<s>
Banker	B-Operating_System
's	I-Operating_System
algorithm	I-Operating_System
is	O
a	O
resource	B-Algorithm
allocation	I-Algorithm
and	O
deadlock	B-Operating_System
avoidance	O
algorithm	O
developed	O
by	O
Edsger	O
Dijkstra	O
that	O
tests	O
for	O
safety	O
by	O
simulating	O
the	O
allocation	O
of	O
predetermined	O
maximum	O
possible	O
amounts	O
of	O
all	O
resources	B-General_Concept
,	O
and	O
then	O
makes	O
an	O
"	O
s-state	O
"	O
check	O
to	O
test	O
for	O
possible	O
deadlock	B-Operating_System
conditions	O
for	O
all	O
other	O
pending	O
activities	O
,	O
before	O
deciding	O
whether	O
allocation	O
should	O
be	O
allowed	O
to	O
continue	O
.	O
</s>
<s>
The	O
algorithm	O
was	O
developed	O
in	O
the	O
design	O
process	O
for	O
the	O
THE	B-Operating_System
operating	I-Operating_System
system	I-Operating_System
and	O
originally	O
described	O
(	O
in	O
Dutch	O
)	O
in	O
EWD108	O
.	O
</s>
<s>
When	O
a	O
new	O
process	O
enters	O
a	O
system	O
,	O
it	O
must	O
declare	O
the	O
maximum	O
number	O
of	O
instances	O
of	O
each	O
resource	O
type	O
that	O
it	O
may	O
ever	O
claim	O
;	O
clearly	O
,	O
that	O
number	O
may	O
not	O
exceed	O
the	O
total	O
number	O
of	O
resources	B-General_Concept
in	O
the	O
system	O
.	O
</s>
<s>
Also	O
,	O
when	O
a	O
process	O
gets	O
all	O
its	O
requested	O
resources	B-General_Concept
it	O
must	O
return	O
them	O
in	O
a	O
finite	O
amount	O
of	O
time	O
.	O
</s>
<s>
For	O
the	O
Banker	B-Operating_System
's	I-Operating_System
algorithm	I-Operating_System
to	O
work	O
,	O
it	O
needs	O
to	O
know	O
three	O
things	O
:	O
</s>
<s>
Resources	B-General_Concept
may	O
be	O
allocated	O
to	O
a	O
process	O
only	O
if	O
the	O
amount	O
of	O
resources	B-General_Concept
requested	O
is	O
less	O
than	O
or	O
equal	O
to	O
the	O
amount	O
available	O
;	O
otherwise	O
,	O
the	O
process	O
waits	O
until	O
resources	B-General_Concept
are	O
available	O
.	O
</s>
<s>
Some	O
of	O
the	O
resources	B-General_Concept
that	O
are	O
tracked	O
in	O
real	O
systems	O
are	O
memory	B-General_Concept
,	O
semaphores	B-Operating_System
and	O
interface	B-Application
access	O
.	O
</s>
<s>
The	O
Banker	B-Operating_System
's	I-Operating_System
algorithm	I-Operating_System
derives	O
its	O
name	O
from	O
the	O
fact	O
that	O
this	O
algorithm	O
could	O
be	O
used	O
in	O
a	O
banking	O
system	O
to	O
ensure	O
that	O
the	O
bank	O
does	O
not	O
run	O
out	O
of	O
resources	B-General_Concept
,	O
because	O
the	O
bank	O
would	O
never	O
allocate	O
its	O
money	O
in	O
such	O
a	O
way	O
that	O
it	O
can	O
no	O
longer	O
satisfy	O
the	O
needs	O
of	O
all	O
its	O
customers	O
.	O
</s>
<s>
By	O
using	O
the	O
Banker	B-Operating_System
's	I-Operating_System
algorithm	I-Operating_System
,	O
the	O
bank	O
ensures	O
that	O
when	O
customers	O
request	O
money	O
the	O
bank	O
never	O
leaves	O
a	O
safe	O
state	O
.	O
</s>
<s>
Basic	O
data	O
structures	O
to	O
be	O
maintained	O
to	O
implement	O
the	O
Banker	B-Operating_System
's	I-Operating_System
algorithm	I-Operating_System
:	O
</s>
<s>
Available	O
:	O
A	O
vector	O
of	O
length	O
m	O
indicates	O
the	O
number	O
of	O
available	O
resources	B-General_Concept
of	O
each	O
type	O
.	O
</s>
<s>
Allocation	O
:	O
An	O
×	O
matrix	O
defines	O
the	O
number	O
of	O
resources	B-General_Concept
of	O
each	O
type	O
currently	O
allocated	O
to	O
each	O
process	O
.	O
</s>
<s>
Total	O
system	B-General_Concept
resources	I-General_Concept
are	O
:	O
</s>
<s>
Available	O
system	B-General_Concept
resources	I-General_Concept
are	O
:	O
</s>
<s>
Processes	O
(	O
currently	O
allocated	O
resources	B-General_Concept
)	O
:	O
</s>
<s>
Processes	O
(	O
maximum	O
resources	B-General_Concept
)	O
:	O
</s>
<s>
Processes	O
(	O
possibly	O
needed	O
resources	B-General_Concept
)	O
:	O
</s>
<s>
Since	O
the	O
system	O
cannot	O
know	O
when	O
a	O
process	O
will	O
terminate	O
,	O
or	O
how	O
many	O
resources	B-General_Concept
it	O
will	O
have	O
requested	O
by	O
then	O
,	O
the	O
system	O
assumes	O
that	O
all	O
processes	O
will	O
eventually	O
attempt	O
to	O
acquire	O
their	O
stated	O
maximum	O
resources	B-General_Concept
and	O
terminate	O
soon	O
afterward	O
.	O
</s>
<s>
This	O
is	O
a	O
reasonable	O
assumption	O
in	O
most	O
cases	O
since	O
the	O
system	O
is	O
not	O
particularly	O
concerned	O
with	O
how	O
long	O
each	O
process	O
runs	O
(	O
at	O
least	O
not	O
from	O
a	O
deadlock	B-Operating_System
avoidance	O
perspective	O
)	O
.	O
</s>
<s>
Given	O
that	O
assumption	O
,	O
the	O
algorithm	O
determines	O
if	O
a	O
state	O
is	O
safe	O
by	O
trying	O
to	O
find	O
a	O
hypothetical	O
set	O
of	O
requests	O
by	O
the	O
processes	O
that	O
would	O
allow	O
each	O
to	O
acquire	O
its	O
maximum	O
resources	B-General_Concept
and	O
then	O
terminate	O
(	O
returning	O
its	O
resources	B-General_Concept
to	O
the	O
system	O
)	O
.	O
</s>
<s>
We	O
can	O
show	O
that	O
the	O
state	O
given	O
in	O
the	O
previous	O
example	O
is	O
a	O
safe	O
state	O
by	O
showing	O
that	O
it	O
is	O
possible	O
for	O
each	O
process	O
to	O
acquire	O
its	O
maximum	O
resources	B-General_Concept
and	O
then	O
terminate	O
.	O
</s>
<s>
P3	O
acquires	O
1	O
B	O
and	O
4	O
C	O
resources	B-General_Concept
and	O
terminates	O
.	O
</s>
<s>
When	O
the	O
system	O
receives	O
a	O
request	O
for	O
resources	B-General_Concept
,	O
it	O
runs	O
the	O
Banker	B-Operating_System
's	I-Operating_System
algorithm	I-Operating_System
to	O
determine	O
if	O
it	O
is	O
safe	O
to	O
grant	O
the	O
request	O
.	O
</s>
<s>
Whether	O
the	O
system	O
denies	O
or	O
postpones	O
an	O
impossible	O
or	O
unsafe	O
request	O
is	O
a	O
decision	O
specific	O
to	O
the	B-Operating_System
operating	I-Operating_System
system	I-Operating_System
.	O
</s>
<s>
Processes	O
(	O
currently	O
allocated	O
resources	B-General_Concept
)	O
:	O
</s>
<s>
Processes	O
(	O
maximum	O
resources	B-General_Concept
)	O
:	O
</s>
<s>
Available	O
system	B-General_Concept
resources	I-General_Concept
:	O
</s>
<s>
Processes	O
(	O
currently	O
allocated	O
resources	B-General_Concept
)	O
:	O
</s>
<s>
Processes	O
(	O
maximum	O
resources	B-General_Concept
)	O
:	O
</s>
<s>
Like	O
the	O
other	O
algorithms	O
,	O
the	O
Banker	B-Operating_System
's	I-Operating_System
algorithm	I-Operating_System
has	O
some	O
limitations	O
when	O
implemented	O
.	O
</s>
<s>
In	O
most	O
systems	O
,	O
this	O
information	O
is	O
unavailable	O
,	O
making	O
it	O
impossible	O
to	O
implement	O
the	O
Banker	B-Operating_System
's	I-Operating_System
algorithm	I-Operating_System
.	O
</s>
<s>
Moreover	O
,	O
the	O
requirement	O
that	O
a	O
process	O
will	O
eventually	O
release	O
all	O
its	O
resources	B-General_Concept
(	O
when	O
the	O
process	O
terminates	O
)	O
is	O
sufficient	O
for	O
the	O
correctness	O
of	O
the	O
algorithm	O
,	O
however	O
it	O
is	O
not	O
sufficient	O
for	O
a	O
practical	O
system	O
.	O
</s>
<s>
Waiting	O
for	O
hours	O
(	O
or	O
even	O
days	O
)	O
for	O
resources	B-General_Concept
to	O
be	O
released	O
is	O
usually	O
not	O
acceptable	O
.	O
</s>
