Information Technology Reference
In-Depth Information
bisection method because the mean packet delay
Delay
is a monotonic decreasing function
ij
i
d
. The details of determining the channel requirement
d
of the number of channels
for all
ij
1,
ij N
≤≤
are given as follows.
low
ij
up
ij
d
d
Delay
>
Delay
*
1.
Select
and
such that
and
ij
low
dd
=
ij
ij
*
Delay
≤
Delay
.
ij
up
dd
=
ij
ij
up
low
up
2.
If
(
dd
−
)
=
then
1
dd
=
and STOP.
ij
ij
ij
ij
up
low
3.
While
(
dd
−
)
>
do the following
1
ij
ij
4.
Begin
⎢
low
up
⎥
dd
+
ij
ij
mid
ij
5.
d
=
⎢
⎥
2
⎢
⎥
⎣
⎦
mid
Delay
=
Delay
*
dd
=
6.
If
, then
and STOP.
ij
mid
ij
ij
dd
=
ij
ij
*
low
mid
7.
Else if
Delay
>
Delay
, then
d
=
d
.
ij
ij
ij
mid
dd
=
ij
ij
*
dd
up
=
mid
8.
Else if
Delay
<
Delay
, then
.
ij
ij
ij
mid
dd
=
ij
ij
9.
End_while
10.
dd
=
up
and STOP.
ij
ij
We now consider a specific traffic model based on the above framework. Let the packet
arrival process from node
i
to node
j
be Poisson with mean packet rate
i
α
, and the packet
size be exponentially distributed with mean packet transmission time
1 β
. The
communication subsystem from node
i
to node
j
can be modeled as an
Md
queueing
M
/
/
ij
system. The mean packet delay
Delay
can be found to be [25]:
ij
d
(
d
ρ
)
C
ij
1
ij
ij
(1)
=
+
Delay
ij
2
β
dd
!(1
−
ρ
)
β
ij
ij
ij
where
ρ αβ
=
d
and
ij
ij
ij
1
(2)
C
=
d
d
−
1
k
(
d
ρ
)
(
d
ρ
)
ij
ij
∑
ij
ij
ij
ij
+
k
!
d
!(1
−
ρ
)
k
=
0
ij
ij
