<s>
In	O
communication	O
networks	O
,	O
multiplexing	B-Architecture
and	O
the	O
division	O
of	O
scarce	O
resources	O
,	O
max-min	B-Algorithm
fairness	I-Algorithm
is	O
said	O
to	O
be	O
achieved	O
by	O
an	O
allocation	O
if	O
and	O
only	O
if	O
the	O
allocation	O
is	O
feasible	O
and	O
an	O
attempt	O
to	O
increase	O
the	O
allocation	O
of	O
any	O
participant	O
necessarily	O
results	O
in	O
the	O
decrease	O
in	O
the	O
allocation	O
of	O
some	O
other	O
participant	O
with	O
an	O
equal	O
or	O
smaller	O
allocation	O
.	O
</s>
<s>
In	O
best-effort	O
statistical	B-Algorithm
multiplexing	I-Algorithm
,	O
a	O
first-come	O
first-served	O
(	O
FCFS	O
)	O
scheduling	O
policy	O
is	O
often	O
used	O
.	O
</s>
<s>
The	O
advantage	O
with	O
max-min	B-Algorithm
fairness	I-Algorithm
over	O
FCFS	O
is	O
that	O
it	O
results	O
in	O
traffic	O
shaping	O
,	O
meaning	O
that	O
an	O
ill-behaved	O
flow	O
,	O
consisting	O
of	O
large	O
data	O
packets	O
or	O
bursts	O
of	O
many	O
packets	O
,	O
will	O
only	O
punish	O
itself	O
and	O
not	O
other	O
flows	O
.	O
</s>
<s>
Network	B-Protocol
congestion	I-Protocol
is	O
consequently	O
to	O
some	O
extent	O
avoided	O
.	O
</s>
<s>
Fair	B-Algorithm
queuing	I-Algorithm
is	O
an	O
example	O
of	O
a	O
max-min	B-Algorithm
fair	I-Algorithm
packet	O
scheduling	O
algorithm	O
for	O
statistical	B-Algorithm
multiplexing	I-Algorithm
and	O
best-effort	O
networks	O
,	O
since	O
it	O
gives	O
scheduling	O
priority	O
to	O
users	O
that	O
have	O
achieved	O
lowest	O
data	O
rate	O
since	O
they	O
became	O
active	O
.	O
</s>
<s>
In	O
case	O
of	O
equally	O
sized	O
data	O
packets	O
,	O
round-robin	B-Algorithm
scheduling	I-Algorithm
is	O
max-min	B-Algorithm
fair	I-Algorithm
.	O
</s>
<s>
Generally	O
,	O
policies	O
for	O
sharing	O
resources	O
that	O
are	O
characterized	O
by	O
low	O
level	O
of	O
fairness	B-Protocol
(	O
see	O
fairness	B-Protocol
measures	I-Protocol
)	O
provide	O
high	O
average	O
throughput	O
but	O
low	O
stability	O
in	O
the	O
service	O
quality	O
,	O
meaning	O
that	O
the	O
achieved	O
service	O
quality	O
is	O
varying	O
in	O
time	O
depending	O
on	O
the	O
behavior	O
of	O
other	O
users	O
.	O
</s>
<s>
Max-min	B-Algorithm
fair	I-Algorithm
resource	O
sharing	O
results	O
in	O
higher	O
average	O
throughput	O
(	O
or	O
system	O
spectral	O
efficiency	O
in	O
wireless	O
networks	O
)	O
and	O
better	O
utilization	O
of	O
the	O
resources	O
than	O
a	O
work-conserving	O
equal	O
sharing	O
policy	O
of	O
the	O
resources	O
.	O
</s>
<s>
In	O
equal	O
sharing	O
,	O
some	O
dataflows	B-Application
may	O
not	O
be	O
able	O
to	O
utilize	O
their	O
"	O
fair	O
share	O
"	O
of	O
the	O
resources	O
.	O
</s>
<s>
A	O
policy	O
for	O
equal	O
sharing	O
would	O
prevent	O
a	O
dataflow	B-Application
from	O
obtaining	O
more	O
resources	O
than	O
any	O
other	O
flow	O
,	O
and	O
from	O
utilizing	O
free	O
resources	O
in	O
the	O
network	O
.	O
</s>
<s>
On	O
the	O
other	O
hand	O
,	O
max-min	B-Algorithm
fairness	I-Algorithm
provides	O
lower	O
average	O
throughput	O
than	O
maximum	B-Algorithm
throughput	I-Algorithm
resource	I-Algorithm
management	I-Algorithm
,	O
where	O
the	O
least	O
expensive	O
flows	O
are	O
assigned	O
all	O
capacity	O
they	O
can	O
use	O
,	O
and	O
no	O
capacity	O
might	O
remain	O
for	O
the	O
most	O
expensive	O
flows	O
.	O
</s>
<s>
However	O
,	O
a	O
maximum	O
throughput	O
policy	O
would	O
result	O
in	O
starvation	B-Operating_System
of	O
expensive	O
flows	O
,	O
and	O
may	O
result	O
in	O
fewer	O
"	O
happy	O
customers	O
"	O
.	O
</s>
<s>
A	O
compromise	O
between	O
max-min	B-Algorithm
fairness	I-Algorithm
and	O
maximum	B-Algorithm
throughput	I-Algorithm
scheduling	I-Algorithm
is	O
proportional	B-Algorithm
fairness	I-Algorithm
,	O
where	O
the	O
resources	O
are	O
divided	O
with	O
the	O
goal	O
to	O
achieve	O
the	O
same	O
cost	O
to	O
each	O
user	O
,	O
or	O
to	O
minimize	O
the	O
maximum	O
cost	O
per	O
unit	O
that	O
a	O
dataflow	B-Application
reaches	O
.	O
</s>
<s>
Expensive	O
data	B-Application
flows	I-Application
achieve	O
lower	O
service	O
quality	O
than	O
others	O
in	O
proportional	B-Algorithm
fairness	I-Algorithm
,	O
but	O
do	O
not	O
suffer	O
from	O
starvation	B-Operating_System
.	O
</s>
<s>
Max-min	B-Algorithm
fairness	I-Algorithm
results	O
in	O
more	O
stable	O
service	O
quality	O
,	O
and	O
therefore	O
,	O
perhaps	O
,	O
more	O
"	O
happy	O
customers	O
"	O
.	O
</s>
<s>
Max-min	B-Algorithm
fairness	I-Algorithm
in	O
communication	O
networks	O
assumes	O
that	O
resources	O
(	O
capacities	O
of	O
communication	O
links	O
)	O
are	O
allocated	O
to	O
flows	O
in	O
advance	O
,	O
as	O
opposed	O
to	O
best-effort	O
networks	O
.	O
</s>
<s>
Consider	O
i	O
data	B-Application
flows	I-Application
,	O
sometimes	O
called	O
users	O
or	O
sources	O
.	O
</s>
<s>
Each	O
data	B-Application
flow	I-Application
has	O
a	O
defined	O
initial	O
node	O
,	O
a	O
destination	O
node	O
,	O
and	O
a	O
desired	O
data	O
rate	O
.	O
</s>
<s>
A	O
flow	O
on	O
its	O
path	O
through	O
the	O
network	O
may	O
be	O
divided	O
between	O
"	O
parallel	O
"	O
links	O
,	O
in	O
a	O
load	B-Application
balancing	I-Application
scheme	O
.	O
</s>
<s>
An	O
allocation	O
of	O
rate	O
x	O
is	O
“	O
max-min	B-Algorithm
fair	I-Algorithm
”	O
if	O
and	O
only	O
if	O
an	O
increase	O
of	O
any	O
rate	O
within	O
the	O
domain	O
of	O
feasible	O
allocations	O
must	O
be	O
at	O
the	O
cost	O
of	O
a	O
decrease	O
of	O
some	O
already	O
smaller	O
rate	O
.	O
</s>
<s>
Depending	O
on	O
the	O
problem	O
,	O
a	O
max-min	B-Algorithm
fair	I-Algorithm
allocation	O
may	O
or	O
may	O
not	O
exist	O
.	O
</s>
<s>
A	O
bottleneck	B-Protocol
link	I-Protocol
for	O
a	O
data	B-Application
flow	I-Application
i	O
is	O
a	O
link	O
that	O
is	O
fully	O
utilized	O
(	O
is	O
saturated	O
)	O
and	O
of	O
all	O
the	O
flows	O
sharing	O
this	O
link	O
,	O
the	O
data	B-Application
flow	I-Application
i	O
achieves	O
overall	O
maximum	O
data	O
rate	O
.	O
</s>
<s>
Note	O
that	O
this	O
definition	O
is	O
substantially	O
different	O
from	O
a	O
common	O
meaning	O
of	O
a	O
bottleneck	B-Protocol
.	O
</s>
<s>
Also	O
note	O
,	O
that	O
this	O
definition	O
does	O
not	O
forbid	O
a	O
single	O
bottleneck	B-Protocol
link	I-Protocol
to	O
be	O
shared	O
between	O
multiple	O
flows	O
.	O
</s>
<s>
A	O
data	O
rate	O
allocation	O
is	O
max-min	B-Algorithm
fair	I-Algorithm
if	O
and	O
only	O
if	O
a	O
data	B-Application
flow	I-Application
between	O
any	O
two	O
nodes	O
has	O
at	O
least	O
one	O
bottleneck	B-Protocol
link	I-Protocol
.	O
</s>
<s>
If	O
resources	O
are	O
allocated	O
in	O
advance	O
in	O
the	O
network	O
nodes	O
,	O
max-min	B-Algorithm
fairness	I-Algorithm
can	O
be	O
obtained	O
by	O
using	O
an	O
algorithm	O
of	O
progressive	O
filling	O
.	O
</s>
<s>
All	O
the	O
sources	O
that	O
are	O
stopped	O
have	O
a	O
bottleneck	B-Protocol
link	I-Protocol
.	O
</s>
<s>
Lastly	O
,	O
when	O
the	O
algorithm	O
terminates	O
,	O
all	O
sources	O
have	O
been	O
stopped	O
at	O
some	O
time	O
and	O
thus	O
have	O
a	O
bottleneck	B-Protocol
link	I-Protocol
.	O
</s>
<s>
This	O
allocation	O
is	O
max-min	B-Algorithm
fair	I-Algorithm
.	O
</s>
