Information Technology Reference
In-Depth Information
To make
D
(
p
) finite, the coecient of
α
should be zero. i.e.
p
e
c
e
=1
.
e
Then
D
(
p
)=
e
p
e
b
e
+
k
p
e
t
e
.
min
t
k
∈T
k
(5)
e
Its dual problem is
maximize
p≥
0
D
(
p
) subject to
e
p
e
c
e
=1
.
(6)
This dual problem can be resolved into independent sub-problems on different
sessions of applications with a distributed algorithm,
p
ij
t
ij
,
minimize
t
k
∈T
k
(7)
i
j
=
i
The aforementioned solution is the interactive optimization algorithm between
ISP and a P2P application, i.e. the P2P application solves the subproblem (7)
independently and delivers the optimal result
t
k
to iTracker, after which iTracker
solves the main problem (6) to update
p
e
.
Assumption A
In the following analysis, we suppose that there exists
t
k
T
k
∈
that makes
b
e
+
k
t
e
<c
e
,
E
, i.e. there exists feasible flow solution
t
k
that
makes the restraint on the link capacity strictly feasible.
∀
e
∈
2.2 Properties of P-Distance in P4P
t
e
}
Theorem 1.
Suppose that
is the solution
to
(6)
. Then there exists at least one link
e
whose link utilization is maximal and
its corresponding
p
e
>
0
.The
p
e
whose corresponding links utilization doesn't
achieve maximum is 0.
{
is the solution to
(4)
,and
{
p
e
}
Proof:
(4) is an instance of convex programming, and according to assump-
tion A, we know that the Slater constraint specification is true; hence, the strong
dual theory is true. As a result, the solution of (4) and of its dual problem (6)
satisfy the following:
b
e
+
k
t
e
≤
αc
e
,
∀
e
∈
E
(8a)
1
−
p
e
c
e
=0
(8b)
e
p
e
≥
0
,
∀
e
∈
E
(8c)
p
e
(
b
e
+
k
t
e
−
αc
e
)=0
,
∀
e
∈
E
(8d)