Close
About
FAQ
Home
Collections
Login
USC Login
Register
0
Selected
Invert selection
Deselect all
Deselect all
Click here to refresh results
Click here to refresh results
USC
/
Digital Library
/
Computer Science Technical Report Archive
/
USC Computer Science Technical Reports, no. 690 (1998)
(USC DC Other)
USC Computer Science Technical Reports, no. 690 (1998)
PDF
Download
Share
Open document
Flip pages
Contact Us
Contact Us
Copy asset link
Request this asset
Transcript (if available)
Content
STRESS T esting using Reduced Reac habilit y Analysis
A Case Study for a Multicast Routing Proto col
Ahmed AG Helm y Deb orah Estrin Sandeep Gupta
Computer ScienceComputer Engineering Departmen t
Univ ersit y of Southern California
Los Angeles CA
email fahelm y estrin guscedu sandeepb o oleuscedu
A bstr act Recen t gro wth of the In ternet and the in tro duc
tion of new net w ork services ha v e led to the increased
complexit y of net w ork proto cols and proto col in terac
tion In particular the adv entof IPm ulticast has con
tributed to this added complexit y Multicast enables
group comm unication in an ecien t manner Unlik e
traditional unicast proto cols a m ulticast group ma y
in v olvem ultiple senders and receiv ers and hence is in
heren tly more complex Multicast proto cols supp ort
applications ranging from teleconferencing to net w ork
games
In addition increased heterogeneit y of net w ork
comp onen ts and tec hnologies has in tro duced new fail
ure mo des that ha v e not b een considered traditionally
in the design of m ulticast proto cols suc h as unicast
routing anomalies and selectiveloss o v er LANs The
presence of these failures exacerbates the problem of
designing and testing robust m ulticast proto cols T o
date little eort has b een exerted to form ulate prac
tical metho ds and to ols that aid in the design and
testing of these proto cols
In this pap er w e presen t an algorithm for automatic
testing of m ulticast routing The algorithm pro cesses
a nite state mac hine FSM mo del of the proto col
and uses a forw ard searc h tec hnique to generate the
tests W e apply this algorithm to a simplied v ersion
of a m ulticast routing proto col PIMDM to in v esti
gate its beha vior in the presence of selectiv e pac k et
loss o v er LANs
I Intr oduction
A Brief Overview of Multic ast
Multicast proto cols are the class of proto cols that
supp ort group comm unication A m ulticast group
ma y in v olv e m ultiple receiv ers and one or more
senders In this pap er w e address m ulticast proto
cols for the In ternet based on the IP m ulticast mo del
These proto cols include m ulticast routing proto cols
eg D VMRP MOSPF PIMDM CBT and PIMSM m ulticast transp ort proto cols eg
SRM R TP and R TCP and m ultipart y appli
cations eg WB v at vic n te and
sdr This study fo cuses on m ulticast routing
proto cols whic h deliv er pac k ets ecien tly to group
mem bers b y establishing distribution trees Figure sho ws a v ery simple example of a source S sending
to a group of receiv ers R
i
S
R1
R2
R3
R4 R5
S: sender to the group
Ri: receiver i of the group
Fig Establishing m ulticast deliv ery tree
Multicast distribution trees ma y b e established b y
either broadcastandprune or explicit join proto cols
In the former suc has D VMRP or PIMDM a m ulti
cast pac k et is broadcast to all leaf subnet w orks Sub
net w orks with no lo cal mem b ers for the group send
prune messages to w ards the sources of the pac k ets
to stop further broadcasts Link state proto cols suc h
as MOSPF broadcast mem b ership information to all
no des In con trast in explicit join proto cols suc h
as CBT or PIMSM routers send hopb yhop join
messages for the groups and sources for whic h they
ha v e lo cal mem bers When receiv ed these messages
build routing state in routers and cause further mes
sages to b e sen t upstream un til the distribution tree
is established Up on receiving a m ulticast pac k et a
router forw ards the pac k et according to the routing
state
W e are particularly in terested in m ulticast routing
proto cols because they are vulnerable to failure
mo des suc h as selectiv e loss that ha v e not b een tra
ditionally studied in the area of proto col design
F or most m ulticast proto cols when routers are
connected via a m ultiaccess net w ork or LAN
hop b yhop messages are m ulticast on the LAN and ma y
exp erience selectiv e loss ie ma y b e receiv ed bysome
no des but not others The lik eliho o d of selectiveloss
is increased b y the fact that LANs often con tain h ubs
bridges switc hes and other net w ork devices Selec
tivelossma y aect proto col robustness
Similarly endtoend m ulticast proto cols and ap
plications m ust deal with situations of selectiv e loss
This dieren tiates these applications most clearly
from their unicast coun terparts and raises in terest
ing robustness questions
Our case study illustrates wh y selectiv e loss should
be considered when ev aluating proto col robustness
This lesson is lik ely to extend to the design of higher
la y er proto cols that op erate on top of m ulticast and
can ha v e similar selectiv e loss
II Rela ted W ork
The related w ork falls mainly in the eld of proto
col v erication Most of the literature on m ulticast
proto col design addresses arc hitecture sp ecication
and comparisons b et w een dieren t proto cols
There is a large b o dy of literature dealing with v er
ication of comm unication proto cols Proto col v er
ication t ypically addresses w elldened prop erties
suc h as safety liveness and r esp onsiveness prop er
ties Safet y prop erties include freedom from
deadlo c ks assertion violations improp er termina
tions and unsp ecied receptions Liv eness prop erties
include detection of acceptance cycles and absence of
nonprogress cycles while resp onsiv eness prop erties
W e use the term LAN to designate a connected net w ork
with resp ect to IPm ulticast This includes shared media suc h
as Ethernet or FDDI h ubs switc hes etc
include timeliness and fault tolerance Most proto col
v erication systems aim to detect violations of part
of these proto col prop erties
In general the t w o main approac hes for proto
col v erication are theorem pro ving and reac habil
it y analysis or mo del c hec king Theo
rem pro ving systems dene a set of axioms and con
struct relations on these axioms Desirable prop
erties of the proto col are then pro v en mathemat
ically Theorem pro ving includes mo delb ase d for
malisms suc h as Z and Vienna Dev elopmen t
Metho d VDM and lo gicb ase d formalisms in
cluding rst order logic suc h as Nqthm and
higher order logic suc h as Protot yp e V erication
System PVS An attempt to apply formal v er
ication to TCP and TTCP has b een giv en in
In general ho w ev er the n um ber of axioms and re
lations in theorem pro ving systems gro ws with the
complexit y of the proto col W e b eliev e that these
systems will b e ev en more complex and p erhaps in
tractable for m ulticast proto cols Moreo v er these
systems w ork with abstract sp ecication of the pro
to col and hence tend to abstract out some proto col
mec hanisms that ma y cause problems w e are address
ing in this study Reac habilit y analysis algorithms on the
other hand try to generate and insp ect all the pro
to col states that are reac hable from giv en initial
states Suc h algorithms suer from the state space
explosion problem esp ecially for complex proto cols
T o circum v en t this problem state reduction and
con trolled partial searc h tec hniques could
be used These tec hniques fo cus only on parts of
the state space and mayuse probabilistic ran
dom or guided searc hes W e note that some
of the reduction tec hniques use equiv alence relations
to prune a w a y that part of the searchpro v en to b e ir
relev an t or redundan t 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 In our ap
proac h w e adopt the global FSM mo del and attempt
to establish equiv alence relations for the m ulticast
routing proto col under study In w e presen ted a sim ulationbased STRESS
framew ork that utilizes heuristics and top ological
equiv alence to establish the test scenarios Ho w ev er
w e did not address automatic generation of host sce
narios Our w ork in this pap er complemen ts and can
be in tegrated with our previous w ork on STRESS
In w e ha veproposed a faultorien ted algorithm
for the automatic generation of test scenarios Ho w
ev er the algorithm ma y in v estigate nonreac hable
states and hence the complexityof the searchma y
increase On the other hand the faultorien ted ap
proac h generates the top ology as part of the output
test while the algorithm presen ted in this pap er tak es
the top ology as input
III Framew ork O ver view
In general the robustness of a proto col is its abil
it y to resp ond correctly in the face of net w ork fail
ures and pac k et loss This w ork presen ts an algo
rithm for studying and ev aluating robustness of m ul
ticast routing proto cols with p oten tial extension to
m ulticast proto cols in general This section presen ts
an o v erview of the test generation approac hes The
mo del used to represen t the proto col and the system
is presen ted along with denitions of the terms used
A T est Gener ation
The core con tribution of our w ork lies in the de
v elopmen t of systematic test generation algorithms
for proto col robustness In general there are t w o
approac hes for test generation TG random TG
R TG and deterministic TG R TG in v olv es only the
generation of random test patterns see section III B for the denition of test patterns and hence is
simple Ho w ev er a large set of test patterns is needed
to ac hiev e a high measure of error co v erage and ev en
then determining the test qualityma y b e exp ensiv e
Also the cost of running long test sequences ma ybe
high R TG generally do es not takein to accountthe
function or the structure of the proto col under test
and do es not attempt to minimize the test length
Deterministic TG on the other hand pro duces
tests based on a mo del of the proto col Hence it ma y
be more exp ensiv e than R TG Ho w ev er the kno wl
edge built in to the proto col mo del enables the pro
duction of shorter and higherqualit y test sequences
Deterministic TG can be man ual or automatic In
this study w e fo cus on automatic TG A TG
Deterministic TG can b e a faultindep enden t or
b faultorien ted F aultorien ted tests are generated
for sp ecied faults F aultorien ted test generation
starts from the fault eg a lost message and syn
thesizes the necessary conditions to driv e the proto col
in to error This algorithm uses a mix of forw ard and
bac kw ard searc hes
In con trast faultindep enden t TG w orks without
targeting individual faults as dened b y the fault
mo del Suc h an approac h ma y emplo y a forw ard
searchtec hnique to insp ect the proto col state space
or an equiv alen t subset thereof after in tegrating
the fault in to the proto col mo del In this sense it
ma y be considered a v arian t of reac habilit y analy
sis with sym b olic represen tation and state and fault
equiv alence used to reduce the state space
Throughout this do cumen t w e adopt the fault
indp enden t approac h extend it to t our problem
domain and apply it to a v arian t of PIMDM as an
illustrativ e case study In the remainder of this section w e describ e our
system mo del and denition
B System Mo del and Denition
B The system mo del
The system mo del consists of the net w ork ele
men ts top ology elemen ts and the fault mo del
Ba Elemen ts of the net w ork The net w ork con
sists of links and no des routers and hosts A link
ma y be poin ttop oin t or m ultiaccess eg LAN
In this do cumentw e assume bidirectional links with
symmetric dela ys while future w ork will address uni
directional and asymmetric links A no de runs a set
of net w ork proto cols suc h as unicast and m ulticast
routing W e assume the existence of a MA C la y er
proto col to resolv e media access and collision issues
but w e do not mo del suc h proto col A host runs end
toend proto cols or applications
Bb Elemen ts of the top ology In this do cu
mentw e consider only lo cal top ology Nrouter LAN
mo deled at the net w ork lev el ie connecting h ubs
switc hes bridges and other datalinkla y er devices
are abstracted out The b oundary of our top ology
is the m ulticast routing domain whic h con tains only
a single m ulticast routing proto col Ho w ev er the
top ology ma y span m ultiple unicast routing domains
or Autonomous Systems ASs Cascade of LANs or
uniform top ologies are men tioned in the future w ork
section
Bc The fault mo del W e distinguish b et w een the
terms err or and fault An error is a failure of the
proto col as dened in the proto col design require
men t and sp ecication F or example duplication in
pac k et deliv ery is an error for m ulticast routing A
fault is a lo w lev el eg ph ysical la y er anomalous
beha vior that ma y aect the b eha vior of the proto
col under test and include for example pac k et loss
or unicast route apping among others Note that a
fault ma y not necessarily b e an error for the lo w lev el
proto col
The fault mo del ma y include
Loss of pac k ets mo del pac k et loss on a link due
to an y queue congestion o v ero w link failures or
pac k et corruption in the in terconnect devices suc has
net w ork in terfaces switc hes h ubs etc W e assume
that the pac k ets are either deliv ered correctlyorare
dropp ed ie pac k et corruption is disco v ered using
c hec ksum or other error detection co des
Loss of state suc hm ulticast andor unicast routing
tables due to failure of the routing proto col crashes
or insucien t memory resources
The dela y mo del Dela ys in the net w ork ma y be
due to transmission propagation or queuing dela ys
W e assume that the pro cessing dela ys are negligible
with resp ect to the time gran ularit y the analysis is
addressing Sometimes dela y fault problems maybe
translated in to ev en t sequencing problems as w ewill
showb y example later in this do cumen t
Unicast routing anomalies suc h as route inconsis
tencies oscillations or apping
Usually a fault mo del is dened in conjunction
with the robustness criteria for the proto col under
study in our case PIM A fault mo del ma y include
a single fault or m ultiple faults In our study w e
adopt a singlefault mo del where only a single fault
ma y o ccur during a scenario or a test sequence A
design requiremen t for PIM is b eing robust to single
proto col message loss
F uture w ork will consider other fault mo dels suc h
as loss of state or unicast route apping
B T est Sequence Denition
Giv en t w o sequences T e
e
e
n
where
e
i
is an ev en t and T
e
e
e
k
fe
j
a
n
where f is a fault
Let P q T bethe sequence of
states and stim uli of proto col P under test T start
ing from the initial state q According to one of the
follo wing denitions T
ma y b e said to b e a test se
quence if
P q T P q T
This means that the b eha vior
of the system in the presence of the fault is dieren t
than that without the fault Note that this denition
ma y include sequences that including and excluding
F or PIM b eing robust to a single message loss implies that
transitions causing the proto col to mo v e from one stable state
to another b e correct ev en in the presence of single message
loss F or the sak e of analyzing erroneous b eha vior ho w ev er w e
consider single message loss p er test sequence T est sequences
and stable states are describ ed in later sections
The fault ma y b e empt y in whichcase T T
the fault pro duce same correct nal states but with
dieren t transien t b eha vior or
Final P q T P q T
ie the stable state af
ter the o ccurrence of the fault is dieren t for the
t w o outputs This denition ignores transien tbeha v
ior but ma y include sequences that including and
excluding the fault pro duce dieren t correct nal
states or
Final P q T
is incorrect
ie the stable
state reac hed after the o ccurrence of the fault do es
not satisfy the correctness conditions irresp ectiv e
of P q T In case of a faultfree sequence where
T T
the error is attributed to a proto col design
error Whereas when T T
and nal P q T is
correct the error is manifested b y the fault
Since w e are only concerned with the stable ie
nontransien t beha vior of a proto col w e will only
use the second and third denition for our study B T est Input P attern
A test input pattern is dened b y a list of host
ev en ts Ev a top ology T and a fault mo del F
W e dene a test input pattern as a tuple Ev T F Ev en ts Ev ev
ev
ev
n
is a list of host
ev en ts host scenarios or call patterns Eachev en t
ev
j
consists of action time where action is the
host or no de ev entinput for example join lea v e
send pac k et etc
T op ology T N L is the routed top ology of
set of no des N and links L N n
n
n
k
is
the list of no des eachrunningaset of proto cols A
proto col ma y b e mo deled b y
timer s messag es stateV ar s mechanisms L l
l
l
m
are the links connecting the
no des t woin case of a p oin ttop oin t link or more
for LANs A link has a dela y and a bandwidth
F aults F is the fault mo del used to inject the fault
in to the test According to our singlemessage loss
mo del for example a fault ma y denote the loss of
the second message tra v ersing link l
i
of t yp e pr une Kno wing the lo cation and the triggering action of the
fault is imp ortan t in analyzing the proto col b eha vior
As a case studyw e apply our automatic test gen
eration algorithms to a v ersion of the Proto col Inde
p enden t MulticastDense Mo de or PIMDM
PIMDM uses broadcastandprune to establish
the m ulticast distribution trees In this mo de of op er
ation a m ulticast pac k et is broadcast to all leaf sub
net w orks Subnet w orks with no lo cal mem b ers send
Correctness is dened b y the proto col sp ecication
prune messages to w ards the sources of the pac k ets
to stop further broadcasts
Routers with new mem b ers joining the group trig
ger Gr aft messages to w ards previously pruned sources
to reestablish the branc hes of the deliv ery tree Gr aft
messages are ac kno wledged explicitly at eac h hop us
ing the Gr aftA ck message
PIMDM uses the underlying unicast routing ta
bles to get the nexthop information needed for the
RPF rev ersepathforw arding c hec ks This ma y
lead to situations where there are m ultiple forw arders
for a LAN The Assert mec hanism prev en ts these sit
uations and ensures there is at most one forw arder
for a LAN
Ba PIM Proto col Errors In this study w e tar
get proto col design and sp ecication errors W e
are in terested mainly in erroneous stable ie non
transien t states W e assume that these errors are
pro vided b y the proto col designer or the proto col
sp ecication
A proto col error ma y manifest itself in one of the
follo wing w a ys
black holes consecutivepac k et loss b et w een p eri
ods of pac k et deliv ery p acket lo oping the same pac k et tra v erses the same
set of links m ultiple times
p acket duplic ation m ultiple copies of the same
pac k et are receiv ed b y the same receiv ers
join latency time tak en b y a receiv er joining
the group to start receiving pac k ets destined to the
group
le ave latency time tak en after a receiv er lea v es
the group to stop the pac k ets from o wing do wn the
branc hes that no longer lead to receiv ers
Some of these manifestations concern the correct
deliv ery of pac k ets while others eg lea v e latency
concern eciency and conserv ation of net w ork re
sources
Bb Correctness Conditions W e assume that cor
rectness conditions are pro vided b y the proto col de
signer or the proto col sp ecication These conditions
are necessary to a v oid the ab o v e proto col errors in a
LAN en vironmen t and include
If one or more of the routers is exp ecting to re
ceiv e pac k ets from the link ie ha ving the link as
their nexthop then one other router m ust b e a for
w arder for the link Violation of this condition ma y
lead to data pac k et loss eg join latency or blac k
holes
The link m ust ha v e at most one forw arder at a
time Violation of this condition ma y lead to data
pac k et duplication
The deliv ery tree m ust b e lo opfree
a An y router should accept pac k ets for SG from
one incoming in terface only This condition is en
forced b y the RPF Rev erse P ath F orw arding c hec k
b The underlying unicast top ology should be
lo opfree
Violation of this condition ma y lead to data pac k et
lo oping
If one of the routers is a forw arder for the link
then there m ust be at least one router exp ecting
pac k ets from the link ie ha ving the link as their
nexthop Violation of this condition ma y lead to
lea velatency These are the correctness conditions for stable
states ie not during transien ts and are dened
in terms of proto col states as opp osed to end p oin t
beha vior They are used in the faultindep enden t
and faultorien ted test generation where the proto
col mo del do es not capture end p oin t traces Wealso
use these conditions for top ological equiv alence in the
heuristic test generation
B The Proto col Mo del
As men tioned earlier the deterministic test gener
ation whether faultindep enden t or faultorien ted
requires the denition of a proto col mo del F ormally w e presen t the proto col b y a nite state mac hine
FSM and the LAN b y a global FSM mo del as
follo ws
Ba FSM mo del A deterministic nite state ma
c hine mo deling the b eha vior of a router R
i
is repre
sen ted b y the mac hine M
i
Q i
i
where
Q is a nite set of state sym bols
i
is the set of op erations causing state transitions
and
i
is the state transition function Q i
Q Bb Global FSM mo del With resp ect to a partic
ular LAN the global state is dened as the comp o
sition of individual router states wrt to that LAN
The beha vior of a LAN with n routers ma y be de
scrib ed b y the global FSM M
G
Q
G
G
G
where
Q
G
Q
Q
Q
n
is the global state space
G
n
S
i
i
is the set of op erations causing the tran
sitions and
Some esoteric scenarios of route apping ma y lead to m ul
ticast lo ops in spite of RPF c hec ks Curren tly our study do es
not address this issue as it do es not p ertain to a lo calized
b eha vior
G
is the global state transition function Q
G
G
Q
G
IV F a ul tindependent Test Genera tion
In this section w ein v estigate a faultindep enden t
approac h for automatic test generation W e use a
v arian t of reac habilit y analysis to insp ect a reduced
subset of the state space of the system for errors
Wedev elop equiv alence relations and sym b olic repre
sen tation tec hniques to reduce the complexityofthe
used algorithm from exp onen tial to linear in the n um
ber of routers on the LAN T o examine the robust
ness of the proto col against single message loss w e
incorp orate selectiv e loss scenarios in the insp ected
space
T o illustrate the pro cedures of this metho d weap ply it to a v ersion of PIMDM
A F ormalism
A formalism is used to represen t the proto col as
a nite state mac hine FSM A m ultiaccess LAN
is used as the target system and is represen ted bya
global FSM
W e use the FSM mo del explained earlier in sec
tion I I IB to mo del the proto col
A FSM mo del
M
i
Q i
i
Aa System States Q W e dene the states wrt
a sp ecic LAN to whic h the router R
i
is attac hed A
router is represen ted b y its state as a forw arder or a
receiv er of pac k ets to or from the LAN
The p ossible states are describ ed in the follo wing
table
Sym bol Meaning
F
i
Router i forw arder for the LAN
NH
i
Router i has the LAN as its nexthop
NC
i
Router i has a negativ ecac he en try
E
i
Router i do es not ha veanen try ie is empt y
W e also dieren tiate whether a router is upstr e am
or downstr e am F or example
Q fE F g if the router is upstream fE N H N C g if the router is do wnstream F
i
and NH
i
are equiv alen t to Router i ha ving the LAN in
its outgoing in terface list or as an incoming in terface resp ec
tiv ely Ab Stim uli and Ev en ts i
fG J P k P r L Pr G J g where the ev en t with paren thesis indicates the
transmission of a message and the ev en t without
indicates reception G Gr af t J J oin P k P ack et P r Prune L Leav e Figure giv es a nite state mac hine for one no de
implemen ting a simplied v ersion of PIMDM
When an upstream router receiv es data pac k ets from
{}
{}
{F}
Pk/G/J Pr
G/J
Pk: received a packet
G: received Graft
J: received Join
Pr: received Prune
/: or
{NH} {NC}
Pk.M/G/J (G) Pk.NM/Pr (Pr)
L/Pr (Pr)
J/G (G)
. : and
M: downstream member exists
NM: no downstream member exists
(Pr): sending a Prune upstream
(G): sending a Graft upstream
Upstream Node
Downstream Node
Fig Finite state mac hine for no de
the nexthop neigh b or a Graft or Join from do wn
stream it creates a forw arding state fF g If the
upstream router receiv ers a Prune from do wnstream
it remo v es the forw arding en try F or a do wnstream
router data pac k ets trigger the creation of the state
as follo ws a if there exists do wnstream mem b ers
a receiving state ie fNH g is created and a Graft
is triggered upstream else b a negativ e cac he state
fNC g is created and a Prune is triggered upstream
Receiving a Graft or Join creates a receiving state
and triggering a Graft upstream while receiving a
Prune or Lea v e creates a negativ e cac he state and
triggers a Prune upstream Asserts are not sho wn
for simplicit y A Global FSM mo del
An example global state for a top ology of routers
connected to a LAN with router as a forw arder
router exp ecting pac k ets from the LAN router and ha v e negativ e cac hes and router is empt y
is giv en b y fF
N H
N C
N C
E
g Con v enien tly wema y omit the emptystate E
Weha vet w o p ossible state sym b ols for upstream
routers and three for do wnstream routers hence the
total n um ber of p ossible global states for nrouter
LAN is jQ
G
j
jupstr eamj
jdow nstr eamj
where
jupstr eamj jdow nstr eamj n B F aultindep endent T est Gener ation A lgorithm
Our approac h emplo ys a v arian t of reac habilit y
analysis to in v estigate the global FSM mo del dev el
op ed for the system in section I I IB W e start from
a subset of the correct states and in v estigate the
system transitions according to v arious op erators in
addition to selectiv e loss The output if an y is a
set of ev en t sequences that driv e the system in to er
roneous states The approac h includes the follo wing
steps
Establish the correct states for the giv en top ol
ogy according to the correctness conditions Weuse
equiv alence tec hniques to reduce the n um b er of cor
rect states to b e insp ected
Start from a correct state and searc h for a se
quence of transitions p ossibly including a selectiv e
loss scenario that lead to an erroneous state ie
those nontransien t states in whic h correctness con
ditions are violated The transitions obtained are
those dened for the FSM and not necessarily host
ev en ts suc h as JoinorLea v e The n um ber of loss
scenarios in v estigated is reduced based on equiv a
lence relations
If a sequence is obtained in this step go to the next
step Otherwise restart from the rst step ie an
other correct state
Establish external host ev en ts leading to the tran
sitions obtained b y the previous step Call this se
quence of ev en ts S
er r
The sequence of host ev en ts
in this case ma y not b e unique A prune for exam
ple ma y b e triggered due to v arious ev en ts a joined
host lea ving or receiving pac k ets with no do wnstream
mem b ers
Establish external host ev en ts leading to the cor
rect state Again suc h sequence of ev en ts ma y not
b e unique Call this sequence S
cor r
The input test pattern of ev en ts is the concatena
tion of S
cor r
and S
er r
ie S
cor r
S
er r
C Obtaining Corr e ct States
Theoretically all states that satisfy the correct
ness conditions ma y be considered correct states
Ho w ev er not all of these states are normally reac h
able F or example all do wnstream mem b ers build
state whenev er they get a data pac k et whether it
is a receiving state NH or negativ e cac he NC
hence for a top ology of one upstream router
and t w o do wnstream routers and the global
state fF
N H
E
g although theoretically correct
is practically unreac hable
W e fo cus on the practi
cally reac hable correct states in this section and de
v elop the follo wing algorithm to obtain those states
Reac hableCorrectStatesupstrmdnstrm f
add Empt ySet to setOfStates
j dnstrm
add NC
j
to State
add State to setOfStates
i upstrm f
for mask to jdnstr mj
f
add F
i
to State
p osition j dnstrm f
if p osition mask add NH
j
to State
else
add NC
j
to State
p osition p osition
g
add State to setOfStates
g
g
g
The set of correct states or C S is a subset of
the state space ie C S Q
G
The n um ber of
reac hable correct states generated b y the algorithm
is jC S j jupstr eamj
jdow nstr eamj
Reac habilit y Analysis and Reduction T ec h
niques
Exhaustiv e searc h A ttempts to generate and
analyze all system states that are reac hable from an
initial system state
In a system of n routers jQj m states for a
router the n um b er of reac hable states in the system
is b ounded b y m n
T o in v estigate all the transi
tions with j G
j l p ossible transitions w e obtain
l m n
state visits to complete the pro cess
under sp ecic crash scenarios this state ma ybe reac hed
But with the singlefault mo del w eha v e adopted this state
cannot b e reac hed as w e assume without loss of generalit y that the fault will o ccur after the correct states one of whic h
b eing the initial state is reac hed
Sym b olic represen tation
An alternativ e represen tation of the system maybe
obtained through sym b olic represen tation where r
routers in state q are represen ted b y q
r
The global
state for a system of n routers is represen ted b y S q
r q
r q
r m
m
where m jQj r
i
n and r
i
is or more and is or more
F or our case study q
i
f F N H N C E g T o satisfy correctness conditions and giv en
in section I I IBb the correct stable global states
are those con taining no forw arders and no routers
exp ecting pac k ets or those con taining one forw arder
and one or more routers exp ecting pac k ets from the
link sym b olically this is giv en b y
S F
N H
N C
E
and
S F
N H
N C
E
Coun ting equiv alence Tw o system states
q
q
q
n
and p
p
p
n
are strictly equiv
alen t i q
i
p
i
q
i
p
i
Q i n Ho w ev er
the b eha vior of all routers is giv en b y a common
deterministic FSM hence all n! perm utations of a
q
q
q
n
are equiv alen t b ecause the order of the
tuple is not imp ortan t
A state for a system with n routers ma y be repre
sen ted as
Q
jQj
i
q
k i
i
where k
i
is the n um b er of routers
in state q
i
Q and jQj
i
k
i
n Counting Equivalenc e Two system states
Q
jQj
i q
k i
i
and
Q
jQj
i
q
l i
i
aree quivalent if k
i
l
i
i In other w ords t w o system states are equiv alentif the
n um b er of routers in a sp ecic state in one system is
equal to the n um b er of routers in the same state in
the other system for all router states
In our analysis w e do not attempt to in v estigate
the whole state space rather w e start from the cor
rect states under relaxed practical assumptions and
analyze the successor stable states Ho w ev er ev en
with this approac h ie the reac hable correct states
algorithm the n um b er of correct states gro ws exp o
nen tially with the n um ber of do wnstream routers In
addition w e need to in v estigate v arious loss scenar
ios and that is also exp onen tial in the n um ber of
routers
W e use the coun ting equiv alence to reduce the
n um ber of correct states explored and the n um ber
of in v estigated loss scenarios
Exploring correct states F rom the coun ting
equiv alence relationship and the symmetry giv en
in the LAN top ology w e can reduce the com
plexit y of the algorithm F or example the state
fF
N H
N C
g is equiv alen t to fF
N C
N H
g since b oth of these states corresp onds to the sym b olic
represen tation F
NH
NC
Using this equiv a
lence relation w e mo dify the correct states algorithm
as follo ws
ExploredCorrectStatesupstrmdnstrm f
add Empt ySet to setOfStates
j dnstrm
add NC
j
to State
add State to setOfStates
i upstrm f
for mask to jdnstr mj f
add F
i
to State
p osition j dnstrm f
if p osition mask
add NH
j
to State
else
add NC
j
to State
p osition p osition
g
add State to setOfStates
g
g
g
An example output of the ab o v e algorithm for an
upstream router R
and three do wnstream routers
R
R
and R
w ould b e
ffg fNC
N C
N C
g fF
N H
N C
N C
g fF
N H
N H
N C
g fF
N H
N H
N H
gg W e note that the new algorithm has a complexit y
of O jupstr eamN odesjj dow nstr eamN odesjas op p osed to O jupstr eamN odesj jdow nstr eamN odesj
for
the previous algorithm W e can further reduce this
complexityb y considering all upstream routers equiv
alen t hence w e can remo v e the i upstreamNo des
lo op whic h giv es O jdow nstr eamN odesj complex
it y Exploring selectiv e loss scenarios In gen
eral similar equiv alence relation ma y be applied
to the selectiv e loss patterns explored F or ex
ample a prune sen t b y a do wnstream router R
i
ma y be lost b y either do wnstream routers R
j
and
R
k
If b oth these routers ha v e the same state
eg NH
j
Gl obS tate and NH
k
Gl obS tate
then the scenarios fR
j
l ostP r une R
k
R xv dP r uneg
and fR
k
l ostP r une R
j
Rxv dP r uneg are equiv alen t
F or con v enience w e omit the E state
By lo oking closely at the prune mec hanism w e nd that an
in teresting scenario or distinguishing sc enario is one where
R
dst
Rxv dP r une Q
i
R
i
l ostP r une i st NH
i
Gl obS tate
D Obtaining Stable States
T o establish the erroneous stable states w e need
to dene the transition mec hanisms bet w een suc h
states Wein tro duce the concept of transition classi
cation and completion to distinguish b et w een tran
sien t and stable states Then w e presen t the proto col
mec hanisms and the stable state c hec king algorithm
D Classication of T ransitions
W e iden tify t w o t yp es of transitions external ly
trigger e d ET and internal ly trigger e d IT transi
tions The rst t yp e is stim ulated b y actions exter
nal to the system suc h as hostjoin or hostlea v e
whereas the second t yp e is stim ulated b y actions in
ternal to the system suc h as prune and assert
W e note that some transitions ma y be triggered
due to both in ternal and external actions dep end
ing on the scenario F or example a prune ma y be
triggered due to forw arding pac k ets b y an upstream
router whic h is an in ternal action or a hostlea v e
whic h is an external ev en t
The global state is c hec k ed for correctness only at
the end of an ET transition and after completing all
dep endentITs F ollo wing is a table of host ev en ts their dep enden t
ETs and their dep endentITs Host Ev en ts Send HostJoin Lea v e
ETs F orw ard Graft Prune
ITs Assert Prune GraftAc k Join
Join
D FSM Reduction
Consider the transition diagram and top ology in
gure When the upstream router receiv es data
pac k ets it b ecomes the forw arder fF
g Dep ending
on do wnstream mem b ership status router either
a creates a receiving state NH
mo ving the global
state to fF
N H
g or b creates a negativ e cac he
state NC
ie global state fF
N C
g then sends
a Prune upstream resulting in router remo ving
its forw arding state and mo ving the global state to
fNC
g Ifado wnstream mem b er joins router creates
a receiving state fNH
g and send a Graft upstream
Similarly for the join mec hanism w e nd that the only dis
tinguishing scenario is where R
dst
l ostJ oin where R
dst
the
destination of the join regardless of loss or receipt of the join
b y others routers
{}
{F1,NC2}
{F1,NH2}
{NH2}
{NC2}
{F1}
1
2
upstream
downstream
Pk1
M2 NM2
L2
(Pr2)
J2/G2
(G2)
Pk1: Node 1 received a packet
M2: member exists downstream of Node 2
NM2: no member exists downstream of Node 2
L2: Node 2 received a leave message
J2: Node 2 received a join message
G2: Node 2 received a Graft message
(Pr2): Node 2 sends a prune upstream
(G2): Node 2 sends a Graft upstream
Fig Reac habilit y graph for a no de PIMDM
causing router to create a forw arding state and
the global state b ecomes fF
N H
g W e note that Grafts are sen t reliably hence the
state fNH
g is a transien t state and the transition
from state fNC
g to fF
N H
g is considered reli
able
Similarly datatriggered actions suc h as prunes
on p oin ttop oin t links and creation of do wnstream
state whether receiving or negativ e cac he ma y be
considered reliable Subsequen tly the states fF
g
and fF
N C
g are also considered transien t states
As w as alluded to earlier transien t states are not
c hec k ed for correctness and hence ma yb e remo v ed
from the diagram The resulting transition diagram
is sho wn in gure D T ransition Completion
F rom the previous section w e sho w ed that tran
sien t states can b e remo v ed from the insp ected state
space based up on the reliabilit ybywhic h the transi
tion out of these states is accomplished It seems as
though the error can be detected b y insp ecting the
nontransien t state space Toin v estigate the ecacy
of suc h approac h w e analyze a top ology with some
unreliable transitions suc h as that giv en in gure The reader is encouraged to view the gure in de
tails Ho w ev er w e only concen trate on the transi
tions aected b yloss One suc h transition is sho wn
in gure It is apparen t from the gure that the global state
{}
1
23
{F1}
{F1,NC2,NC3}
{F1,NH2,NC3} {F1,NC2,NH3}
{F1,NH2,NH3}
{NC2,NC3}
{NH2,NC3}
LPr
LJ
{NC2,NH3}
LJ
Pk1
NM2.NM3
M2.M3
(i)
(ii)
(iii) (iv)
(v)
(vi)
(vii) (viii)
(ix)
(G2)
(G3)
(G3)
(G2)
L2
L3
L3
L2
(Pr2)
J3 J2
(Pr3)
(Pr2)/(Pr3)
M2.NM3
NM2.M3
Fig Reac habilit y graph for a no de PIMDM LAN
1
2
upstream
downstream
{}
{NC2}
{F1,NH2}
Pk1.M2 Pk1.NM2 (Pr2)
L2 (Pr2)
J2/G2 (G2)
Pk1: Node 1 received a packet
M2: member exists downstream of Node 2
NM2: no member exists downstream of Node 2
L2: Node 2 received a leave message
J2: Node 2 received a join message
G2: Node 2 received a Graft message
(Pr2): Node 2 sends a prune upstream
(G2): Node 2 sends a Graft upstream
Fig Reduced reac habilit y graph for a no de PIMDM
fNH
N C
g can be considered a transien t state
that ma y transit to a correct state fF
N H
N C
g
in some cases and a stable error state in others and
hence cannot b e simply remo v ed from the state ma
c hine A t the same time an error is not encoun tered
b y the mere reac habilit y of that state ie the state
should not b e alw a ys c hec k ed for correctness Whic h
leadsusto in tro duce the notion of tr ansition c omple
tion explained next
{F1,NH2,NC3}
loss
{NH2,NC3} {NH2,NC3}
loss
LPr1.(J2)/LPr1.LPr2 (Pr3)
LPr1
(J2) LJ1
no loss
no loss
Error
Transient
LPri: loss of Prune by Node i
LJi: loss of Join by Node i
(J2): Node 2 sends Join upstream
(Pr3): Node 3 sends Prune upstream
Fig no de PIMDM partial detailed reac habilit y graph
Toc hec k for the global system correctness all stim
ulated in ternal transitions should be completed to
bring the system in to a stable ie nontransien t
state In termediate transien t states should not b e
c hec k ed for correctness since in most cases they vi
olate the correctness conditions set forth for stable
states and hence ma ygiv e false error indication
The pro cess of iden tifying complete transitions de
p ends on the nature of the proto col In general ho w
ev er w emayiden tify a complete transition sequence
as the sequence of all transitions triggered due to a
single external stim ulus eg hostjoin or hostlea v e
Therefore w e should b e able to iden tify a transition
based up on its stim uli either external or in ternal
A t the end of eac h complete transition sequence the
system exists in either a correct or erroneous stable
state This transition completion concept suggests
that starting from a correct state only one complete
transition sequence needs to b e explored Hence if all
the correct states or a subset equiv alen t thereto are
in v estigated all erroneous states will b e disco v ered
{F1,NH2,NC3}
{NH2,NC3}
(Pr3).LPr2/
(Pr3).(J2).LJ1
LPr1.LPr2/
(Pr3).LPr1/
(Pr3).(J2)
LPri: loss of Prune by Node i
LJi: loss of Join by Node i
(J2): Node 2 sends Join upstream
(Pr3): Node 3 sends Prune upstream
Fig no de PIMDM reduced reac habilitygraph
A phase con tains all transitions that are considered
complete F or PIMDM the follo wing sequences of
transitions are considered complete for the purp oses
of this study
sending prunes then sending joins if an y or PJ for short
sending pac k ets prune if an y join if an y asserts
if an y SP J A
A PJ complete phase do es not mean that a join
cannot b e lost rather an y loss pattern maybe ap
plied to the join message but the pro cessing of the
join after applying the loss pattern should b e com
pleted b efore the state is c hec k ed for correctness
E Pr oto c ol me chanisms
F ollo wing are the mec hanisms represen ting the
PIMDM proto col from the perspectiv e of a router
R
i
connected to the link F or brevit y w e simplify
some of the proto col mec hanisms suc h as assuming
Grafts to b e reliable and not considering timers
Pruning
pro cedure S endP r une
i dst
if F
dst
Gl obS tate
remo v e F
dst
from Gl obS tate join j dow nstr eam j i
apply selectiv eloss
if NH
j
Gl obS tate
join if join
SendJoin
CheckState end of a phase Joining Pruneo v erriding
pro cedure S endJ oin
i dst
apply message loss if F
dst
Gl obS tate
add F
dst
to Gl obS tate Grafting
pro cedure Send Graft
if F
dst
Gl obS tate
add F
dst
to Gl obS tate CheckState end of a phase Asserting
pro cedure Send Assert
j upstr eam
if j max max address wins assert remo v e F
j
from Gl obS tate Receiving data pac k ets
pro cedure F or w ar dP ack ets
i
if F
i
Gl obS tate
add F
i
to Gl obS tate assert k upstr eam
if F
k
Gl obS tate
add F
k
to Gl obS tate assert if assert
SendAssert
prune j dow nstr eam
if NC
j
Gl obS tate
prune else if NH
j
Gl obS tate
add NH
j
to Gl obS tate if prune
SendPrune
CheckState end of a phase Chec kState Gl obS tate
oifs j upstr eam
if F
j
Gl obS tate
oifs if oifs Error
iifs k dow nstr eam
if NH
k
Gl obS tate
iifs if iifs and oifs Error
else if oifs and iifs Error
F Mapping err or tr ansitions into host events
Externally triggered ev en ts leading to the error are
recorded then translated in to host ev en ts according
to the follo wing rules i ev ery forw ardP ac k ets ev en t
is preceded b y a sendP ac k ets ev en t ii ev ery send
Prune ev en t is preceded byaLea veev en t and
iii ev ery sendJoin ev en t is preceded b y a HostJoin
ev en t
G Getting to the c orr e ct state using host events
T o obtain the sequence of host ev en ts leading to
a sp ecic correct global state with upstream routers
upstr m and do wnstream routers dnstr mw e use the
follo wing simple pro cedure
i dnstr m
if NH
i
g l obstate
add H ostJ oin
i
to S
cor r
else if NC
i
g l obstate
add Leav e
i
to S
cor r
j upstr m
if F
j
g l obstate
add sendP ack ets
j
to S
cor r
H Example
F or brevit yw e will only presen t one example illus
trating the approac h Our future w ork will presenta
more complete list of the errors disco v ered using this
approac h F ollo wing is one case where w e captured a
design error using the faultindep enden t approac h
The top ology has one upstream router R
and
t w o do wnstream routers R
R
Starting from
the correct state fF
N H
N C
g the follo wing se
quence of ev en ts w as found to driv e the system
in to the error state fNH
N C
g F or w ar dP ack et
sendP r une
sendJ oin
R
l ostJ oin The externally triggered ev en ts from the ab o v e
list are the forw arding and the loss ev en ts The
F or w ar dP ack et
maps in to a sendP ack et
host
ev en t Hence S
er r
fsendP ack et
R
l ostJ oing T o get to the correct state w e ha v e S
cor r
fH ostJ oin
Leav e
sendP ack et
g The test sequence is
fH ostJ oin
Leav e
sendP ack et
R
l ostJ oing V Summar y and Future W ork
In this pap er weha v e presen ted an algorithm for
automatic test generation that targets proto col ro
bustness W e ha v e used a LAN mo del to study
proto col beha vior in the presence of selectiv e loss
Our metho d w as applied to a simplied v ersion of
PIMDM F or our case studyw eha veac hiev ed state
space reduction from exp onen tial to linear complex
ityinthe n um b er of routers connected to the LAN
W e ha v e presen ted an example where errors w ere
disco v ered in the proto col beha vior in the presence
of message loss and the ev en ts leading to the error
w ere generated The metho dology ma y b e applied to
other faults eg unicast routing anomalies or router
crashes as w ell as other proto cols that ma y b e rep
resen ted using the GFSM mo del used in this pap er
References
D W aitzman S Deering C P artridge Distance V ector
Multicast Routing Proto col No v em b er RF C
J Mo y Multicast Extension to OSPF Internet Dr aft Septem b er
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
A J Ballardie PF F rancis and J Cro w croft Core
Based T rees In Pr o c e e dings of the A CM SIGCOMM San F rancisco 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 ose d Exp erimen
tal RF C URL httpnetwebusce dupimpimsmPIM
A r ch ftxtps ggz Octob er 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 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
S McCanne A Distributed Whiteb oard for Net w ork Con
ferencing UC Berkeley Computer Scienc epr oje ctMa y
V Jacobson and S McCanne v at LBNL Audio Confer
encing T o ol URL httpwwwnr ge elblgovvat
S McCanne and V Jacobson vic A Flexible F rame
w ork for P ac k et Video A CM Multime dia No v em ber
M Handley NTE The UCL Net w ork T ext
Editor URL httpwwwmic ensccsuclacukmic e
nscto olsnthelpab outhtml M Handley The sdr Session Directory An Mb one
Conference Sc heduling and Bo oking System URL
httpugwwwe dacukmic ear chivesdrhtml
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 A Helm y A Surv ey on Kernel Sp ecication and V erica
tion T e chnic al R ep ort of the Computer Scienc e
Dep artment University of Southern California URL
httpwwwusce dudeptcste chnic al r ep ortshtml J Spiv ey Understanding Z a Sp ecication Language and
its F ormal Seman tics Cambridge University Pr ess
C Jones Systematic Soft w are Dev elopmen t using VDM
Pr entic eHal l Intl R Bo y er and J Mo ore A Computational Logic Hand
book A c ademic Pr ess Boston S Owre J Rush b yN Shank er and F Henk e F ormal
v erication for faulttoleran tarc hitectures Prolegomena
to the design of PVS IEEE T r ansactions on Softwar e
Engine ering pages F ebruary M Smith F ormal V erication of Comm unication Proto
cols F OR TEPSTV Confer enc e Octob er
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 F Lin P Ch u and M Liu Proto col V erication using
Reac habilit y Analysis the state explosion problem and
relief strategies Pr o c e e dings of the A CM SIGCOMM D Probst Using partialorder seman tics to a v oid the
state explosion problem in async hronous systems Pr o c
nd Workshop on ComputerA idedV eric ation Springer
V erlag New Y ork 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
N Maxemc h uc k and K Sabnani Probabilistic v erica
tion of comm unication proto cols Pr o c th IFIP WG
Int Workshop on Pr oto c ol Sp e cic ation T esting and
V eric ation NorthHol land Publ A mster dam C W est Proto col V alidation b y Random State Explo
ration Pr o c th IFIP WG Int Workshop on Pr oto c ol
Sp e cic ation T esting and V eric ation NorthHol land
Publ A mster dam J P ageot and C Jard Exp erience in guiding sim ulation
Pr o c VIIIth Workshop on Pr oto c ol Sp e cic ation T est
ing and V eric ation A tlantic City NorthHol land
Publ A mster dam 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
A Helm y and D Estrin Sim ulationbased STRESS T est
ing Case Study A Multicast Routing Proto col Sixth In
ternational Symp osium on Mo deling A nalysis and Sim
ulation of Computer and T ele c ommunic ation Systems
MASCOTS July 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
Abstract (if available)
Linked assets
Computer Science Technical Report Archive
Conceptually similar
PDF
USC Computer Science Technical Reports, no. 727 (2000)
PDF
USC Computer Science Technical Reports, no. 673 (1998)
PDF
USC Computer Science Technical Reports, no. 674 (1998)
PDF
USC Computer Science Technical Reports, no. 726 (2000)
PDF
USC Computer Science Technical Reports, no. 657 (1997)
PDF
USC Computer Science Technical Reports, no. 696 (1999)
PDF
USC Computer Science Technical Reports, no. 730 (2000)
PDF
USC Computer Science Technical Reports, no. 755 (2002)
PDF
USC Computer Science Technical Reports, no. 801 (2003)
PDF
USC Computer Science Technical Reports, no. 644 (1997)
PDF
USC Computer Science Technical Reports, no. 860 (2005)
PDF
USC Computer Science Technical Reports, no. 809 (2003)
PDF
USC Computer Science Technical Reports, no. 663 (1998)
PDF
USC Computer Science Technical Reports, no. 743 (2001)
PDF
USC Computer Science Technical Reports, no. 672 (1998)
PDF
USC Computer Science Technical Reports, no. 816 (2004)
PDF
USC Computer Science Technical Reports, no. 775 (2002)
PDF
USC Computer Science Technical Reports, no. 811 (2003)
PDF
USC Computer Science Technical Reports, no. 753 (2002)
PDF
USC Computer Science Technical Reports, no. 678 (1998)
Description
Ahmed Helmy, Deborah Estrin, Sandeep Gupta. "STRESS testing using reduced reachability analysis: A case study for a multicast routing protocol." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 690 (1998).
Asset Metadata
Creator
Estrin, Deborah
(author),
Gupta, Sandeep
(author),
Helmy, Ahmed
(author)
Core Title
USC Computer Science Technical Reports, no. 690 (1998)
Alternative Title
STRESS testing using reduced reachability analysis: A case study for a multicast routing protocol (
title
)
Publisher
Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA
(publisher)
Tag
OAI-PMH Harvest
Format
13 pages
(extent),
technical reports
(aat)
Language
English
Unique identifier
UC16270716
Identifier
98-690 STRESS Testing using Reduced Reachability Analysis A Case Study for a Multicast Routing Protocol (filename)
Legacy Identifier
usc-cstr-98-690
Format
13 pages (extent),technical reports (aat)
Rights
Department of Computer Science (University of Southern California) and the author(s).
Internet Media Type
application/pdf
Copyright
In copyright - Non-commercial use permitted (https://rightsstatements.org/vocab/InC-NC/1.0/
Source
20180426-rozan-cstechreports-shoaf
(batch),
Computer Science Technical Report Archive
(collection),
University of Southern California. Department of Computer Science. Technical Reports
(series)
Access Conditions
The author(s) retain rights to their work according to U.S. copyright law. Electronic access is being provided by the USC Libraries, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright.
Repository Name
USC Viterbi School of Engineering Department of Computer Science
Repository Location
Department of Computer Science. USC Viterbi School of Engineering. Los Angeles\, CA\, 90089
Repository Email
csdept@usc.edu
Inherited Values
Title
Computer Science Technical Report Archive
Coverage Temporal
1991/2017
Repository Email
csdept@usc.edu
Repository Name
USC Viterbi School of Engineering Department of Computer Science
Repository Location
Department of Computer Science. USC Viterbi School of Engineering. Los Angeles\, CA\, 90089
Publisher
Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA
(publisher)
Copyright
In copyright - Non-commercial use permitted (https://rightsstatements.org/vocab/InC-NC/1.0/