Information Technology Reference
In-Depth Information
a set of points. In fact, a PID can also represent PoP, or a set of points with the
same congestion state. In this study, each PID represents an aggregation point.
In particular,
T
k
is made up of
t
k
that satisfy the constraint condition as
follows,
t
ij
≤
u
i
,
∀
i,
(2a)
j
:
j
=
i
t
ji
≤ d
i
, ∀i,
(2b)
j
:
j
=
i
t
ij
≥
0
,
∀
i
=
j,
(2c)
ij
j
=
i
t
ij
≥
ρ
k
t
ij
,
∀
i, j
=
i,
(2d)
t
ij
≥
β
∗
OPT,
(2e)
i
j
=
i
where
u
i
denotes the aggregation uploading capacity from PID
−
i
to other
PIDs in session
k
,and
d
i
denotes the aggregation downloading capacity from
i
in session
k
.
ρ
ij
is the lower bound on the percentage of
trac from PID
−i
to PID
−j
among all the trac from PID
−i
to other PIDs.
Note that 0
<ρ
ij
<
1and
j
=
i
ρ
ij
<
1
, ∀i
.
β
is the ecient factor that can be
configured particularly to P2P applications in engineering. The
OPT
in (2e) is
the lower bound of P2P applications performance. Because the cooperation of the
ISP and the P2P application aims at improving the performance of both sides,
the cooperation should not compromise the performance of P2P applications.
Hence, in general,
OPT
can be set as the optimal value in the independent
optimization of P2P applications . Typically, it can be set as follows:
OPT
=
maximize
t
k
∈T
k
i
other PIDs to PID
−
t
ij
,
(3)
j
=
i
i.e. P2P aims at matching downloading and uploading.
Suppose that
t
e
=
i
j
t
ij
I
e
(
i,j
), i.e. the total tra
c produced by P2P in
link
e
, then (1) equals to:
minimize
ʱ,t
k
∈T
k
,∀k
α
(4a)
b
e
+
k
t
e
≤
subject
to
αc
e
,
∀
e
∈
E,
(4b)
The Lagrange dual function of (4a) is as follows:
p
e
(
b
e
+
k
t
e
)+(
e
D
(
p
)=
min
ʱ,∀t
k
∈T
k
,k
p
e
c
e
−
1)
α.
e
