a direct substitution in equations " see Section VIB F or dela y ranges of
msec for all dela ys w e get a and
b hence weget Exp
j
msec and if w e
tak e Exp
j
w eget Exp
i
msec
F or dela y ranges of msec for all dela ys w e
get a and b hence w e get Exp
j
msec and if w e tak e Exp
j
w eget Exp
i

msec
These timer settings w ould trigger the best case
beha vior for the giv en dela y ranges
Note that for the w orstcase analysis w ew ere only
able to get relativ e timer settings whereas for the
b estcase analysis w e could obtain absolute timer v al
ues
VIII Response Time Anal ysis
In this section w e conduct the p erformance anal
ysis with resp ect to the resp onse time whic h is the
time for the requester to receiv e the resp onse and re
co v er from the pac k et loss F or our analysis w e allo w
the loss of at most a single resp onse message during
the reco v ery phase Suc h loss ma y b e selectiv e ie
the resp onse ma y be receiv ed b y some systems but
not others T ransition rules are applied to only those
systems that receiv e the message
The algorithm obtains p ossible sequences leading
to the target ev en t and calculates the resp onse time
for eac h sequence T o syn thesize the w orst case sce
nario that maximizes the resp onse time for example
the sequence with maxim um time is c hosen
A T ar get event
The resp onse time is the time tak en b y the mec h
anism to reco v er from the pac k et loss ie un til the
requester receiv es the resp onse p and resets its re
quest timer b y transitioning out of the R
T
state In
other w ords the resp onse time is t p
r Q
t q
t Q

t p
r Q
t
The designer iden ties t p
r Q
as the target time
hence p
r Q
is the target ev en t
B The se ar ch
F or illustrativ e purp oses w e presentin detail the
case of single resp onder then discuss the m ultiple
resp onders case
Bac kw ard searc h Starting from p
r Q
the bac k
w ard searc h yields
p
r Q
R
Q
R
T Q
p
t j
D
j
D
T j
R es
j
R
T Q
q
r j
D
T j
D
j
R
T Q
A t whic h poin t the algorithm reac hes a branc hing
poin t where t w o p ossible preceding states could
cause q
r j
The rst is transition loss q
t Q
R
T Q
R
Q
D
j
and that ends the bac kw ard searc h for this branchas
the initial state R
Q
is reac hed
The second is transition r e q tmr Req
Q
q
t Q
R
T Q
D
j
Note that Req
Q
indicates the need for a transition to
R
T Q
and thesearc h for this last state yields ev en tu
ally q
t Q
R
T Q
R
Q
D
j
F orw ard searc h The algorithm p erforms a for
w ard searchand c hec ks for consistency of the GFSM
The GFSM ma y b e represen ted b y comp osition of individ
ual states eg S tate
S tate
or tr ansition
S tate

The forw ard searc h step ma y lead to con tradiction
with the original bac kw ard searc h causing rejection
of that branc h as a feasible sequence F or example
one p ossible forw ard sequence from the initial state
giv es
q
t Q
R
Q
R
T Q
D
j
q
r j
D
j
D
T j
R
T Q
Res
j
D
T j
D
j
p
t j
R
T Q
The algorithm then searc hes t w o p ossible next states
If p
t j
is not lost and hence causes p
r Q
then
the next state is D
j
R
Q
But the original bac kw ard
searc h started from q
t Q
R eq
Q
R
T Q
D
j
whic h cannot
be reac hed from D
j
R
Q
Hence w e get con tradiction
and the algorithm rejects this sequence
If the resp onse p is lost b y Qw eget D
j
R
T Q
that
leads to q
t Q
R eq
Q
R
T Q
D
j
The algorithm iden ties
this as a feasible sequence
Calculating the resp onse time for eac h sequence the
algorithm pic ks the latter sequence as one of max
resp onse time
F or m ultiple resp onders the algorithm auto
matically explores the dieren t p ossible selectiveloss
patterns of the resp onse message The only feasible
sequence obtained b y the searc h is when the requester
loses the resp onse and is a sequence in whic h only one
resp onder eg j triggers a resp onse and the rest
suppress Otherwise the forw ard searc h with single
resp onse loss reac hes con tradiction
T o satisfy this condition the algorithm creates
conditions and inequalities similar to those form u
lated for the b estcase analysis with resp ect to n um
b er of resp onses see Section VIB
IX Issues and Future W ork
In this pap er weha v e presen ted our rst endea v or
to automate the test syn thesis as applies to p erfor
mance ev aluation of m ultip oin t proto cols Our case
studies w ere b y no means exhaustiv e ho w ev er they
ga v e us insigh ts in to the researc h issues in v olv ed F u
ture w ork should explore p oten tial extensions and ap
plications of our metho d Automated generation of sim ulation test
suites
Sim ulation is a v aluable to ol for designing and ev al
uating net w ork proto cols Researc hers usually use
their insigh t and exp ertise to dev elop sim ulation in
puts and test suites Our metho d ma y be used to
assist in automating the pro cess of c ho osing sim ula
tion inputs and scenarios
The inputs to the sim ulation ma y include the top ol
ogy the host ev en ts suc h as trac mo dels and net
w ork dynamics suc h as link failures or pac k et loss
F or the class of m ultip oin t proto cols the inputs are
ev en more complex than inputs for traditional p oin t
top oin t proto cols since it includes mem b ership dis
tribution and dynamics
Our future w ork includes implemen ting a more com
plete to ol to automate our metho d including searc h
algorithms and mo deling seman tics and tie it to a
net w ork sim ulator to b e applied to a wider range of
m ultip oin t proto cols
The top ology syn thesis ma y b e used to assign top ol
ogy dela ys to routes b et w een group mem b ers In ad
dition it ma y b e used for a giv en la y out to deter
mine the spatial distribution of mem b ers where the
mem b ers are lo cated their sparseness or denseness
and temp oral distribution of mem b ers when they
joinlea v e or send pac k ets to the group Our metho d
ma y also b e used to assign loss patterns suc has se lectiv e loss to test certain proto col b eha viors
V alidating proto col building blo c ks
The design of new proto cols and applications of
ten b orro ws from existing proto cols or mec hanisms
Hence there is a go o d c hance of reusing estab
lished mec hanisms as appropriate in the design pro
cess Iden tifying v erifying and understanding build
ing blo c ks for suc h mec hanisms is necessary to in
crease their reusabilit y Our metho d ma y b e used as
a to ol to impro v e that understanding in a systematic
and automatic manner
Ultimatelyone ma yen vision that a library of these
building blo c ks will be a v ailable from whic h proto
cols or parts thereof will b e readily comp osable and
v eriable using CAD to ols similar to the w aycircuit
and c hip design is carried out to da y using VLSI de
sign to ols
A related researc h area then ma y b e to classify net
w orking problems eg timing problems in to cate
gories and iden tify mec hanistic building blo c ks that
deal with dieren t kinds of problems
Proto col comparison and b enc hmarking
Dieren t proto cols ma y b e group ed in the same class
based on their functionalit y The absence of a com
mon test suite for a giv en class of proto cols mak es it
hard to compare these proto cols in a neutral w a y Our metho d ma y b e extended to dev elop tests that
w ould functionally stress proto cols with resp ect to
giv en criteria th us enabling the establishmen t of
common test suites These tests w ould be used to
compare dieren t proto cols within the same class
Also they ma y b e used to test dieren tv ersions re
nemen ts or implemen tations of the same proto col
and hence facilitate in terop erabilit y testing
Design space exploration and sensitivit y
analysis
Proto col design usually en tails the conguration and
setting of v arious parameters Changing these pa
rameters ma y lead to c hange in b eha vior or p erfor
mance It is often prohibitiv ely complex to in v esti
gate suc h parameter design space man ually or ex
haustiv ely This problem ma y be alleviated b y the use of au
tomatic generation of test suites for giv en parame
ter sets F or example examining ho w the w orstcase
beha vior or scenarios c hange with parameter v alues
ma y help in making b etter design tradeos
This kind of sensitivit y analysis ma y also b e carried
out for en vironmen t parameters suc h as dela y band
width or mem b ership distribution Changing these
parameters mayc hange the b eha vior of the proto col
in some resp ect Our metho d ma y be used to tune
proto col parameters automaticallyfor w orst or b est
case b eha viors as w eha vesho wn for the case of the
timer conguration task
Unlik e our approac h in this pap er whic hin v estigated
only a single poin t in the design space sensitivit y
analysis in v estigates a broader sp ectrum of param
eter v alues Th us it ma y require more ecien t al
gorithms and w a ys of ltering and pro cessing of the
output results in a manner useful to the researc her
Generalization to p erformance b ound anal
ysis
An approac h similar to the one weha vetak en in this
pap er ma y be based on some p erformance b ounds
insteadofw orst or b est case analyses Wecall suc h
approac h conditionorien ted test generation or anal
ysis
F or example a target ev en t ma y be dened as the
resp onse time exceeding certain dela y b ounds either
absolute b ounds or as a function of some parameter
If suc h a scenario is not feasible that indicates that
the proto col giv es absolute guaran tees under the as
sumptions of the study This maybe usedto design
or analyze qualit yofservice or realtime proto cols
for example
Applicabilit y to other problem domains
So far our metho d has b een applied to case studies
on m ulticast routing correctness and m ultip oin t pro
to col p erformance ev aluation in the con text of the
In ternet
Other problem and application domains ma y in
tro duce new mec hanistic seman tics or assumptions
ab out the system or en vironmen t One example of
suc h domains includes sensor net w orks These net
w orks similar to adho c net w orks assume dynamic
top ologies lossy c hannels and deal with stringen t
po w er constrain ts whic h dieren tiates their proto
cols from In ternet proto cols P ossible researc h directions in this resp ect include
extending the top ology represen tation or mo del
to capture dynamics where dela ys v ary with time
dening new ev aluation criteria that apply to the
sp ecic problem domain suc haspo w er usage and
in v estigating the algorithms and searc h tec h
niques that b est t the new mo del or ev aluation cri
teria
X Conclusion
Weha v e presen ted a metho dology for test syn thesis
for p erformance ev aluation of m ultip oin t proto cols
In this pap er our metho d w as applied to ev aluate the
p erformance of the timer suppression mec hanism a
common building blo c k for v arious m ultip oin t proto
cols W e used a virtual LAN mo del to representthe
underlying net w ork top ology and an extended global
FSM to represen t the proto col mec hanism
W e adopted the faultorien ted test generation al
gorithm for searc h and extended it to capture timing
and dela y seman tics and to deal with p erformance
issues for endtoend m ultip oin t proto cols
Tw o p erformance criteria w ere used for ev aluation
of the w orst and b est case scenarios the n um ber of
resp onses p er request and the resp onse dela y Our
algorithm w as used in sev eral examples to illustrate
ho w to apply the metho d to sim ulation and test syn
thesis problems relating to real proto cols
W e do not claim to ha vea generalized algorithm
that applies to an y arbitrary proto col Ho w ev er w e
hop e that similar approac hes maybe used to iden tify
and analyze other proto col building blo c ks W e be lievethatsuc h systematic analysis to ols will b e essen
tial in designing and testing proto cols of the future
This topic b ears more researc h Ho w ev er our initial
ndings are promising and w e are optimistic ab out
building a more complete set of to ols that applies to
more proto cols and applications
References
Ahmed Helm y Deb orah Estrin and Sandeep Gupta
F aultorien ted test generation for m ulticast routing pro
to col design F ormal Description T e chniques F OR TE
XI Pr oto c ol Sp e cic ation T esting and V eric ation
PSTV XVIII IFIP TCWG Joint Interna
tional Confer enc e Paris F r anc e No v em b er
Hari Balakrishnan V enk at P admanabhan Sriniv asan Se
shan and Randy H Katz A comparison of mec h
anisms for impro ving tcp p erformance o v er wireless
links IEEEA CM T r ansactions on Networking Decem
ber D Estrin D F arinacci A Helm y V Jacobson and
L W ei Proto col Indep enden t Multicast Dense Mo de
PIMDM Proto col Sp ecication Pr op ose d Exp erimen
tal RF C URL httpnetwebusce dupimpimdmPIM
DM ftxtps ggz Septem b er
D Estrin D F arinacci A Helm y D Thaler S Deering
M Handley V Jacobson C Liu P Sharma and
L W ei Proto col Indep enden t Multicast Sparse Mo de
PIMSM Proto col Sp ecication RF C URL
httpnetwebusce dupimpimsmPIMSMvExp
RF C ftxtps ggz Marc h W F enner In ternet Group Managemen t Proto col V er
sion IDMR InternetDr aft pr op ose d standar dNo v em
ber S Flo yd V Jacobson C Liu S McCanne and L Zhang
A Reliable Multicast F ramew ork for Ligh tw eigh t Sessions
and Application Lev el F raming IEEEA CM T r ansac
tions on NetworkingNo v em ber R Go vindan H Y u and D Estrin Large
scale w eakly consisten t replication using m ulti
cast T ec hnical Rep ort USC sep
h ttpwwwisiedu haob o ylesrrmpsgz
K Miller K Rob ertson A Tw eedly and M White Star
Burst Multicast File T ransfer Proto col MFTP Sp eci
cation InternetDr aft H Sc h ulzrinne S Casner R F rederic k and V Jacobson
R TP A T ransp ort Proto col for RealTime Applications
RFC Jan uary
M Handley The Address Allo cation Proto col Internet
Dr aft August M Handley Session Directories and Scalable In ternet
Multicast Address Allo cation Pr o c e e dings of A CM SIG
COMM Septem b er
K Kumar P Radosla v o v D Thaler C Alaettinoglu
D Estrin and M Handley The MASCBGMP Arc hi
tecture for In terDomain Multicast Routing Pr o c A CM
Sigc omm Septem b er
L Zhang S Mic hel K Nguy en A Rosenstein S Flo yd
and V Jacobson Adaptiv eW eb Cac hing T o w ards a New
Global Cac hing Arc hitecture r d International WWW
Caching Workshop June Elan Amir Stev e McCanne and Randy Katz An ac
tiv e service framew ork and its application to realtime
m ultimedia transco ding A CM SIGCOMM Septem
b er A Helm y and D Estrin Sim ulationbased STRESS T est
ing Case Study A Multicast Routing Proto col July K Saleh I Ahmed K AlSaqabi and A Agarw al A
reco v ery approac h to the design of stabilizing comm uni
cation proto cols Journal of Computer Communic ation
V ol No pages April E Clark e and J Wing F ormal Metho ds State of the
Art and F uture Directions A CM Workshop on Str ate gic
Dir e ctions in Computing R ese ar ch V ol No pages
Decem b er R Bo y er and J Mo ore A Computational Logic Hand
book A c ademic Pr ess Boston J Spiv ey Understanding Z a Sp ecication Language and
its F ormal Seman tics Cambridge University Pr ess
F Lin PCh u and M Liu Proto col V erication us
ing Reac habilit y Analysis Computer Communic ation R e
view V ol No P Go defroid Using partial orders to impro v e automatic
v erication metho ds Pr o c nd Workshop on Computer
A idedV eric ation Springer V erlag New Y ork
F P ong and M Dub ois V erication T ec hniques for Cac he
Coherence Proto cols A CM Computing Surveys V olume
No pages Marc h M Abramo vici M Breuer and A F riedman Digital
Systems T esting and T estable Design A T T L abs Sandeep Ba ja j Lee Breslau Deb orah Estrin Kevin
F all Sally Flo yd P adma Haldar Mark Handley Ahmed
Helm y John Heidemann P olly Huang Satish Kumar
Stev en McCanne Reza Rejaie Puneet Sharma Scott
Shenk er Kannan V aradhan Haob o Y u Y a Xu and
Daniel Zappala Virtual In terNet w ork T estb ed Status
and researc h agenda T ec hnical Rep ort July R Go vindan C Alaettinoglu and D Estrin SCAN
LargeScale F ault Isolation work in pr o gr ess J A t w o o d O Catrina J F en ton and W Stra y er Reli
able Multicasting in the Xpress T ransp ort Proto col Pr o
c e e dings of the st L o c al Computer Networks Confer
enc e Octob er D Estrin D F arinacci A Helm y D Thaler S Deering
M Handley V Jacobson C Liu P Sharma and L W ei
Proto col Indep enden t Multicast Sparse Mo de PIM
SM Motiv ation and Arc hitecture Pr op osedExp erimen
tal RF C URL httpnetwebusce dupimpimsmPIM
A r ch ftxtps ggz Octob er Deb orah Estrin Ramesh Go vindan and John Heide
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nic al R ep ort University of Southern California Jan uary Appendix
I Conditions and Inequalities f or
O verhead Anal ysis
Giv en the target ev en t transitions are iden tied
as either w an ted or un w an ted transitions according
to the maximization or minimization ob jectiv e F or
maximization w an ted transitions are those that es
tablish conditions to trigger the target ev en t while
un w an ted transitions are those that n ullify these con
ditions and vice v ersa
Let C b e the condition for the w an ted transition
and t C is the time at whichit is established Let
W and U b e the ev en ts of the w an ted and un w an ted
transitions resp ectiv ely and their times b e t W and
t U Wew an t to establish and main tain C un til W oc curs ie in the duration t C tW Hence U ma y
only o ccur outside b efore or after that in terv al In
gure this means that U can only o ccur in region
or region time
(1) (2) (3)
U U
t(C) t(W)
Fig The timeline for transition ordering
Hence the inequalities m ust satisfy the follo wing
the condition for the w an ted transition C m ust
b e established b efore the ev entfor the w an ted tran
sition W triggers ie t C t W and
one of the follo wing t w o conditions m ust b e satis
ed
a the un w an ted transition U m ust o ccur b efore
C ie t U t C or
b the un w an ted transition U m ust occur after
the w an ted transition W ie t W t U These conditions m ust b e satised for all systems
In addition the algorithm needs to v erify using bac k
w ard searc h and implication rules that no con tra
diction exists b et w een the ab o v e conditions and the
nature of the ev en ts of the giv en problem
A Worstc ase Overhe ad A nalysis
The target ev en t for the o v erhead analysis is p
t
The ob jectivefor the w orst case analysis is to max
imize the n um b er of resp onses p
t
The w an ted tran
sition is transition r es tmr Res D
T
D p
t
see
Section V Hence t W t p
t
The condition for
the w an ted transition is D
T
and its time from tran
sition tx r e q q
r
D D
T
is t C t q
r
The un w an ted transition is one that n ullies the
condition D
T
T ransition r cv r es p
r
D
T
D is
iden tied b y the algorithm as the un w an ted transi
tion hence t U t p
r
F or a giv en system i the inequalities b ecome
t q
r i
t p
t i
and
either t p
r i
t q
r i
or t p
t i
t p
r i
But from bac kw ard implication rules w e get
Res
i
D
i
D
T i
p
t i
q
r i
D
T i
D
i
and t p
t i
t q
r i
Exp
i
Hence
t q
r i
t p
t i
is readily satised
Th us the inequalities form ulated b y the algorithm
to pro duce w orstcase b eha vior are
t p
r i
t q
r i
or
t p
t i
t p
r i
B Bestc ase A nalysis
Using a similar approac h to the ab o v e analysis the
algorithm iden ties transition r cv r es p
r
D
T
D as the w an ted transition Hence t W t p
r
and
t C t q
r
The un w ated transition is transition
r es tmrand t U t p
t
F or system i the inequalities b ecome
t q
r i
t p
r i
and
either t p
t i
t q
r i
or t p
r i
t p
t i
But from the bac kw ard implication w e ha v e
t q
r i
t p
t i
Hence the algorithm encoun ters con
tradiction and the inequalit y t p
t i
t q
r i
cannot
b e satised
Th us the inequalities form ulated b y the algorithm
to pro duce w orstcase b eha vior are
t q
r i
t p
r i
and
t p
r i
t p
t i

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Description

Ahmed Helmy, Deborah Estrin, Sandeep Gupta. "Test synthesis applied to performance evaluation of multipoint protocols." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 696 (1999).

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Creator Estrin, Deborah (author), Gupta, Sandeep (author), Helmy, Ahmed (author)

Core Title USC Computer Science Technical Reports, no. 696 (1999)

Alternative Title Test synthesis applied to performance evaluation of multipoint protocols (title)

Publisher Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA (publisher)

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Repository Name USC Viterbi School of Engineering Department of Computer Science

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