Information Technology Reference
In-Depth Information
Fig. 3.1
An example of three
links under the protocol
interference model
T
3
R
3
R
1
T
1
T
2
R
2
I
i
define the interference ranges of transmitters. Let
denote the set of receivers
I
i
denote the set of transmitters that
causes interference to receiver
R
i
. In a time-slotted system, each user
i
contends for
the opportunity of data transmission with probability
q
i
that transmitter
T
i
causes interference to, and
[0, 1] in a time slot. If
multiple interfering links contend in the same time slot, a collision occurs and no
link can grab the transmission opportunity. Then the probability
b
i
that user
i
can
grab the transmission opportunity is given by
∈
q
i
j
∈
I
i
b
i
(
q
i
,
q
−
i
)
=
(1
−
q
j
)
.
(3.1)
We assume that the individual utility of user
i
is given by
u
i
(
q
i
,
q
i
)
=
log (
ʸ
i
b
i
)
−
c
i
q
i
(3.2)
−
where
ʸ
i
>
0 represents user
i
's efficiency of utilizing the transmission opportunity
(e.g., transmission rate), and
c
i
>
0 represents user
i
's cost of contention. Note that
the logarithmic function is widely used for modeling the utility of wireless users
[
3
,
4
]. Then, under the SGUM framework, we define the SGUM-based random
access control game as
G
(
N
,
{
q
i
}
,
{
f
i
}
), where
⊛
⊝
ʸ
i
q
i
j
∈
I
i
⊞
⊠
−
f
i
(
q
i
,
q
−
i
)
=
log
(1
−
q
j
)
c
i
q
i
⊡
⊣
⊛
⊝
⊞
⊠
−
⊤
⊦
ʸ
j
q
j
k
∈
I
j
s
ij
log
(1
−
p
k
)
c
j
q
j
.
(3.3)
j
=
i
