<s>
Weighted	B-Algorithm
fair	I-Algorithm
queueing	I-Algorithm
(	O
WFQ	B-Algorithm
)	O
is	O
a	O
network	B-Application
scheduling	I-Application
algorithm	O
.	O
</s>
<s>
WFQ	B-Algorithm
is	O
both	O
a	O
packet-based	O
implementation	O
of	O
the	O
generalized	B-Algorithm
processor	I-Algorithm
sharing	I-Algorithm
(	O
GPS	O
)	O
policy	O
,	O
and	O
a	O
natural	O
extension	O
of	O
fair	B-Algorithm
queuing	I-Algorithm
(	O
FQ	O
)	O
.	O
</s>
<s>
Whereas	O
FQ	O
shares	O
the	O
link	O
's	O
capacity	O
in	O
equal	O
subparts	O
,	O
WFQ	B-Algorithm
allows	O
schedulers	O
to	O
specify	O
,	O
for	O
each	O
flow	O
,	O
which	O
fraction	O
of	O
the	O
capacity	O
will	O
be	O
given	O
.	O
</s>
<s>
Weighted	B-Algorithm
fair	I-Algorithm
queuing	I-Algorithm
is	O
also	O
known	O
as	O
packet-by-packet	O
GPS	O
(	O
PGPS	O
or	O
P-GPS	O
)	O
since	O
it	O
approximates	O
generalized	B-Algorithm
processor	I-Algorithm
sharing	I-Algorithm
"	O
to	O
within	O
one	O
packet	O
transmission	O
time	O
,	O
regardless	O
of	O
the	O
arrival	O
patterns.	O
"	O
</s>
<s>
By	O
regulating	O
the	O
WFQ	B-Algorithm
weights	O
dynamically	O
,	O
WFQ	B-Algorithm
can	O
be	O
utilized	O
for	O
controlling	O
the	O
quality	O
of	O
service	O
,	O
for	O
example	O
,	O
to	O
achieve	O
guaranteed	O
data	O
rate	O
.	O
</s>
<s>
Proportionally	B-Algorithm
fair	I-Algorithm
behavior	O
can	O
be	O
achieved	O
by	O
setting	O
the	O
weights	O
to	O
,	O
where	O
is	O
the	O
cost	O
per	O
data	O
bit	O
of	O
data	O
flow	O
.	O
</s>
<s>
For	O
example	O
in	O
CDMA	B-Protocol
spread	O
spectrum	O
cellular	O
networks	O
,	O
the	O
cost	O
may	O
be	O
the	O
required	O
energy	O
(	O
the	O
interference	O
level	O
)	O
,	O
and	O
in	O
dynamic	B-Protocol
channel	I-Protocol
allocation	I-Protocol
systems	O
,	O
the	O
cost	O
may	O
be	O
the	O
number	O
of	O
nearby	O
base	O
station	O
sites	O
that	O
can	O
not	O
use	O
the	O
same	O
frequency	O
channel	O
,	O
in	O
view	O
to	O
avoid	O
co-channel	O
interference	O
.	O
</s>
<s>
In	O
WFQ	B-Algorithm
,	O
a	O
scheduler	O
handling	O
flows	O
is	O
configured	O
with	O
one	O
weight	O
for	O
each	O
flow	O
.	O
</s>
<s>
A	O
WFQ	B-Algorithm
scheduler	O
where	O
all	O
weights	O
are	O
equal	O
is	O
a	O
FQ	O
scheduler	O
.	O
</s>
<s>
Like	O
all	O
fair-queuing	O
schedulers	O
,	O
each	O
flow	O
is	O
protected	O
from	O
the	O
others	O
,	O
and	O
it	O
can	O
be	O
proved	O
that	O
if	O
a	O
data	O
flow	O
is	O
leaky	B-Algorithm
bucket	I-Algorithm
constrained	O
,	O
an	O
end-to-end	O
delay	O
bound	O
can	O
be	O
guaranteed	O
.	O
</s>
<s>
The	O
algorithm	O
of	O
WFQ	B-Algorithm
is	O
very	O
similar	O
to	O
the	O
one	O
of	O
FQ	O
.	O
</s>
<s>
WFQ	B-Algorithm
,	O
under	O
the	O
name	O
PGPS	O
,	O
has	O
been	O
designed	O
as	O
"	O
an	O
excellent	O
approximation	O
to	O
GPS	O
"	O
,	O
and	O
it	O
has	O
been	O
proved	O
that	O
it	O
approximates	O
GPS	O
"	O
to	O
within	O
one	O
packet	O
transmission	O
time	O
,	O
regardless	O
of	O
the	O
arrival	O
patterns.	O
"	O
</s>
<s>
Since	O
WFQ	B-Algorithm
implementation	O
is	O
similar	O
to	O
fair	B-Algorithm
queuing	I-Algorithm
,	O
it	O
has	O
the	O
same	O
O(log(n )	O
)	O
complexity	O
,	O
where	O
n	O
is	O
the	O
number	O
of	O
flows	O
.	O
</s>
<s>
After	O
WFQ	B-Algorithm
,	O
several	O
other	O
implementations	O
of	O
GPS	O
have	O
been	O
defined	O
.	O
</s>
<s>
Even	O
if	O
WFQ	B-Algorithm
is	O
at	O
most	O
"	O
one	O
packet	O
"	O
late	O
w.r.t.	O
</s>
<s>
The	O
Worst-case	O
Fair	O
Weighted	B-Algorithm
Fair	I-Algorithm
Queueing	I-Algorithm
(	O
WF2Q	O
)	O
fixes	O
it	O
by	O
adding	O
a	O
virtual	O
start	O
of	O
service	O
to	O
each	O
packet	O
,	O
and	O
selects	O
a	O
packet	O
only	O
if	O
its	O
virtual	O
start	O
of	O
service	O
is	O
not	O
less	O
than	O
the	O
current	O
time	O
.	O
</s>
<s>
Then	O
,	O
other	O
approximations	O
of	O
GPS	O
have	O
been	O
defined	O
with	O
less	O
complexity	O
,	O
like	O
deficit	B-Algorithm
round	I-Algorithm
robin	I-Algorithm
.	O
</s>
