<s>
Paxos	B-Operating_System
is	O
a	O
family	O
of	O
protocols	O
for	O
solving	O
consensus	B-Operating_System
in	O
a	O
network	O
of	O
unreliable	O
or	O
fallible	O
processors	O
.	O
</s>
<s>
Consensus	B-Operating_System
is	O
the	O
process	O
of	O
agreeing	O
on	O
one	O
result	O
among	O
a	O
group	O
of	O
participants	O
.	O
</s>
<s>
Consensus	B-Operating_System
protocols	O
are	O
the	O
basis	O
for	O
the	O
state	B-Operating_System
machine	I-Operating_System
replication	I-Operating_System
approach	O
to	O
distributed	B-Architecture
computing	I-Architecture
,	O
as	O
suggested	O
by	O
Leslie	O
Lamport	O
and	O
surveyed	O
by	O
Fred	O
Schneider	O
.	O
</s>
<s>
State	B-Operating_System
machine	I-Operating_System
replication	I-Operating_System
is	O
a	O
technique	O
for	O
converting	O
an	O
algorithm	O
into	O
a	O
fault-tolerant	O
,	O
distributed	O
implementation	O
.	O
</s>
<s>
The	O
Paxos	B-Operating_System
protocol	I-Operating_System
was	O
first	O
submitted	O
in	O
1989	O
and	O
named	O
after	O
a	O
fictional	O
legislative	O
consensus	B-Operating_System
system	O
used	O
on	O
the	O
Paxos	B-Operating_System
island	O
in	O
Greece	O
,	O
where	O
Lamport	O
wrote	O
that	O
the	O
parliament	O
had	O
to	O
function	O
"	O
even	O
though	O
legislators	O
continually	O
wandered	O
in	O
and	O
out	O
of	O
the	O
parliamentary	O
Chamber	O
"	O
.	O
</s>
<s>
The	O
Paxos	B-Operating_System
family	O
of	O
protocols	O
includes	O
a	O
spectrum	O
of	O
trade-offs	O
between	O
the	O
number	O
of	O
processors	O
,	O
number	O
of	O
message	O
delays	O
before	O
learning	O
the	O
agreed	O
value	O
,	O
the	O
activity	O
level	O
of	O
individual	O
participants	O
,	O
number	O
of	O
messages	O
sent	O
,	O
and	O
types	O
of	O
failures	O
.	O
</s>
<s>
Although	O
no	O
deterministic	O
fault-tolerant	O
consensus	B-Operating_System
protocol	O
can	O
guarantee	O
progress	O
in	O
an	O
asynchronous	O
network	O
(	O
a	O
result	O
proved	O
in	O
a	O
paper	O
by	O
Fischer	O
,	O
Lynch	O
and	O
Paterson	O
)	O
,	O
Paxos	B-Operating_System
guarantees	O
safety	O
(	O
consistency	O
)	O
,	O
and	O
the	O
conditions	O
that	O
could	O
prevent	O
it	O
from	O
making	O
progress	O
are	O
difficult	O
to	O
provoke	O
.	O
</s>
<s>
Paxos	B-Operating_System
is	O
usually	O
used	O
where	O
durability	O
is	O
required	O
(	O
for	O
example	O
,	O
to	O
replicate	O
a	O
file	O
or	O
a	O
database	O
)	O
,	O
in	O
which	O
the	O
amount	O
of	O
durable	O
state	O
could	O
be	O
large	O
.	O
</s>
<s>
In	O
1988	O
,	O
Lynch	O
,	O
Dwork	O
and	O
Stockmeyer	O
had	O
demonstrated	O
the	O
solvability	O
of	O
consensus	B-Operating_System
in	O
a	O
broad	O
family	O
of	O
"	O
partially	O
synchronous	O
"	O
systems	O
.	O
</s>
<s>
Paxos	B-Operating_System
has	O
strong	O
similarities	O
to	O
a	O
protocol	O
used	O
for	O
agreement	O
in	O
"	O
viewstamped	O
replication	O
"	O
,	O
first	O
published	O
by	O
Oki	O
and	O
Liskov	O
in	O
1988	O
,	O
in	O
the	O
context	O
of	O
distributed	O
transactions	O
.	O
</s>
<s>
Notwithstanding	O
this	O
prior	O
work	O
,	O
Paxos	B-Operating_System
offered	O
a	O
particularly	O
elegant	O
formalism	O
,	O
and	O
included	O
one	O
of	O
the	O
earliest	O
proofs	O
of	O
safety	O
for	O
a	O
fault-tolerant	O
distributed	B-Operating_System
consensus	I-Operating_System
protocol	O
.	O
</s>
<s>
Reconfigurable	O
state	B-Architecture
machines	I-Architecture
have	O
strong	O
ties	O
to	O
prior	O
work	O
on	O
reliable	O
group	O
multicast	O
protocols	O
that	O
support	O
dynamic	O
group	O
membership	O
,	O
for	O
example	O
Birman	O
's	O
work	O
in	O
1985	O
and	O
1987	O
on	O
the	O
virtually	O
synchronous	O
gbcast	B-Operating_System
protocol	O
.	O
</s>
<s>
However	O
,	O
gbcast	B-Operating_System
is	O
unusual	O
in	O
supporting	O
durability	O
and	O
addressing	O
partitioning	O
failures	O
.	O
</s>
<s>
Most	O
reliable	O
multicast	O
protocols	O
lack	O
these	O
properties	O
,	O
which	O
are	O
required	O
for	O
implementations	O
of	O
the	O
state	B-Operating_System
machine	I-Operating_System
replication	I-Operating_System
model	O
.	O
</s>
<s>
Paxos	B-Operating_System
protocols	I-Operating_System
are	O
members	O
of	O
a	O
theoretical	O
class	O
of	O
solutions	O
to	O
a	O
problem	O
formalized	O
as	O
uniform	O
agreement	O
with	O
crash	O
failures	O
.	O
</s>
<s>
Derecho	O
,	O
a	O
C++	O
software	O
library	O
for	O
cloud-scale	O
state	B-Operating_System
machine	I-Operating_System
replication	I-Operating_System
,	O
offers	O
a	O
Paxos	B-Operating_System
protocol	I-Operating_System
that	O
has	O
been	O
integrated	O
with	O
self-managed	O
virtually	O
synchronous	O
membership	O
.	O
</s>
<s>
This	O
protocol	O
matches	O
the	O
Keidar	O
and	O
Shraer	O
optimality	O
bounds	O
,	O
and	O
maps	O
efficiently	O
to	O
modern	O
remote	B-General_Concept
DMA	I-General_Concept
(	O
RDMA	B-General_Concept
)	O
datacenter	O
hardware	O
(	O
but	O
uses	O
TCP	O
if	O
RDMA	B-General_Concept
is	O
not	O
available	O
)	O
.	O
</s>
<s>
In	O
order	O
to	O
simplify	O
the	O
presentation	O
of	O
Paxos	B-Operating_System
,	O
the	O
following	O
assumptions	O
and	O
definitions	O
are	O
made	O
explicit	O
.	O
</s>
<s>
(	O
That	O
is	O
,	O
Byzantine	B-Operating_System
failures	I-Operating_System
do	O
n't	O
occur	O
.	O
</s>
<s>
See	O
Byzantine	O
Paxos	B-Operating_System
for	O
a	O
solution	O
that	O
tolerates	O
failures	O
that	O
arise	O
from	O
arbitrary/malicious	O
behavior	O
of	O
the	O
processes	O
.	O
)	O
</s>
<s>
(	O
That	O
is	O
,	O
Byzantine	B-Operating_System
failures	I-Operating_System
do	O
n't	O
occur	O
.	O
</s>
<s>
See	O
Byzantine	O
Paxos	B-Operating_System
for	O
a	O
solution	O
which	O
tolerates	O
corrupted	O
messages	O
that	O
arise	O
from	O
arbitrary/malicious	O
behavior	O
of	O
the	O
messaging	O
channels	O
.	O
)	O
</s>
<s>
In	O
general	O
,	O
a	O
consensus	B-Operating_System
algorithm	I-Operating_System
can	O
make	O
progress	O
using	O
processors	O
,	O
despite	O
the	O
simultaneous	O
failure	O
of	O
any	O
processors	O
:	O
in	O
other	O
words	O
,	O
the	O
number	O
of	O
non-faulty	O
processes	O
must	O
be	O
strictly	O
greater	O
than	O
the	O
number	O
of	O
faulty	O
processes	O
.	O
</s>
<s>
For	O
Paxos	B-Operating_System
protocols	I-Operating_System
,	O
these	O
reconfigurations	O
can	O
be	O
handled	O
as	O
separate	O
configurations	O
.	O
</s>
<s>
Paxos	B-Operating_System
describes	O
the	O
actions	O
of	O
the	O
processors	O
by	O
their	O
roles	O
in	O
the	O
protocol	O
:	O
client	O
,	O
acceptor	O
,	O
proposer	O
,	O
learner	O
,	O
and	O
leader	O
.	O
</s>
<s>
Client	O
The	O
Client	O
issues	O
a	O
request	O
to	O
the	O
distributed	B-Architecture
system	I-Architecture
,	O
and	O
waits	O
for	O
a	O
response	O
.	O
</s>
<s>
Leader	O
Paxos	B-Operating_System
requires	O
a	O
distinguished	O
Proposer	O
(	O
called	O
the	O
leader	O
)	O
to	O
make	O
progress	O
.	O
</s>
<s>
Quorums	O
express	O
the	O
safety	O
(	O
or	O
consistency	O
)	O
properties	O
of	O
Paxos	B-Operating_System
by	O
ensuring	O
at	O
least	O
some	O
surviving	O
processor	O
retains	O
knowledge	O
of	O
the	O
results	O
.	O
</s>
<s>
The	O
value	O
corresponding	O
to	O
a	O
numbered	O
proposal	O
can	O
be	O
computed	O
as	O
part	O
of	O
running	O
the	O
Paxos	B-Operating_System
protocol	I-Operating_System
,	O
but	O
need	O
not	O
be	O
.	O
</s>
<s>
In	O
order	O
to	O
guarantee	O
safety	O
(	O
also	O
called	O
"	O
consistency	O
"	O
)	O
,	O
Paxos	B-Operating_System
defines	O
three	O
properties	O
and	O
ensures	O
the	O
first	O
two	O
are	O
always	O
held	O
,	O
regardless	O
of	O
the	O
pattern	O
of	O
failures	O
:	O
</s>
<s>
Note	O
that	O
Paxos	B-Operating_System
is	O
not	O
guaranteed	O
to	O
terminate	O
,	O
and	O
thus	O
does	O
not	O
have	O
the	O
liveness	O
property	O
.	O
</s>
<s>
As	O
Paxos	B-Operating_System
's	O
point	O
is	O
to	O
ensure	O
fault	O
tolerance	O
and	O
it	O
guarantees	O
safety	O
,	O
it	O
cannot	O
also	O
guarantee	O
liveness	O
.	O
</s>
<s>
In	O
most	O
deployments	O
of	O
Paxos	B-Operating_System
,	O
each	O
participating	O
process	O
acts	O
in	O
three	O
roles	O
;	O
Proposer	O
,	O
Acceptor	O
and	O
Learner	O
.	O
</s>
<s>
The	O
benefit	O
of	O
the	O
Paxos	B-Operating_System
protocols	I-Operating_System
(	O
including	O
implementations	O
with	O
merged	O
roles	O
)	O
is	O
the	O
guarantee	O
of	O
its	O
safety	O
properties	O
.	O
</s>
<s>
A	O
typical	O
implementation	O
's	O
message	O
flow	O
is	O
covered	O
in	O
the	O
section	O
Multi-Paxos	O
.	O
</s>
<s>
This	O
protocol	O
is	O
the	O
most	O
basic	O
of	O
the	O
Paxos	B-Operating_System
family	O
.	O
</s>
<s>
Each	O
"	O
instance	O
"	O
(	O
or	O
"	O
execution	O
"	O
)	O
of	O
the	O
basic	O
Paxos	B-Operating_System
protocol	I-Operating_System
decides	O
on	O
a	O
single	O
output	O
value	O
.	O
</s>
<s>
A	O
Proposer	O
should	O
not	O
initiate	O
Paxos	B-Operating_System
if	O
it	O
cannot	O
communicate	O
with	O
at	O
least	O
a	O
Quorum	O
of	O
Acceptors	O
.	O
</s>
<s>
It	O
does	O
not	O
have	O
to	O
answer	O
in	O
this	O
case	O
for	O
Paxos	B-Operating_System
to	O
work	O
.	O
</s>
<s>
However	O
,	O
for	O
the	O
sake	O
of	O
optimization	O
,	O
sending	O
a	O
denial	O
(	O
Nack	B-Protocol
)	O
response	O
would	O
tell	O
the	O
Proposer	O
that	O
it	O
can	O
stop	O
its	O
attempt	O
to	O
create	O
consensus	B-Operating_System
with	O
proposal	O
n	O
.	O
</s>
<s>
If	O
an	O
Acceptor	O
receives	O
an	O
Accept	O
message	O
,	O
(	O
n	O
,	O
v	O
)	O
,	O
from	O
a	O
Proposer	O
,	O
it	O
must	O
accept	O
it	O
if	O
and	O
only	O
if	O
it	O
has	O
not	O
already	O
promised	O
(	O
in	O
Phase	O
1b	O
of	O
the	O
Paxos	B-Operating_System
protocol	I-Operating_System
)	O
to	O
only	O
consider	O
proposals	O
having	O
an	O
identifier	O
greater	O
than	O
n	O
.	O
</s>
<s>
Note	O
that	O
consensus	B-Operating_System
is	O
achieved	O
when	O
a	O
majority	O
of	O
Acceptors	O
accept	O
the	O
same	O
identifier	O
number	O
(	O
rather	O
than	O
the	O
same	O
value	O
)	O
.	O
</s>
<s>
However	O
,	O
the	O
Paxos	B-Operating_System
protocol	I-Operating_System
guarantees	O
that	O
consensus	B-Operating_System
is	O
permanent	O
and	O
the	O
chosen	O
value	O
is	O
immutable	O
.	O
</s>
<s>
Notice	O
that	O
a	O
Proposer	O
in	O
Paxos	B-Operating_System
could	O
propose	O
"	O
I	O
am	O
the	O
leader	O
,	O
"	O
(	O
or	O
,	O
for	O
example	O
,	O
"	O
Proposer	O
X	O
is	O
the	O
leader	O
"	O
)	O
.	O
</s>
<s>
Because	O
of	O
the	O
agreement	O
and	O
validity	O
guarantees	O
of	O
Paxos	B-Operating_System
,	O
if	O
accepted	O
by	O
a	O
Quorum	O
,	O
then	O
the	O
Proposer	O
is	O
now	O
known	O
to	O
be	O
the	O
leader	O
to	O
all	O
other	O
nodes	O
.	O
</s>
<s>
The	O
following	O
diagrams	O
represent	O
several	O
cases/situations	O
of	O
the	O
application	O
of	O
the	O
Basic	O
Paxos	B-Operating_System
protocol	I-Operating_System
.	O
</s>
<s>
Some	O
cases	O
show	O
how	O
the	O
Basic	O
Paxos	B-Operating_System
protocol	I-Operating_System
copes	O
with	O
the	O
failure	O
of	O
certain	O
(	O
redundant	O
)	O
components	O
of	O
the	O
distributed	B-Architecture
system	I-Architecture
.	O
</s>
<s>
In	O
this	O
case	O
,	O
the	O
Basic	O
Paxos	B-Operating_System
protocol	I-Operating_System
still	O
succeeds	O
.	O
</s>
<s>
In	O
the	O
following	O
case	O
,	O
one	O
of	O
the	O
(	O
redundant	O
)	O
Learners	O
fails	O
,	O
but	O
the	O
Basic	O
Paxos	B-Operating_System
protocol	I-Operating_System
still	O
succeeds	O
.	O
</s>
<s>
This	O
Proposer	O
then	O
gets	O
all	O
Acceptors	O
to	O
accept	O
V2	O
,	O
achieving	O
consensus	B-Operating_System
.	O
</s>
<s>
As	O
such	O
,	O
even	O
though	O
the	O
Proposer	O
does	O
n't	O
see	O
the	O
existing	O
consensus	B-Operating_System
,	O
the	O
Proposer	O
's	O
only	O
option	O
is	O
to	O
propose	O
the	O
value	O
already	O
agreed	O
upon	O
.	O
</s>
<s>
New	O
Proposers	O
can	O
continually	O
increase	O
the	O
identifier	O
to	O
restart	O
the	O
process	O
,	O
but	O
the	O
consensus	B-Operating_System
can	O
never	O
be	O
changed	O
.	O
</s>
<s>
A	O
typical	O
deployment	O
of	O
Paxos	B-Operating_System
requires	O
a	O
continuous	O
stream	O
of	O
agreed	O
values	O
acting	O
as	O
commands	O
to	O
a	O
distributed	O
state	B-Architecture
machine	I-Architecture
.	O
</s>
<s>
If	O
each	O
command	O
is	O
the	O
result	O
of	O
a	O
single	O
instance	O
of	O
the	O
Basic	O
Paxos	B-Operating_System
protocol	I-Operating_System
,	O
a	O
significant	O
amount	O
of	O
overhead	O
would	O
result	O
.	O
</s>
<s>
Multi-Paxos	O
reduces	O
the	O
failure-free	O
message	O
delay	O
(	O
proposal	O
to	O
learning	O
)	O
from	O
4	O
delays	O
to	O
2	O
delays	O
.	O
</s>
<s>
In	O
the	O
following	O
diagram	O
,	O
only	O
one	O
instance	O
(	O
or	O
"	O
execution	O
"	O
)	O
of	O
the	O
basic	O
Paxos	B-Operating_System
protocol	I-Operating_System
,	O
with	O
an	O
initial	O
Leader	O
(	O
a	O
Proposer	O
)	O
,	O
is	O
shown	O
.	O
</s>
<s>
Note	O
that	O
a	O
Multi-Paxos	O
consists	O
of	O
several	O
instances	O
of	O
the	O
basic	O
Paxos	B-Operating_System
protocol	I-Operating_System
.	O
</s>
<s>
In	O
this	O
case	O
,	O
subsequent	O
instances	O
of	O
the	O
basic	O
Paxos	B-Operating_System
protocol	I-Operating_System
(	O
represented	O
by	O
I+1	O
)	O
use	O
the	O
same	O
leader	O
,	O
so	O
the	O
phase	O
1	O
(	O
of	O
these	O
subsequent	O
instances	O
of	O
the	O
basic	O
Paxos	B-Operating_System
protocol	I-Operating_System
)	O
,	O
which	O
consist	O
of	O
the	O
Prepare	O
and	O
Promise	O
sub-phases	O
,	O
is	O
skipped	O
.	O
</s>
<s>
A	O
common	O
deployment	O
of	O
the	O
Multi-Paxos	O
consists	O
in	O
collapsing	O
the	O
role	O
of	O
the	O
Proposers	O
,	O
Acceptors	O
and	O
Learners	O
to	O
"	O
Servers	O
"	O
.	O
</s>
<s>
The	O
following	O
diagram	O
represents	O
the	O
first	O
"	O
instance	O
"	O
of	O
a	O
basic	O
Paxos	B-Operating_System
protocol	I-Operating_System
,	O
when	O
the	O
roles	O
of	O
the	O
Proposer	O
,	O
Acceptor	O
and	O
Learner	O
are	O
collapsed	O
to	O
a	O
single	O
role	O
,	O
called	O
the	O
"	O
Server	O
"	O
.	O
</s>
<s>
In	O
the	O
subsequent	O
instances	O
of	O
the	O
basic	O
Paxos	B-Operating_System
protocol	I-Operating_System
,	O
with	O
the	O
same	O
leader	O
as	O
in	O
the	O
previous	O
instances	O
of	O
the	O
basic	O
Paxos	B-Operating_System
protocol	I-Operating_System
,	O
the	O
phase	O
1	O
can	O
be	O
skipped	O
.	O
</s>
<s>
Cheap	O
Paxos	B-Operating_System
extends	O
Basic	O
Paxos	B-Operating_System
to	O
tolerate	O
F	O
failures	O
with	O
F+1	O
main	O
processors	O
and	O
F	O
auxiliary	O
processors	O
by	O
dynamically	O
reconfiguring	O
after	O
each	O
failure	O
.	O
</s>
<s>
Fast	O
Paxos	B-Operating_System
generalizes	O
Basic	O
Paxos	B-Operating_System
to	O
reduce	O
end-to-end	O
message	O
delays	O
.	O
</s>
<s>
In	O
Basic	O
Paxos	B-Operating_System
,	O
the	O
message	O
delay	O
from	O
client	O
request	O
to	O
learning	O
is	O
3	O
message	O
delays	O
.	O
</s>
<s>
Fast	O
Paxos	B-Operating_System
allows	O
2	O
message	O
delays	O
,	O
but	O
requires	O
that	O
(	O
1	O
)	O
the	O
system	O
be	O
composed	O
of	O
3f+	O
1	O
acceptors	O
to	O
tolerate	O
up	O
to	O
f	O
faults	O
(	O
instead	O
of	O
the	O
classic	O
2f+1	O
)	O
,	O
and	O
(	O
2	O
)	O
the	O
Client	O
to	O
send	O
its	O
request	O
to	O
multiple	O
destinations	O
.	O
</s>
<s>
The	O
Acceptors	O
would	O
respond	O
as	O
in	O
Basic	O
Paxos	B-Operating_System
,	O
sending	O
Accepted	O
messages	O
to	O
the	O
leader	O
and	O
every	O
Learner	O
achieving	O
two	O
message	O
delays	O
from	O
Client	O
to	O
Learner	O
.	O
</s>
<s>
Generalized	O
consensus	B-Operating_System
explores	O
the	O
relationship	O
between	O
the	O
operations	O
of	O
the	O
replicated	O
state	B-Architecture
machine	I-Architecture
and	O
the	O
consensus	B-Operating_System
protocol	O
that	O
implements	O
it	O
.	O
</s>
<s>
The	O
main	O
discovery	O
involves	O
optimizations	O
of	O
Paxos	B-Operating_System
when	O
conflicting	O
proposals	O
could	O
be	O
applied	O
in	O
any	O
order	O
.	O
</s>
<s>
i.e.	O
,	O
when	O
the	O
proposed	O
operations	O
are	O
commutative	O
operations	O
for	O
the	O
state	B-Architecture
machine	I-Architecture
.	O
</s>
<s>
In	O
order	O
to	O
illustrate	O
Generalized	O
Paxos	B-Operating_System
,	O
the	O
example	O
below	O
shows	O
a	O
message	O
flow	O
between	O
two	O
concurrently	O
executing	O
clients	O
and	O
a	O
replicated	O
state	B-Architecture
machine	I-Architecture
implementing	O
read/write	O
operations	O
over	O
two	O
distinct	O
registers	O
A	O
and	O
B	O
.	O
</s>
<s>
The	O
above	O
message	O
flow	O
shows	O
us	O
that	O
Generalized	O
Paxos	B-Operating_System
can	O
leverage	O
operation	O
semantics	O
to	O
avoid	O
collisions	O
when	O
the	O
spontaneous	O
ordering	O
of	O
the	O
network	O
fails	O
.	O
</s>
<s>
This	O
allows	O
the	O
protocol	O
to	O
be	O
in	O
practice	O
quicker	O
than	O
Fast	O
Paxos	B-Operating_System
.	O
</s>
<s>
However	O
,	O
when	O
a	O
collision	O
occurs	O
,	O
Generalized	O
Paxos	B-Operating_System
needs	O
two	O
additional	O
round	O
trips	O
to	O
recover	O
.	O
</s>
<s>
This	O
makes	O
the	O
protocol	O
more	O
expensive	O
than	O
Paxos	B-Operating_System
when	O
conflicts	O
are	O
frequent	O
.	O
</s>
<s>
Hopefully	O
two	O
possible	O
refinements	O
of	O
Generalized	O
Paxos	B-Operating_System
are	O
possible	O
to	O
improve	O
recovery	O
time	O
.	O
</s>
<s>
Paxos	B-Operating_System
may	O
also	O
be	O
extended	O
to	O
support	O
arbitrary	O
failures	O
of	O
the	O
participants	O
,	O
including	O
lying	O
,	O
fabrication	O
of	O
messages	O
,	O
collusion	O
with	O
other	O
participants	O
,	O
selective	O
non-participation	O
,	O
etc	O
.	O
</s>
<s>
These	O
types	O
of	O
failures	O
are	O
called	O
Byzantine	B-Operating_System
failures	I-Operating_System
,	O
after	O
the	O
solution	O
popularized	O
by	O
Lamport	O
.	O
</s>
<s>
Byzantine	O
Paxos	B-Operating_System
introduced	O
by	O
Castro	O
and	O
Liskov	O
adds	O
an	O
extra	O
message	O
(	O
Verify	O
)	O
which	O
acts	O
to	O
distribute	O
knowledge	O
and	O
verify	O
the	O
actions	O
of	O
the	O
other	O
processors	O
:	O
</s>
<s>
Fast	O
Byzantine	O
Paxos	B-Operating_System
introduced	O
by	O
Martin	O
and	O
Alvisi	O
removes	O
this	O
extra	O
delay	O
,	O
since	O
the	O
client	O
sends	O
commands	O
directly	O
to	O
the	O
Acceptors	O
.	O
</s>
<s>
Note	O
the	O
Accepted	O
message	O
in	O
Fast	O
Byzantine	O
Paxos	B-Operating_System
is	O
sent	O
to	O
all	O
Acceptors	O
and	O
all	O
Learners	O
,	O
while	O
Fast	O
Paxos	B-Operating_System
sends	O
Accepted	O
messages	O
only	O
to	O
Learners	O
)	O
:	O
</s>
<s>
With	O
the	O
emergence	O
of	O
very	O
high	O
speed	O
reliable	O
datacenter	O
networks	O
that	O
support	O
remote	B-General_Concept
DMA	I-General_Concept
(	O
RDMA	B-General_Concept
)	O
,	O
there	O
has	O
been	O
substantial	O
interest	O
in	O
optimizing	O
Paxos	B-Operating_System
to	O
leverage	O
hardware	O
offloading	O
,	O
in	O
which	O
the	O
network	O
interface	O
card	O
and	O
network	O
routers	O
provide	O
reliability	O
and	O
network-layer	O
congestion	O
control	O
,	O
freeing	O
the	O
host	O
CPU	O
for	O
other	O
tasks	O
.	O
</s>
<s>
The	O
is	O
an	O
open-source	O
Paxos	B-Operating_System
implementation	O
that	O
explores	O
this	O
option	O
.	O
</s>
<s>
Derecho	O
offers	O
both	O
a	O
classic	O
Paxos	B-Operating_System
,	O
with	O
data	O
durability	O
across	O
full	O
shutdown/restart	O
sequences	O
,	O
and	O
vertical	O
Paxos	B-Operating_System
(	O
atomic	O
multicast	O
)	O
,	O
for	O
in-memory	O
replication	O
and	O
state-machine	B-Architecture
synchronization	O
.	O
</s>
<s>
The	O
Paxos	B-Operating_System
protocols	I-Operating_System
employed	O
by	O
Derecho	O
needed	O
to	O
be	O
adapted	O
to	O
maximize	O
asynchronous	O
data	O
streaming	O
and	O
remove	O
other	O
sources	O
of	O
delay	O
on	O
the	O
leader	O
's	O
critical	O
path	O
.	O
</s>
<s>
So	O
doing	O
enables	O
Derecho	O
to	O
sustain	O
the	O
full	O
bidirectional	O
RDMA	B-General_Concept
data	O
rate	O
.	O
</s>
<s>
In	O
contrast	O
,	O
although	O
traditional	O
Paxos	B-Operating_System
protocols	I-Operating_System
can	O
be	O
migrated	O
to	O
an	O
RDMA	B-General_Concept
network	O
by	O
simply	O
mapping	O
the	O
message	O
send	O
operations	O
to	O
native	O
RDMA	B-General_Concept
operations	O
,	O
doing	O
so	O
leaves	O
round-trip	O
delays	O
on	O
the	O
critical	O
path	O
.	O
</s>
<s>
In	O
high-speed	O
RDMA	B-General_Concept
networks	O
,	O
even	O
small	O
delays	O
can	O
be	O
large	O
enough	O
to	O
prevent	O
utilization	O
of	O
the	O
full	O
potential	O
bandwidth	O
.	O
</s>
<s>
Google	O
uses	O
the	O
Paxos	B-Operating_System
algorithm	I-Operating_System
in	O
their	O
Chubby	B-Operating_System
distributed	B-Operating_System
lock	I-Operating_System
service	I-Operating_System
in	O
order	O
to	O
keep	O
replicas	O
consistent	O
in	O
case	O
of	O
failure	O
.	O
</s>
<s>
Chubby	B-Operating_System
is	O
used	O
by	O
Bigtable	B-Application
which	O
is	O
now	O
in	O
production	O
in	O
Google	O
Analytics	O
and	O
other	O
products	O
.	O
</s>
<s>
Google	B-Operating_System
Spanner	I-Operating_System
and	O
Megastore	O
use	O
the	O
Paxos	B-Operating_System
algorithm	I-Operating_System
internally	O
.	O
</s>
<s>
The	O
uses	O
Paxos	B-Operating_System
to	O
maintain	O
replicas	O
for	O
an	O
open	O
access	O
system	O
that	O
enables	O
users	O
to	O
create	O
fault-tolerant	O
objects	O
.	O
</s>
<s>
IBM	O
supposedly	O
uses	O
the	O
Paxos	B-Operating_System
algorithm	I-Operating_System
in	O
their	O
IBM	B-Application
SAN	I-Application
Volume	I-Application
Controller	I-Application
product	O
to	O
implement	O
a	O
general	O
purpose	O
fault-tolerant	O
virtual	O
machine	O
used	O
to	O
run	O
the	O
configuration	O
and	O
control	O
components	O
of	O
the	O
storage	B-Application
virtualization	I-Application
services	O
offered	O
by	O
the	O
cluster	O
.	O
</s>
<s>
Microsoft	O
uses	O
Paxos	B-Operating_System
in	O
the	O
from	O
Bing	O
,	O
and	O
in	O
Windows	O
Server	O
Failover	O
Clustering	O
.	O
</s>
<s>
WANdisco	B-General_Concept
have	O
implemented	O
Paxos	B-Operating_System
within	O
their	O
DConE	O
active-active	O
replication	O
technology	O
.	O
</s>
<s>
XtreemFS	B-Application
uses	O
a	O
Paxos-based	O
lease	B-Operating_System
negotiation	O
algorithm	O
for	O
fault-tolerant	O
and	O
consistent	O
replication	O
of	O
file	O
data	O
and	O
metadata	O
.	O
</s>
<s>
Heroku	O
uses	O
which	O
implements	O
Paxos	B-Operating_System
for	O
its	O
consistent	O
distributed	O
data	O
store	O
.	O
</s>
<s>
Ceph	B-Operating_System
uses	O
Paxos	B-Operating_System
as	O
part	O
of	O
the	O
monitor	O
processes	O
to	O
agree	O
which	O
OSDs	O
are	O
up	O
and	O
in	O
the	O
cluster	O
.	O
</s>
<s>
The	O
MariaDB	O
Xpand	O
distributed	O
SQL	O
database	O
uses	O
Paxos	B-Operating_System
for	O
.	O
</s>
<s>
Amazon	O
DynamoDB	O
uses	O
the	O
Paxos	B-Operating_System
algorithm	I-Operating_System
for	O
.	O
</s>
