<s>
Gbcast	B-Operating_System
(	O
also	O
known	O
as	O
group	O
broadcast	O
)	O
is	O
a	O
reliable	B-Operating_System
multicast	I-Operating_System
protocol	O
that	O
provides	O
ordered	O
,	O
fault-tolerant	O
(	O
all-or-none	O
)	O
message	O
delivery	O
in	O
a	O
group	O
of	O
receivers	O
within	O
a	O
network	O
of	O
machines	O
that	O
experience	O
crash	O
failure	O
.	O
</s>
<s>
The	O
protocol	O
is	O
capable	O
of	O
solving	O
Consensus	B-Operating_System
in	O
a	O
network	O
of	O
unreliable	O
processors	O
,	O
and	O
can	O
be	O
used	O
to	O
implement	O
state	B-Operating_System
machine	I-Operating_System
replication	I-Operating_System
.	O
</s>
<s>
Gbcast	B-Operating_System
can	O
be	O
used	O
in	O
a	O
standalone	O
manner	O
,	O
or	O
can	O
support	O
the	O
virtual	O
synchrony	O
execution	O
model	O
,	O
in	O
which	O
case	O
Gbcast	B-Operating_System
is	O
normally	O
used	O
for	O
group	O
membership	O
management	O
while	O
other	O
,	O
faster	O
,	O
protocols	O
are	O
often	O
favored	O
for	O
routine	O
communication	O
tasks	O
.	O
</s>
<s>
Introduced	O
in	O
1985	O
,	O
Gbcast	B-Operating_System
was	O
the	O
first	O
widely	O
deployed	O
reliable	B-Operating_System
multicast	I-Operating_System
protocol	O
to	O
implement	O
state	B-Operating_System
machine	I-Operating_System
replication	I-Operating_System
with	O
dynamically	O
reconfigurable	O
membership	O
.	O
</s>
<s>
Although	O
this	O
problem	O
had	O
been	O
treated	O
theoretically	O
under	O
various	O
models	O
in	O
prior	O
work	O
,	O
Gbcast	B-Operating_System
innovated	O
by	O
showing	O
that	O
the	O
same	O
multicasts	O
used	O
to	O
update	O
replicated	O
data	O
within	O
the	O
state	O
machine	O
can	O
also	O
be	O
used	O
to	O
dynamically	O
reconfigure	O
the	O
group	O
membership	O
,	O
which	O
can	O
then	O
evolve	O
to	O
permit	O
members	O
to	O
join	O
and	O
leave	O
at	O
will	O
,	O
in	O
addition	O
to	O
being	O
removed	O
upon	O
failure	O
.	O
</s>
<s>
The	O
term	O
state	B-Operating_System
machine	I-Operating_System
replication	I-Operating_System
was	O
first	O
suggested	O
by	O
Leslie	O
Lamport	O
and	O
was	O
widely	O
adopted	O
after	O
publication	O
of	O
a	O
survey	O
paper	O
written	O
by	O
Fred	O
B	O
.	O
Schneider	O
.	O
</s>
<s>
Some	O
state	O
machine	O
protocols	O
can	O
also	O
ride	O
out	O
the	O
temporary	O
unavailability	O
of	O
a	O
subset	O
of	O
the	O
current	O
members	O
without	O
requiring	O
reconfiguration	O
when	O
such	O
situations	O
arise	O
,	O
including	O
Gbcast	B-Operating_System
and	O
also	O
Paxos	B-Operating_System
,	O
Lamport	O
's	O
widely	O
cited	O
protocol	O
for	O
state	B-Operating_System
machine	I-Operating_System
replication	I-Operating_System
.	O
</s>
<s>
State	B-Operating_System
machine	I-Operating_System
replication	I-Operating_System
is	O
closely	O
related	O
to	O
the	O
distributed	B-Operating_System
Consensus	I-Operating_System
problem	O
,	O
in	O
which	O
a	O
collection	O
of	O
processes	O
must	O
agree	O
upon	O
some	O
decision	O
outcome	O
,	O
such	O
as	O
the	O
winner	O
of	O
an	O
election	O
.	O
</s>
<s>
In	O
particular	O
,	O
it	O
can	O
be	O
shown	O
that	O
any	O
solution	O
to	O
the	O
state	B-Operating_System
machine	I-Operating_System
replication	I-Operating_System
problem	O
would	O
also	O
be	O
capable	O
of	O
solving	O
distributed	B-Operating_System
consensus	I-Operating_System
.	O
</s>
<s>
As	O
a	O
consequence	O
,	O
impossibility	O
results	O
for	O
distributed	B-Operating_System
consensus	I-Operating_System
apply	O
to	O
solutions	O
to	O
the	O
state	B-Operating_System
machine	I-Operating_System
replication	I-Operating_System
problem	O
.	O
</s>
<s>
Implications	O
of	O
this	O
finding	O
are	O
discussed	O
under	O
liveness	B-Application
.	O
</s>
<s>
Gbcast	B-Operating_System
is	O
somewhat	O
unusual	O
in	O
that	O
most	O
solutions	O
to	O
the	O
state	B-Operating_System
machine	I-Operating_System
replication	I-Operating_System
problem	O
are	O
closely	O
integrated	O
with	O
the	O
application	O
being	O
replicated	O
.	O
</s>
<s>
Gbcast	B-Operating_System
,	O
in	O
contrast	O
,	O
is	O
designed	O
as	O
a	O
multicast	O
API	O
and	O
implemented	O
by	O
a	O
library	O
that	O
delivers	O
messages	O
to	O
group	O
members	O
.	O
</s>
<s>
Lamport	O
,	O
Malkhi	O
and	O
Zhou	O
note	O
that	O
few	O
reliable	B-Operating_System
multicast	I-Operating_System
protocols	O
have	O
the	O
durability	O
properties	O
required	O
to	O
correctly	O
implement	O
the	O
state	O
machine	O
model	O
.	O
</s>
<s>
Gbcast	B-Operating_System
does	O
exhibit	O
the	O
necessary	O
properties	O
.	O
</s>
<s>
The	O
Gbcast	B-Operating_System
protocol	O
was	O
first	O
described	O
in	O
a	O
1985	O
publication	O
that	O
discussed	O
infrastructure	O
supporting	O
the	O
virtual	O
synchrony	O
model	O
in	O
the	O
Isis	O
Toolkit	O
.	O
</s>
<s>
The	O
fundamental	O
problem	O
solved	O
by	O
Gbcast	B-Operating_System
is	O
this	O
:	O
we	O
are	O
given	O
an	O
initial	O
set	O
of	O
group	O
members	O
and	O
wish	O
to	O
support	O
a	O
multicast	O
abstraction	O
,	O
permitting	O
members	O
of	O
the	O
group	O
to	O
send	O
messages	O
that	O
encode	O
various	O
commands	O
or	O
requests	O
.	O
</s>
<s>
The	O
set	O
of	O
group	O
members	O
changes	O
each	O
time	O
a	O
member	O
fails	O
or	O
joins	O
,	O
and	O
Gbcast	B-Operating_System
is	O
also	O
used	O
to	O
maintain	O
group	O
membership	O
by	O
means	O
of	O
special	O
multicasts	O
that	O
are	O
delivered	O
to	O
the	O
application	O
as	O
"	O
new	O
view	O
"	O
events	O
,	O
but	O
that	O
also	O
adjust	O
the	O
group	O
membership	O
list	O
maintained	O
by	O
the	O
Gbcast	B-Operating_System
protocol	O
library	O
.	O
</s>
<s>
Gbcast	B-Operating_System
offers	O
protection	O
against	O
this	O
threat	O
:	O
the	O
protocol	O
ensures	O
that	O
progress	O
occurs	O
only	O
in	O
a	O
single	O
primary	O
partition	O
of	O
the	O
group	O
.	O
</s>
<s>
Any	O
dynamically	O
reconfigurable	O
system	O
,	O
including	O
both	O
Gbcast	B-Operating_System
and	O
Paxos	B-Operating_System
,	O
can	O
enter	O
states	O
from	O
which	O
no	O
further	O
progress	O
is	O
possible	O
.	O
</s>
<s>
This	O
is	O
in	O
contrast	O
to	O
the	O
behavior	O
of	O
non-reconfigurable	O
(	O
vanilla	B-General_Concept
)	O
Paxos	B-Operating_System
,	O
which	O
can	O
tolerate	O
disruptions	O
of	O
unlimited	O
duration	O
and	O
then	O
will	O
resume	O
once	O
enough	O
group	O
members	O
are	O
accessible	O
,	O
without	O
intervention	O
of	O
the	O
management	O
infrastructure	O
.	O
</s>
<s>
The	O
network	O
conditions	O
required	O
for	O
Gbcast	B-Operating_System
to	O
guarantee	O
progress	O
are	O
discussed	O
below	O
.	O
</s>
<s>
In	O
practice	O
Gbcast	B-Operating_System
is	O
normally	O
used	O
within	O
data	O
centers	O
;	O
these	O
have	O
networks	O
that	O
can	O
experience	O
transient	O
failures	O
,	O
but	O
in	O
which	O
partitioning	O
failures	O
are	O
rare	O
,	O
and	O
generally	O
impact	O
just	O
small	O
subsets	O
of	O
the	O
nodes	O
.	O
</s>
<s>
To	O
simplify	O
the	O
presentation	O
,	O
we	O
assume	O
that	O
a	O
TCP-like	O
acknowledgement	O
/	O
retransmission	O
scheme	O
is	O
employed	O
,	O
creating	O
the	O
illusion	O
of	O
a	O
reliable	O
,	O
sequenced	O
,	O
non-repeating	O
message	O
channel	O
between	O
each	O
pair	O
of	O
processes	O
.	O
</s>
<s>
Using	O
the	O
same	O
TCP-like	O
channels	O
,	O
we	O
can	O
also	O
support	O
a	O
1-to-all	O
capability	O
,	O
whereby	O
a	O
single	O
process	O
sends	O
some	O
message	O
over	O
its	O
channels	O
to	O
all	O
the	O
other	O
members	O
of	O
some	O
view	O
of	O
some	O
group	O
.	O
</s>
<s>
Gbcast	B-Operating_System
is	O
defined	O
with	O
respect	O
to	O
a	O
"	O
process	O
group	O
:	O
"	O
a	O
set	O
of	O
processes	O
.	O
</s>
<s>
Subsequent	O
membership	O
views	O
arise	O
by	O
applying	O
add	O
and	O
remove	O
commands	O
and	O
are	O
identified	O
by	O
sequence	B-Protocol
number	I-Protocol
.	O
</s>
<s>
The	O
Gbcast	B-Operating_System
protocol	O
carries	O
out	O
these	O
operations	O
with	O
a	O
series	O
of	O
guarantees	O
,	O
discussed	O
below	O
.	O
</s>
<s>
Gbcast	B-Operating_System
is	O
best	O
understood	O
in	O
terms	O
of	O
a	O
set	O
of	O
roles	O
.	O
</s>
<s>
An	O
application	O
process	O
belonging	O
to	O
a	O
group	O
initiates	O
new	O
multicasts	O
by	O
invoking	O
Gbcast	B-Operating_System
.	O
</s>
<s>
Incoming	O
Gbcast	B-Operating_System
messages	O
are	O
delivered	O
via	O
upcalls	O
,	O
as	O
are	O
view	O
change	O
notifications	O
.	O
</s>
<s>
Quorums	O
are	O
used	O
to	O
guarantee	O
the	O
safety	B-Application
properties	I-Application
of	O
Gbcast	B-Operating_System
by	O
ensuring	O
that	O
there	O
is	O
a	O
single	O
globally	O
agreed-upon	O
sequence	O
of	O
group	O
views	O
and	O
multicast	O
messages	O
and	O
by	O
preventing	O
progress	O
in	O
more	O
than	O
one	O
partition	O
if	O
a	O
group	O
becomes	O
fragmented	O
into	O
two	O
or	O
more	O
partitions	O
(	O
disjoint	O
subsets	O
of	O
members	O
that	O
can	O
communicate	O
with	O
other	O
members	O
of	O
their	O
subsets	O
,	O
but	O
not	O
with	O
members	O
of	O
other	O
subsets	O
)	O
.	O
</s>
<s>
Notice	O
that	O
this	O
is	O
in	O
contrast	O
to	O
the	O
way	O
the	O
term	O
is	O
defined	O
in	O
systems	O
that	O
have	O
a	O
static	O
underlying	O
membership	O
:	O
for	O
Gbcast	B-Operating_System
,	O
the	O
quorum	O
size	O
will	O
change	O
over	O
time	O
as	O
the	O
membership	O
of	O
a	O
group	O
changes	O
and	O
new	O
views	O
become	O
defined	O
.	O
</s>
<s>
In	O
order	O
to	O
guarantee	O
safety	O
,	O
Gbcast	B-Operating_System
defines	O
three	O
safety	B-Application
properties	I-Application
and	O
ensures	O
they	O
hold	O
,	O
regardless	O
of	O
the	O
pattern	O
of	O
failures	O
:	O
</s>
<s>
Liveness	B-Application
cannot	O
be	O
guaranteed	O
under	O
all	O
conditions	O
,	O
hence	O
we	O
impose	O
a	O
further	O
condition	O
:	O
we	O
require	O
this	O
property	O
only	O
while	O
sufficiently	O
many	O
processes	O
remain	O
non-faulty	O
(	O
we	O
'll	O
discuss	O
this	O
further	O
below	O
)	O
.	O
</s>
<s>
Recall	O
that	O
in	O
Gbcast	B-Operating_System
,	O
each	O
operational	O
process	O
has	O
a	O
current	O
view	O
,	O
and	O
each	O
view	O
defines	O
a	O
leader	O
.	O
</s>
<s>
The	O
leader	O
proposes	O
some	O
sequence	O
of	O
one	O
or	O
more	O
multicast	O
messages	O
by	O
using	O
the	O
1-to-all	O
reliable	O
network	O
layer	O
to	O
send	O
the	O
message(s )	O
to	O
the	O
members	O
of	O
the	O
most	O
current	O
view	O
,	O
identifying	O
each	O
by	O
means	O
of	O
an	O
integer	O
sequence	B-Protocol
number	I-Protocol
.	O
</s>
<s>
The	O
sequence	B-Protocol
numbers	I-Protocol
reset	O
to	O
1	O
as	O
each	O
new	O
view	O
is	O
defined	O
(	O
via	O
a	O
special	O
kind	O
of	O
multicast	O
,	O
as	O
explained	O
below	O
)	O
.	O
</s>
<s>
If	O
some	O
message	O
is	O
re-proposed	O
with	O
the	O
same	O
sequence	B-Protocol
number	I-Protocol
,	O
a	O
recipient	O
simply	O
repeats	O
its	O
promise	O
.	O
</s>
<s>
To	O
take	O
over	O
as	O
the	O
leader	O
,	O
the	O
new	O
leader	O
first	O
runs	O
a	O
takeover	O
protocol	O
,	O
and	O
then	O
the	O
new	O
leader	O
can	O
run	O
basic	O
Gbcast	B-Operating_System
as	O
above	O
.	O
</s>
<s>
To	O
show	O
that	O
Gbcast	B-Operating_System
satisfies	O
non-triviality	O
we	O
start	O
by	O
tracing	O
backwards	O
from	O
an	O
arbitrary	O
delivery	O
action	O
to	O
the	O
point	O
at	O
which	O
a	O
client	O
requested	O
the	O
corresponding	O
event	O
;	O
clearly	O
,	O
only	O
messages	O
that	O
were	O
legitimately	O
sent	O
will	O
be	O
delivered	O
.	O
</s>
<s>
The	O
Gbcast	B-Operating_System
protocol	O
will	O
make	O
progress	O
provided	O
that	O
at	O
all	O
times	O
in	O
the	O
execution	O
,	O
if	O
view	O
holds	O
at	O
time	O
,	O
then	O
less	O
than	O
a	O
quorum	O
of	O
members	O
of	O
fail	O
(	O
or	O
are	O
suspected	O
as	O
failing	O
)	O
within	O
some	O
subset	O
of	O
the	O
members	O
of	O
the	O
view	O
.	O
</s>
<s>
This	O
property	O
is	O
similar	O
to	O
but	O
"	O
stronger	O
"	O
than	O
<>	O
W	O
,	O
the	O
"	O
weakest	O
failure	O
detector	O
"	O
for	O
achieving	O
consensus	B-Operating_System
,	O
as	O
defined	O
by	O
Chandra	O
and	O
Toueg	O
.	O
</s>
<s>
Gbcast	B-Operating_System
will	O
not	O
make	O
progress	O
and	O
,	O
indeed	O
,	O
the	O
group	O
will	O
need	O
to	O
shut	O
down	O
and	O
restart	O
.	O
</s>
<s>
Arguably	O
,	O
such	O
runs	O
would	O
be	O
unlikely	O
in	O
the	O
kinds	O
of	O
data	O
centers	O
where	O
Gbcast	B-Operating_System
is	O
typically	O
used	O
,	O
but	O
clearly	O
they	O
can	O
be	O
constructed	O
in	O
an	O
adversarial	O
manner	O
.	O
</s>
<s>
The	O
Gbcast	B-Operating_System
protocol	O
presumes	O
that	O
the	O
probability	O
of	O
incorrect	O
failure	O
suspicions	O
will	O
be	O
low	O
;	O
the	O
scheme	O
breaks	O
down	O
if	O
failure	O
suspicions	O
occur	O
frequently	O
and	O
operational	O
processes	O
are	O
often	O
suspected	O
as	O
faulty	O
.	O
</s>
<s>
By	O
analogy	O
,	O
consider	O
the	O
TCP	B-Protocol
protocol	I-Protocol
,	O
in	O
which	O
the	O
failure	O
to	O
receive	O
an	O
acknowledgement	O
will	O
eventually	O
cause	O
a	O
connection	O
to	O
break	O
.	O
</s>
<s>
TCP	B-Protocol
is	O
used	O
nearly	O
universally	O
,	O
a	O
tremendous	O
disruption	O
to	O
the	O
Web	O
would	O
result	O
if	O
TCP	B-Protocol
connections	O
frequently	O
were	O
to	O
break	O
when	O
neither	O
endpoint	O
has	O
failed	O
.	O
</s>
<s>
A	O
similar	O
assumption	O
is	O
required	O
for	O
systems	O
that	O
use	O
Gbcast	B-Operating_System
.	O
</s>
<s>
Some	O
protocols	O
,	O
including	O
Paxos	B-Operating_System
,	O
are	O
able	O
to	O
tolerate	O
incorrect	O
failure	O
suspicions	O
without	O
any	O
costly	O
consequence	O
.	O
</s>
<s>
We	O
simply	O
underscore	O
that	O
the	O
approaches	O
differ	O
,	O
and	O
that	O
Gbcast	B-Operating_System
would	O
be	O
ineffective	O
if	O
timeouts	O
are	O
set	O
overly	O
aggressively	O
.	O
</s>
<s>
Such	O
cases	O
are	O
treated	O
as	O
failures	O
in	O
Gbcast	B-Operating_System
,	O
but	O
if	O
the	O
surviving	O
,	O
connected	O
members	O
include	O
a	O
sufficiently	O
large	O
number	O
of	O
processes	O
,	O
the	O
majority	O
portion	O
of	O
the	O
system	O
will	O
simply	O
reconfigure	O
itself	O
to	O
exclude	O
the	O
disconnected	O
member	O
.	O
</s>
<s>
In	O
such	O
cases	O
one	O
could	O
imagine	O
a	O
group	O
in	O
which	O
all	O
members	O
begin	O
to	O
suspect	O
all	O
other	O
members	O
;	O
Gbcast	B-Operating_System
will	O
not	O
progress	O
in	O
this	O
case	O
and	O
the	O
management	O
infrastructure	O
would	O
need	O
to	O
relaunch	O
the	O
entire	O
application	O
.	O
</s>
<s>
This	O
said	O
,	O
there	O
are	O
protocols	O
,	O
such	O
as	O
Paxos	B-Operating_System
,	O
that	O
could	O
ride	O
out	O
such	O
an	O
outage	O
if	O
the	O
machines	O
themselves	O
were	O
to	O
remain	O
operational	O
and	O
later	O
regained	O
adequate	O
connectivity	O
.	O
</s>
<s>
The	O
Transis	O
system	O
explored	O
extensions	O
to	O
the	O
Gbcast	B-Operating_System
protocol	O
that	O
permit	O
multiple	O
partitions	O
to	O
form	O
,	O
to	O
make	O
independent	O
progress	O
,	O
and	O
then	O
to	O
remerge	O
.	O
</s>
<s>
In	O
the	O
Paxos	B-Operating_System
protocol	I-Operating_System
,	O
a	O
situation	O
can	O
arise	O
in	O
which	O
two	O
or	O
more	O
leaders	O
"	O
duel	O
"	O
by	O
proposing	O
different	O
commands	O
for	O
the	O
same	O
slot	O
.	O
</s>
<s>
This	O
can	O
also	O
occur	O
in	O
Gbcast	B-Operating_System
.	O
</s>
<s>
Shunning	O
of	O
leaders	O
in	O
Gbcast	B-Operating_System
occurs	O
in	O
the	O
pre-determined	O
order	O
of	O
leader	O
ranks	O
:	O
a	O
higher-ranking	O
leader	O
only	O
shuns	O
a	O
lower-ranking	O
leader	O
when	O
it	O
tries	O
to	O
take-over	O
its	O
place	O
.	O
</s>
<s>
The	O
Paxos	B-Operating_System
ballots	O
mechanism	O
serves	O
precisely	O
the	O
same	O
purpose	O
,	O
but	O
differs	O
in	O
allowing	O
participants	O
to	O
attempt	O
to	O
take-over	O
repeatedly	O
,	O
eaach	O
time	O
assuming	O
a	O
new	O
ballot	O
(	O
"	O
rank	O
"	O
)	O
.	O
</s>
<s>
The	O
result	O
is	O
that	O
,	O
one	O
the	O
one	O
hand	O
,	O
Paxos	B-Operating_System
leader	O
demotion	O
is	O
reversible	O
,	O
and	O
on	O
the	O
other	O
,	O
dueling	O
leaders	O
could	O
theoretically	O
continue	O
forever	O
.	O
</s>
<s>
Although	O
superficially	O
quite	O
different	O
,	O
upon	O
close	O
study	O
Gbcast	B-Operating_System
is	O
seen	O
to	O
be	O
surprisingly	O
similar	O
to	O
Paxos	B-Operating_System
.	O
</s>
<s>
Indeed	O
,	O
Paxos	B-Operating_System
can	O
be	O
"	O
transformed	O
"	O
into	O
Gbcast	B-Operating_System
with	O
the	O
following	O
(	O
reversible	O
)	O
sequence	O
of	O
steps	O
.	O
</s>
<s>
Gbcast	B-Operating_System
treats	O
durable	O
state	O
as	O
a	O
property	O
of	O
the	O
application	O
,	O
not	O
the	O
protocol	O
,	O
whereas	O
Paxos	B-Operating_System
logs	O
events	O
to	O
a	O
set	O
of	O
durable	O
command	O
logs	O
,	O
and	O
hence	O
can	O
still	O
recover	O
its	O
state	O
even	O
after	O
the	O
whole	O
service	O
is	O
shut	O
down	O
and	O
restarted	O
.	O
</s>
<s>
The	O
equivalent	O
behavior	O
with	O
Gbcast	B-Operating_System
involves	O
having	O
the	O
application	O
log	O
all	O
received	O
messages	O
,	O
but	O
that	O
case	O
will	O
not	O
be	O
considered	O
here	O
.	O
</s>
<s>
Start	O
with	O
the	O
basic	O
Paxos	B-Operating_System
protocol	I-Operating_System
.	O
</s>
<s>
Both	O
protocols	O
permit	O
batching	O
of	O
requests	O
:	O
Basic	O
Paxos	B-Operating_System
has	O
a	O
concurrency	O
parameter	O
,	O
alpha	O
:	O
a	O
leader	O
can	O
concurrently	O
run	O
a	O
maximum	O
of	O
alpha	O
instances	O
of	O
the	O
protocol	O
.	O
</s>
<s>
Gbcast	B-Operating_System
permits	O
the	O
leader	O
to	O
propose	O
multiple	O
events	O
in	O
a	O
single	O
protocol	O
instance	O
,	O
which	O
could	O
be	O
message	O
deliveries	O
or	O
view	O
events	O
.	O
</s>
<s>
Paxos	B-Operating_System
does	O
not	O
normally	O
require	O
reliable	O
,	O
ordered	O
communication	O
.	O
</s>
<s>
Modify	O
the	O
protocol	O
to	O
run	O
over	O
the	O
reliable	O
one-to-one	O
channel	O
abstraction	O
(	O
a	O
one-to-many	O
message	O
would	O
be	O
sent	O
by	O
Paxos	B-Operating_System
over	O
a	O
set	O
of	O
one-to-one	O
channels	O
)	O
.	O
</s>
<s>
The	O
Paxos	B-Operating_System
slot	O
number	O
will	O
become	O
the	O
Gbcast	B-Operating_System
sequence	B-Protocol
number	I-Protocol
.	O
</s>
<s>
The	O
Paxos	B-Operating_System
ballot	O
number	O
is	O
,	O
in	O
effect	O
,	O
transformed	O
into	O
the	O
proposing	O
leader-number	O
used	O
to	O
discriminate	O
between	O
conflicting	O
proposals	O
during	O
the	O
inquire	O
step	O
.	O
</s>
<s>
Introduce	O
a	O
failure	O
detection	O
mechanism	O
as	O
used	O
in	O
Gbcast	B-Operating_System
,	O
asking	O
the	O
leader	O
to	O
remove	O
any	O
timed-out	O
members	O
.	O
</s>
<s>
Basic	O
Paxos	B-Operating_System
can	O
propose	O
a	O
multicast	O
to	O
just	O
a	O
quorum	O
of	O
group	O
members	O
,	O
hence	O
a	O
typical	O
member	O
may	O
have	O
gaps	O
in	O
its	O
command	O
list	O
.	O
</s>
<s>
This	O
is	O
why	O
,	O
in	O
Paxos	B-Operating_System
,	O
a	O
learner	O
must	O
read	O
a	O
quorum	O
of	O
members	O
and	O
merge	O
their	O
command	O
lists	O
.	O
</s>
<s>
Thus	O
unlike	O
Paxos	B-Operating_System
,	O
our	O
modified	O
protocol	O
has	O
the	O
property	O
that	O
any	O
single	O
live	O
member	O
has	O
the	O
full	O
committed	O
event	O
list	O
.	O
</s>
<s>
The	O
same	O
quorum	O
mechanisms	O
that	O
define	O
Paxos	B-Operating_System
,	O
including	O
the	O
inquiry	O
used	O
when	O
a	O
new	O
Paxos	B-Operating_System
leader	O
takes	O
over	O
,	O
are	O
now	O
seen	O
to	O
correspond	O
precisely	O
to	O
the	O
steps	O
of	O
Gbcast	B-Operating_System
.	O
</s>
<s>
The	O
ballot	O
mechanism	O
,	O
generally	O
viewed	O
as	O
the	O
hallmark	O
of	O
Paxos	B-Operating_System
protocols	I-Operating_System
,	O
reduces	O
to	O
a	O
counter	O
that	O
tracks	O
the	O
order	O
of	O
succession	O
of	O
leaders	O
.	O
</s>
<s>
It	O
follows	O
that	O
Gbcast	B-Operating_System
and	O
Paxos	B-Operating_System
can	O
be	O
transformed	O
,	O
each	O
to	O
the	O
other	O
,	O
without	O
changing	O
assumptions	O
and	O
with	O
the	O
identical	O
correctness	O
properties	O
.	O
</s>
<s>
Indeed	O
,	O
one	O
can	O
make	O
a	O
stronger	O
claim	O
:	O
any	O
sequence	O
of	O
delivery	O
events	O
exhibited	O
by	O
Gbcast	B-Operating_System
can	O
also	O
arise	O
in	O
some	O
run	O
of	O
Paxos	B-Operating_System
,	O
and	O
vice	O
versa	O
:	O
any	O
sequence	O
of	O
learned	O
events	O
from	O
Paxos	B-Operating_System
can	O
also	O
arise	O
in	O
some	O
run	O
of	O
Gbcast	B-Operating_System
.	O
</s>
<s>
For	O
example	O
,	O
the	O
Gbcast	B-Operating_System
reporting	O
of	O
new	O
views	O
(	O
events	O
that	O
Paxos	B-Operating_System
lacks	O
)	O
are	O
not	O
treated	O
as	O
output	O
events	O
here	O
.	O
</s>
<s>
Gbcast	B-Operating_System
has	O
no	O
durable	O
state	O
:	O
the	O
protocol	O
does	O
not	O
maintain	O
a	O
log	O
of	O
events	O
on	O
disk	O
,	O
and	O
durability	O
is	O
treated	O
as	O
an	O
application-specific	O
property	O
.	O
</s>
<s>
In	O
contrast	O
,	O
Paxos	B-Operating_System
guarantees	O
durability	O
:	O
after	O
recovering	O
from	O
a	O
complete	O
shutdown	O
of	O
the	O
system	O
,	O
a	O
Paxos	B-Operating_System
application	O
will	O
still	O
be	O
able	O
to	O
learn	O
the	O
full	O
log	O
of	O
received	O
messages	O
.	O
</s>
<s>
In	O
the	O
propose	O
phase	O
,	O
Gbcast	B-Operating_System
must	O
wait	O
for	O
responses	O
from	O
all	O
participants	O
(	O
or	O
for	O
the	O
maximal	O
timeout	O
and	O
then	O
suspect	O
the	O
remaining	O
ones	O
)	O
,	O
instead	O
of	O
making	O
progress	O
with	O
the	O
fastest	O
quorum	O
.	O
</s>
<s>
In	O
Gbcast	B-Operating_System
,	O
the	O
cost	O
of	O
a	O
failure	O
suspicion	O
is	O
high	O
and	O
the	O
protocol	O
may	O
cease	O
to	O
make	O
progress	O
if	O
too	O
many	O
failures	O
are	O
suspected	O
,	O
forcing	O
a	O
management	O
layer	O
to	O
restart	O
the	O
entire	O
application	O
group	O
.	O
</s>
<s>
Thus	O
,	O
in	O
practice	O
,	O
Gbcast	B-Operating_System
requires	O
conservative	O
timeout	O
settings	O
relative	O
to	O
Paxos	B-Operating_System
.	O
</s>
<s>
With	O
Gbcast	B-Operating_System
,	O
if	O
an	O
error	O
does	O
occur	O
(	O
e.g.	O
</s>
<s>
With	O
Paxos	B-Operating_System
,	O
if	O
f>0	O
,	O
should	O
a	O
process	O
be	O
unable	O
to	O
participate	O
in	O
a	O
protocol	O
instance	O
,	O
it	O
can	O
continue	O
to	O
participate	O
in	O
subsequent	O
protocol	O
instances	O
without	O
error	O
.	O
</s>
<s>
Operational	O
members	O
of	O
a	O
view	O
will	O
never	O
have	O
gaps	O
in	O
their	O
command	O
lists	O
with	O
Gbcast	B-Operating_System
(	O
every	O
member	O
has	O
a	O
complete	O
state	O
)	O
.	O
</s>
<s>
Operational	O
members	O
can	O
have	O
gaps	O
in	O
their	O
command	O
lists	O
when	O
using	O
Paxos	B-Operating_System
(	O
learners	O
merge	O
a	O
quorum	O
of	O
lists	O
in	O
Paxos	B-Operating_System
to	O
"	O
fill	O
"	O
these	O
gaps	O
)	O
.	O
</s>
<s>
With	O
Paxos	B-Operating_System
,	O
to	O
propose	O
multiple	O
commands	O
we	O
use	O
alpha>1	O
,	O
but	O
in	O
this	O
case	O
commands	O
can	O
be	O
committed	O
in	O
a	O
different	O
order	O
from	O
the	O
order	O
in	O
which	O
they	O
were	O
initiated	O
(	O
one	O
case	O
in	O
which	O
this	O
problematic	O
scenario	O
is	O
seen	O
involves	O
dueling	O
leaders	O
;	O
leader	O
A	O
proposes	O
commands	O
a1	O
and	O
a2	O
,	O
and	O
leader	O
B	O
proposes	O
commands	O
b1	O
and	O
b2	O
;	O
both	O
then	O
fail	O
and	O
leader	O
C	O
,	O
taking	O
over	O
,	O
ends	O
up	O
committing	O
b2	O
,	O
and	O
then	O
a1	O
:	O
an	O
outcome	O
that	O
might	O
not	O
be	O
desired	O
by	O
the	O
applications	O
that	O
initiated	O
the	O
requests	O
)	O
.	O
</s>
<s>
With	O
Gbcast	B-Operating_System
,	O
the	O
leader	O
can	O
initiate	O
multiple	O
commands	O
by	O
issuing	O
a	O
single	O
propose	O
that	O
describes	O
a	O
series	O
of	O
actions	O
.	O
</s>
<s>
With	O
Gbcast	B-Operating_System
,	O
a	O
command	O
is	O
delivered	O
in	O
the	O
view	O
in	O
which	O
it	O
was	O
initiated	O
.	O
</s>
<s>
Reconfigurable	O
Paxos	B-Operating_System
can	O
commit	O
a	O
command	O
in	O
a	O
slot	O
associated	O
with	O
a	O
membership	O
view	O
prior	O
to	O
the	O
active	O
membership	O
view	O
at	O
the	O
time	O
when	O
the	O
commit	O
occurs	O
.	O
</s>
<s>
Thus	O
,	O
in	O
Paxos	B-Operating_System
,	O
if	O
an	O
application	O
is	O
in	O
some	O
way	O
view	O
sensitive	O
,	O
commands	O
must	O
carry	O
a	O
view	O
identifier	O
,	O
so	O
that	O
recipients	O
can	O
determine	O
whether	O
or	O
not	O
the	O
command	O
is	O
still	O
executable	O
.	O
</s>
<s>
Gbcast	B-Operating_System
does	O
not	O
require	O
that	O
the	O
protocol	O
be	O
halted	O
when	O
changing	O
configurations	O
:	O
the	O
rate	O
of	O
new	O
proposals	O
can	O
be	O
constant	O
even	O
across	O
membership	O
changes	O
.	O
</s>
<s>
For	O
many	O
implementations	O
of	O
reconfigurable	O
Paxos	B-Operating_System
,	O
this	O
would	O
not	O
be	O
the	O
case	O
.	O
</s>
<s>
With	O
both	O
Gbcast	B-Operating_System
and	O
Paxos	B-Operating_System
,	O
reconfiguration	O
is	O
only	O
possible	O
if	O
a	O
quorum	O
of	O
the	O
prior	O
view	O
is	O
accessible	O
and	O
can	O
acknowledge	O
the	O
new	O
view	O
.	O
</s>
<s>
However	O
,	O
in	O
Paxos	B-Operating_System
,	O
the	O
requirement	O
also	O
extends	O
to	O
learning	O
the	O
outcomes	O
of	O
commands	O
proposed	O
for	O
slots	O
associated	O
with	O
the	O
old	O
view	O
.	O
</s>
<s>
In	O
practice	O
,	O
this	O
can	O
cause	O
the	O
Paxos	B-Operating_System
reconfiguration	O
computation	O
to	O
extend	O
over	O
a	O
longer	O
period	O
than	O
for	O
Gbcast	B-Operating_System
,	O
in	O
which	O
any	O
state	O
is	O
stored	O
within	O
the	O
application	O
,	O
not	O
a	O
long-lived	O
command	O
list	O
:	O
Paxos	B-Operating_System
cannot	O
discard	O
the	O
state	O
associated	O
with	O
an	O
old	O
view	O
until	O
the	O
new	O
view	O
is	O
active	O
and	O
any	O
replicas	O
have	O
learned	O
the	O
old	O
state	O
.	O
</s>
<s>
Gbcast	B-Operating_System
does	O
not	O
require	O
a	O
garbage	O
collection	O
protocol	O
because	O
,	O
as	O
each	O
message	O
or	O
view	O
is	O
committed	O
and	O
reported	O
to	O
the	O
application	O
it	O
can	O
be	O
discarded	O
.	O
</s>
<s>
Paxos	B-Operating_System
maintains	O
state	O
using	O
a	O
quorum	O
scheme	O
in	O
the	O
command	O
logs	O
at	O
its	O
acceptors	O
,	O
and	O
requires	O
a	O
garbage	O
collection	O
protocol	O
to	O
free	O
these	O
command	O
slots	O
once	O
the	O
outcome	O
is	O
committed	O
and	O
all	O
learners	O
(	O
replicas	O
)	O
have	O
learned	O
the	O
outcome	O
.	O
</s>
<s>
Both	O
Paxos	B-Operating_System
and	O
Gbcast	B-Operating_System
are	O
subject	O
to	O
the	O
FLP	O
impossibility	O
result	O
.	O
</s>
<s>
At	O
best	O
we	O
can	O
talk	O
about	O
the	O
conditions	O
under	O
which	O
liveness	B-Application
is	O
guaranteed	O
,	O
expressed	O
as	O
predicates	O
on	O
the	O
failure	O
detection	O
mechanism	O
:	O
if	O
the	O
condition	O
for	O
liveness	B-Application
holds	O
,	O
then	O
the	O
protocol	O
will	O
be	O
live	O
.	O
</s>
<s>
The	O
liveness	B-Application
conditions	O
of	O
Basic	O
Paxos	B-Operating_System
and	O
Gbcast	B-Operating_System
are	O
similar	O
but	O
not	O
identical	O
.	O
</s>
<s>
In	O
Gbcast	B-Operating_System
,	O
progress	O
will	O
never	O
resume	O
if	O
a	O
circle	O
of	O
mutual	O
suspicions	O
arises	O
,	O
as	O
noted	O
above	O
:	O
once	O
a	O
quorum	O
of	O
mutually	O
shunning	O
processes	O
arises	O
,	O
the	O
shunning	O
mechanism	O
makes	O
it	O
impossible	O
for	O
any	O
leader	O
to	O
obtain	O
a	O
quorum	O
of	O
promises	O
.	O
</s>
<s>
With	O
an	O
(	O
unmodified	O
)	O
Paxos	B-Operating_System
protocol	I-Operating_System
,	O
this	O
problem	O
will	O
not	O
arise	O
:	O
once	O
the	O
excessive	O
level	O
of	O
mutual	O
suspicions	O
ends	O
,	O
progress	O
resumes	O
.	O
</s>
<s>
Thus	O
Paxos	B-Operating_System
makes	O
progress	O
with	O
any	O
failure-detection	O
mechanism	O
satisfying	O
the	O
<>	O
W	O
condition	O
,	O
even	O
if	O
periods	O
arise	O
during	O
which	O
more	O
than	O
a	O
quorum	O
of	O
mutual	O
suspicions	O
occur	O
.	O
</s>
<s>
For	O
example	O
,	O
if	O
we	O
start	O
with	O
a	O
group	O
containing	O
 { A.B , C } 	O
and	O
cause	O
an	O
extended	O
network	O
partition	O
,	O
Paxos	B-Operating_System
would	O
resume	O
when	O
the	O
network	O
partition	O
resolves	O
but	O
Gbcast	B-Operating_System
will	O
shut	O
down	O
permanently	O
and	O
some	O
form	O
of	O
management	O
infrastructure	O
may	O
need	O
to	O
restart	O
the	O
system	O
.	O
</s>
<s>
In	O
Paxos	B-Operating_System
deployments	O
,	O
it	O
is	O
common	O
to	O
require	O
human	O
operator	O
intervention	O
to	O
reconfigure	O
Paxos	B-Operating_System
.	O
</s>
<s>
In	O
such	O
settings	O
,	O
Gbcast	B-Operating_System
may	O
be	O
able	O
to	O
make	O
progress	O
during	O
period	O
when	O
Paxos	B-Operating_System
cannot	O
.	O
</s>
<s>
Gbcast	B-Operating_System
can	O
continue	O
to	O
operate	O
with	O
even	O
a	O
single	O
member	O
.	O
</s>
<s>
Paxos	B-Operating_System
would	O
cease	O
to	O
make	O
progress	O
during	O
periods	O
when	O
less	O
than	O
a	O
quorum	O
of	O
its	O
view	O
are	O
active	O
.	O
</s>
<s>
Systems	O
such	O
as	O
Isis	O
that	O
implement	O
Gbcast	B-Operating_System
typically	O
provide	O
a	O
state	O
transfer	O
mechanism	O
:	O
at	O
the	O
instant	O
the	O
new	O
view	O
showing	O
some	O
joining	O
member	O
is	O
delivered	O
,	O
some	O
existing	O
member	O
makes	O
a	O
checkpoint	O
of	O
its	O
copy	O
of	O
the	O
group	O
state	O
.	O
</s>
<s>
State	O
transfer	O
is	O
needed	O
because	O
in	O
Gbcast	B-Operating_System
,	O
once	O
a	O
member	O
is	O
dropped	O
from	O
a	O
group	O
,	O
it	O
will	O
no	O
longer	O
receive	O
updates	O
.	O
</s>
<s>
Gbcast	B-Operating_System
is	O
typically	O
used	O
by	O
applications	O
that	O
maintain	O
their	O
state	O
in	O
memory	O
and	O
apply	O
updates	O
one	O
by	O
one	O
as	O
received	O
,	O
hence	O
once	O
a	O
gap	O
arises	O
,	O
a	O
replica	O
is	O
no	O
longer	O
useful	O
.	O
</s>
<s>
Notice	O
that	O
this	O
is	O
in	O
contrast	O
to	O
Paxos	B-Operating_System
.	O
</s>
<s>
The	O
Paxos	B-Operating_System
learner	O
algorithm	O
reads	O
multiple	O
histories	O
and	O
combines	O
them	O
to	O
fill	O
such	O
gaps	O
.	O
</s>
<s>
Thus	O
Paxos	B-Operating_System
will	O
normally	O
ride	O
out	O
transient	O
failures	O
,	O
continuing	O
to	O
operate	O
without	O
actually	O
dropping	O
the	O
failed	O
member	O
from	O
the	O
group	O
.	O
</s>
<s>
The	O
Gbcast	B-Operating_System
protocol	O
was	O
published	O
early	O
in	O
a	O
period	O
when	O
several	O
state	O
machine	O
protocols	O
capable	O
of	O
managing	O
their	O
own	O
membership	O
were	O
introduced	O
:	O
Gbcast	B-Operating_System
,	O
View-Stamped	O
Replication	O
(	O
Oki	O
and	O
Liskov	O
)	O
,	O
Basic	O
Paxos	B-Operating_System
(	O
Lamport	O
)	O
,	O
the	O
partial	O
synchrony	O
protocol	O
of	O
Dwork	O
,	O
Lynch	O
and	O
Stockmeyer	O
,	O
etc	O
.	O
</s>
<s>
Among	O
these	O
,	O
Gbcast	B-Operating_System
was	O
the	O
first	O
to	O
be	O
published	O
,	O
in	O
papers	O
that	O
appeared	O
in	O
1985	O
and	O
1987	O
;	O
the	O
others	O
were	O
published	O
starting	O
in	O
1988	O
.	O
</s>
<s>
One	O
could	O
thus	O
argue	O
that	O
Gbcast	B-Operating_System
was	O
really	O
the	O
first	O
Paxos	B-Operating_System
protocol	I-Operating_System
.	O
</s>
<s>
Such	O
a	O
statement	O
,	O
however	O
,	O
treats	O
"	O
Paxos	B-Operating_System
"	O
as	O
a	O
fairly	O
broad	O
term	O
covering	O
a	O
family	O
of	O
protocols	O
that	O
all	O
implement	O
state	B-Operating_System
machine	I-Operating_System
replication	I-Operating_System
,	O
all	O
support	O
dynamic	O
reconfiguration	O
of	O
their	O
membership	O
,	O
and	O
have	O
identical	O
correctness	O
properties	O
but	O
vary	O
in	O
their	O
liveness	B-Application
conditions	O
.	O
</s>
<s>
Under	O
this	O
definition	O
,	O
Gbcast	B-Operating_System
is	O
a	O
Paxos	B-Operating_System
protocol	I-Operating_System
.	O
</s>
<s>
Under	O
this	O
definition	O
,	O
Gbcast	B-Operating_System
is	O
not	O
a	O
Paxos	B-Operating_System
protocol	I-Operating_System
:	O
although	O
each	O
can	O
exhibit	O
the	O
same	O
runs	O
as	O
the	O
other	O
(	O
viewed	O
purely	O
in	O
terms	O
of	O
requests	O
from	O
the	O
application	O
and	O
notifications	O
to	O
the	O
application	O
)	O
,	O
they	O
have	O
similar	O
,	O
but	O
not	O
identical	O
,	O
liveness	B-Application
conditions	O
.	O
</s>
<s>
However	O
,	O
this	O
sort	O
of	O
stringent	O
definition	O
poses	O
a	O
different	O
problem	O
:	O
if	O
one	O
adopts	O
it	O
,	O
some	O
versions	O
of	O
Paxos	B-Operating_System
are	O
not	O
Paxos	B-Operating_System
protocols	I-Operating_System
.	O
</s>
<s>
For	O
example	O
,	O
"	O
Cheap	O
Paxos	B-Operating_System
"	O
and	O
"	O
Vertical	O
Paxos	B-Operating_System
"	O
are	O
not	O
bisimulation-equivalent	O
to	O
Basic	O
Paxos	B-Operating_System
.	O
</s>
