<s>
Fairness	B-Protocol
measures	I-Protocol
or	O
metrics	O
are	O
used	O
in	O
network	B-Architecture
engineering	I-Architecture
to	O
determine	O
whether	O
users	O
or	O
applications	O
are	O
receiving	O
a	O
fair	O
share	O
of	O
system	O
resources	O
.	O
</s>
<s>
There	O
are	O
several	O
mathematical	O
and	O
conceptual	O
definitions	O
of	O
fairness	B-Protocol
.	O
</s>
<s>
Congestion	O
control	O
mechanisms	O
for	O
new	O
network	O
transmission	O
protocols	O
or	O
peer-to-peer	O
applications	O
must	O
interact	O
well	O
with	O
TCP	B-Protocol
.	O
</s>
<s>
TCP	B-Protocol
fairness	B-Protocol
requires	O
that	O
a	O
new	O
protocol	O
receive	O
a	O
no	O
larger	O
share	O
of	O
the	O
network	O
than	O
a	O
comparable	O
TCP	B-Protocol
flow	O
.	O
</s>
<s>
This	O
is	O
important	O
as	O
TCP	B-Protocol
is	O
the	O
dominant	O
transport	O
protocol	O
on	O
the	O
Internet	O
,	O
and	O
if	O
new	O
protocols	O
acquire	O
unfair	O
capacity	O
they	O
tend	O
to	O
cause	O
problems	O
such	O
as	O
congestion	O
collapse	O
.	O
</s>
<s>
This	O
was	O
the	O
case	O
with	O
the	O
first	O
versions	O
of	O
RealMedia	O
's	O
streaming	O
protocol	O
:	O
it	O
was	O
based	O
on	O
UDP	B-Protocol
and	O
was	O
widely	O
blocked	O
at	O
organizational	O
firewalls	O
until	O
a	O
TCP-based	O
version	O
was	O
developed	O
.	O
</s>
<s>
TCP	B-Protocol
throughput	O
unfairness	O
over	O
WiFi	O
is	O
a	O
critical	O
problem	O
and	O
needs	O
further	O
investigations	O
.	O
</s>
<s>
rates	O
the	O
fairness	B-Protocol
of	O
a	O
set	O
of	O
values	O
where	O
there	O
are	O
users	O
,	O
is	O
the	O
throughput	O
for	O
the	O
th	O
connection	O
,	O
and	O
is	O
the	O
sample	O
coefficient	O
of	O
variation	O
.	O
</s>
<s>
This	O
gives	O
an	O
allocation	O
with	O
a	O
fairness	B-Protocol
close	O
to	O
F	O
,	O
and	O
the	O
allocation	O
can	O
then	O
be	O
refined	O
to	O
get	O
even	O
closer	O
.	O
</s>
<s>
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
flow	O
necessarily	O
results	O
in	O
the	O
decrease	O
in	O
the	O
allocation	O
of	O
some	O
other	O
flow	O
with	O
an	O
equal	O
or	O
smaller	O
allocation	O
.	O
</s>
<s>
A	O
max-min	B-Algorithm
fair	I-Algorithm
allocation	O
is	O
achieved	O
when	O
bandwidth	B-Algorithm
is	O
allocated	O
equally	O
and	O
in	O
infinitesimal	O
increments	O
to	O
all	O
flows	O
until	O
one	O
is	O
satisfied	O
,	O
then	O
amongst	O
the	O
remainder	O
of	O
the	O
flows	O
and	O
so	O
on	O
until	O
all	O
flows	O
are	O
satisfied	O
or	O
the	O
bandwidth	B-Algorithm
is	O
exhausted	O
.	O
</s>
<s>
In	O
packet	B-Application
radio	I-Application
wireless	B-General_Concept
networks	I-General_Concept
,	O
The	O
fairly	O
shared	O
spectrum	B-Protocol
efficiency	I-Protocol
(	O
FSSE	O
)	O
can	O
be	O
used	O
as	O
a	O
combined	O
measure	O
of	O
fairness	B-Protocol
and	O
system	B-Protocol
spectrum	I-Protocol
efficiency	I-Protocol
.	O
</s>
<s>
The	O
system	O
spectral	B-Protocol
efficiency	I-Protocol
is	O
the	O
aggregate	O
throughput	O
in	O
the	O
network	O
divided	O
by	O
the	O
utilized	O
radio	B-Algorithm
bandwidth	I-Algorithm
in	O
hertz	O
.	O
</s>
<s>
The	O
FSSE	O
is	O
the	O
portion	O
of	O
the	O
system	O
spectral	B-Protocol
efficiency	I-Protocol
that	O
is	O
shared	O
equally	O
among	O
all	O
active	O
users	O
(	O
with	O
at	O
least	O
one	O
backlogged	O
data	O
packet	O
in	O
queue	O
or	O
under	O
transmission	O
)	O
.	O
</s>
<s>
In	O
case	O
of	O
scheduling	B-Operating_System
starvation	I-Operating_System
,	O
the	O
FSSE	O
would	O
be	O
zero	O
during	O
certain	O
time	O
intervals	O
.	O
</s>
<s>
In	O
case	O
of	O
equally	O
shared	O
resources	O
,	O
the	O
FSSE	O
would	O
be	O
equal	O
to	O
the	O
system	B-Protocol
spectrum	I-Protocol
efficiency	I-Protocol
.	O
</s>
<s>
To	O
achieve	O
max-min	B-Algorithm
fairness	I-Algorithm
,	O
the	O
FSSE	O
should	O
be	O
maximized	O
.	O
</s>
<s>
FSSE	O
is	O
useful	O
especially	O
when	O
analyzing	O
advanced	O
radio	B-Protocol
resource	I-Protocol
management	I-Protocol
(	O
RRM	O
)	O
schemes	O
,	O
for	O
example	O
channel	O
adaptive	O
scheduling	O
,	O
for	O
cellular	O
networks	O
with	O
best-effort	O
packet	O
data	O
service	O
.	O
</s>
<s>
In	O
such	O
system	O
it	O
may	O
be	O
tempting	O
to	O
optimize	O
the	O
spectrum	B-Protocol
efficiency	I-Protocol
(	O
i.e.	O
</s>
<s>
However	O
,	O
that	O
might	O
result	O
in	O
scheduling	B-Operating_System
starvation	I-Operating_System
of	O
"	O
expensive	O
"	O
users	O
at	O
far	O
distance	O
from	O
the	O
access	O
point	O
,	O
whenever	O
another	O
active	O
user	O
is	O
closer	O
to	O
the	O
same	O
or	O
an	O
adjacent	O
access	O
point	O
.	O
</s>
<s>
Optimizing	O
the	O
FSSE	O
results	O
in	O
a	O
compromise	O
between	O
fairness	B-Protocol
(	O
especially	O
avoiding	O
scheduling	B-Operating_System
starvation	I-Operating_System
)	O
and	O
achieving	O
high	O
spectral	B-Protocol
efficiency	I-Protocol
.	O
</s>
<s>
If	O
the	O
cost	O
of	O
each	O
user	O
is	O
known	O
,	O
in	O
terms	O
of	O
consumed	O
resources	O
per	O
transferred	O
information	O
bit	O
,	O
the	O
FSSE	O
measure	O
may	O
be	O
redefined	O
to	O
reflect	O
proportional	B-Algorithm
fairness	I-Algorithm
.	O
</s>
<s>
In	O
a	O
proportional	B-Algorithm
fair	I-Algorithm
system	O
,	O
this	O
"	O
proportionally	B-Algorithm
fair	I-Algorithm
shared	O
spectrum	B-Protocol
efficiency	I-Protocol
"	O
(	O
or	O
"	O
fairly	O
shared	O
radio	O
resource	O
cost	O
"	O
)	O
is	O
maximized	O
.	O
</s>
<s>
This	O
policy	O
is	O
less	O
fair	O
since	O
"	O
expensive	O
"	O
users	O
are	O
given	O
lower	O
throughput	O
than	O
others	O
,	O
but	O
still	O
scheduling	B-Operating_System
starvation	I-Operating_System
is	O
avoided	O
.	O
</s>
<s>
The	O
idea	O
of	O
QoE	O
fairness	B-Protocol
is	O
to	O
quantify	O
fairness	B-Protocol
among	O
users	O
by	O
considering	O
the	O
Quality	O
of	O
Experience	O
(	O
QoE	O
)	O
as	O
perceived	O
by	O
the	O
end	O
user	O
.	O
</s>
<s>
Several	O
approaches	O
have	O
been	O
proposed	O
to	O
ensure	O
network-wide	O
QoE	O
fairness	B-Protocol
especially	O
for	O
adaptive	O
video	O
streaming	O
.	O
</s>
<s>
Hence	O
,	O
fairness	B-Protocol
measures	I-Protocol
like	O
Jain	B-Protocol
's	I-Protocol
fairness	I-Protocol
index	I-Protocol
cannot	O
be	O
applied	O
,	O
as	O
the	O
measurement	O
scale	O
requires	O
to	O
be	O
a	O
ratio	O
scale	O
with	O
a	O
clearly	O
defined	O
zero	O
point	O
(	O
see	O
examples	O
of	O
misuse	O
for	O
coefficients	O
of	O
variation	O
)	O
.	O
</s>
<s>
While	O
the	O
coefficient	O
of	O
variation	O
is	O
meaningless	O
,	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
provides	O
a	O
measure	O
of	O
the	O
dispersion	O
of	O
QoE	O
among	O
users	O
.	O
</s>
<s>
have	O
proposed	O
a	O
QoE	O
Fairness	B-Protocol
index	I-Protocol
which	O
considers	O
the	O
lower	O
bound	O
and	O
the	O
higher	O
bound	O
of	O
the	O
rating	O
scale	O
.	O
</s>
<s>
The	O
QoE	O
fairness	B-Protocol
index	I-Protocol
has	O
some	O
desired	O
properties	O
like	O
scale	O
and	O
metric	O
independence	O
.	O
</s>
<s>
Any	O
linear	O
transformation	O
of	O
the	O
QoE	O
values	O
does	O
not	O
change	O
the	O
value	O
of	O
the	O
fairness	B-Protocol
index	I-Protocol
.	O
</s>
<s>
The	O
fairness	B-Protocol
index	I-Protocol
is	O
bounded	O
in	O
the	O
interval	O
with	O
1	O
indicating	O
perfect	O
QoE	O
fairness	B-Protocol
–	O
all	O
users	O
experience	O
the	O
same	O
quality	O
.	O
</s>
<s>
Product-based	O
fairness	B-Protocol
indices	O
are	O
based	O
on	O
the	O
general	O
fairness	B-Protocol
formulation	O
:	O
</s>
<s>
As	O
Jain	B-Protocol
's	I-Protocol
fairness	I-Protocol
index	I-Protocol
is	O
said	O
to	O
be	O
unduly	O
sensitive	O
under	O
atypical	O
conditions	O
,	O
the	O
product-based	O
fairness	B-Protocol
can	O
be	O
defined	O
arbitrarily	O
to	O
obtain	O
a	O
desired	O
sensitivity	O
.	O
</s>
<s>
The	O
linear	O
product-based	O
fairness	B-Protocol
index	I-Protocol
has	O
and	O
looks	O
as	O
follows	O
:	O
</s>
<s>
The	O
G	O
's	O
fairness	B-Protocol
index	I-Protocol
is	O
primarily	O
used	O
by	O
telecom	O
operators	O
in	O
the	O
context	O
of	O
bandwidth	B-Algorithm
allocation	O
.	O
</s>
<s>
G	O
's	O
th-order	O
fairness	B-Protocol
index	I-Protocol
scales	O
the	O
fractions	O
of	O
the	O
product-based	O
fairness	B-Protocol
index	I-Protocol
by	O
a	O
powered	O
sine	O
transformation	O
:	O
</s>
<s>
As	O
such	O
,	O
the	O
sensitivity	O
of	O
the	O
product-based	O
fairness	B-Protocol
is	O
decreased	O
for	O
values	O
close	O
to	O
,	O
while	O
the	O
index	O
still	O
outputs	O
a	O
value	O
between	O
0	O
and	O
1	O
.	O
</s>
<s>
Compared	O
to	O
Jain	B-Protocol
's	I-Protocol
fairness	I-Protocol
index	I-Protocol
,	O
G	O
's	O
fairness	B-Protocol
index	I-Protocol
yields	O
smaller	O
values	O
,	O
it	O
is	O
more	O
sensitive	O
to	O
potential	O
unfair	O
bandwidth	B-Algorithm
distribution	O
and	O
can	O
go	O
to	O
zero	O
.	O
</s>
<s>
In	O
the	O
context	O
of	O
networks	O
,	O
the	O
latter	O
is	O
an	O
advantage	O
over	O
Jain	B-Protocol
's	I-Protocol
fairness	I-Protocol
index	I-Protocol
when	O
a	O
few	O
values	O
in	O
a	O
set	O
drop	O
to	O
low	O
levels	O
.	O
</s>
<s>
Moreover	O
,	O
Jain	B-Protocol
's	I-Protocol
fairness	I-Protocol
index	I-Protocol
is	O
deemed	O
as	O
an	O
average	O
user	O
perception	O
of	O
fairness	B-Protocol
whereas	O
G	O
's	O
fairness	B-Protocol
index	I-Protocol
is	O
focused	O
more	O
on	O
equality	O
within	O
a	O
group	O
.	O
</s>
<s>
Whereas	O
G	O
's	O
fairness	B-Protocol
index	I-Protocol
inflates	O
the	O
fractions	O
closer	O
to	O
,	O
the	O
Bossaer	O
's	O
fairness	B-Protocol
index	I-Protocol
inflates	O
the	O
fractions	O
closer	O
to	O
0	O
.	O
</s>
<s>
Bossaer	O
's	O
th-order	O
transformation	O
function	O
yields	O
the	O
fairness	B-Protocol
index	I-Protocol
:	O
</s>
<s>
The	O
linear	O
product-based	O
fairness	B-Protocol
indices	O
is	O
a	O
special	O
case	O
of	O
Bossaer	O
's	O
where	O
.	O
</s>
<s>
Causal	O
fairness	B-Protocol
measures	I-Protocol
the	O
frequency	O
with	O
which	O
two	O
nearly	O
identical	O
users	O
or	O
applications	O
who	O
differ	O
only	O
in	O
a	O
set	O
of	O
characteristics	O
with	O
respect	O
to	O
which	O
resource	O
allocation	O
must	O
be	O
fair	O
receive	O
identical	O
treatment	O
.	O
</s>
<s>
Several	O
other	O
metrics	O
have	O
been	O
defined	O
,	O
such	O
as	O
Worst	O
Case	O
Fairness	B-Protocol
.	O
</s>
