GUO et al.: GREEN PROVISIONING OF MANY-TO-MANY SESSIONS OVER WDM OPTICAL NETWORKS 3291
Fig. 2. Node architecture.
A. GMC-OXC Architecture
As shown in Fig. 2, each GMC-OXC features an OS matrix, a
group of splitters and (de)-multiplexers, an ES matrix with OEO
ports, as well as transponders (transmitters/receivers) and aggre-
gating ports. In addition, optical amplifiers should be equipped
at each physical fiber link to ensure signal quality as needed.
It should be noted that the OEO port and the transponder are
different components.
1) If a certain traffic flow is added from an aggregating port,
the corresponding procedure is indicated by solid lines
in Fig. 2. This traffic flow enters the ES matrix and is
electrically switched to the transmitter, which transmits
it to the OS matrix after EO conversion. If there is no
signal splitting, this traffic flow goes to the output fiber
directly (as indicated by the thick solid line in Fig. 2);
otherwise, the traffic flow will be replicated more than
once (as indicated by the thin solid lines in Fig. 2). It
should be noted that a copy of the lightpath signal does
not consume transponders at its local node.
2) If a certain traffic flow is dropped, the corresponding pro-
cedure is indicated by thin and dashed lines in Fig. 2.
The lightpath that carries this traffic flow is received by
the receiver and then enters the OS matrix. After being
filtered out, this traffic flow enters the ES matrix after
OE conversion and is finally dropped via an aggregating
port.
3) If a certain lightpath bypasses the GMC-OXC, this light-
path will be switched into the output fiber directly through
a single iteration of OS. This process is indicated by thick
dashed lines in Fig. 2. It should be noted that “a single
iteration of OS” is considered because we are focused on
the traffic-related power consumption of OS and ES ma-
trices. In other words, if a lightpath traverses a node, one
iteration of OS is required; if a traffic flow traverses the
ES matrix, one iteration of ES is required.
B. Problem Statement
1) Given: The network topology is denoted by the graph G =
(N,L,W,T, Ψ), where N is a set of GMC-OXC nodes
and L is a set of bidirectional fiber links. We consider a
monofiber network with a fixed number of wavelengths
|W |. T is a set of transponders per GMC-OXC node. Ψ is
the wavelength capacity.
2) Parameters: The total power consumption of the network
is mainly determined by the power consumption per ag-
gregating port E
ap
, per iteration of ES E
es
, per iteration
of OS E
os
, per EO port E
eo
, per OE port E
oe
, per trans-
mitter E
tx
, per receiver E
rx,
and per amplifier E
oa
.Be-
cause the splitter and (de)-multiplexer are both passive
devices, their power consumption is negligibly small. All
power-consuming parameters are expressed in units of
watts. However, for the tractability of analysis, we drive
the relative power consumption for each operation. d is
the distance between adjacent optical amplifiers.
3) Notations
P
mn
: Binary number equal to 1 if there is a fiber link
from node m ∈ N to node n ∈ N ; otherwise, it is set to 0
(P
mn
= P
nm
).
l
m
n
: The distance of the fiber link from node m to node n
(P
mn
=1).
K: The number of sessions in the network.
b
r
k
: The required bandwidth of each traffic flow in session
r
k
. In other words, we assume uniformity of traffic within
the same session, 1 ≤ b
r
k
≤ Ψ.
M
r
k
: The set of member nodes in session r
k
.
B
r
k
p
: Binary number equal to 1 if p ∈ M
r
k
;otherwise,it
is set to 0.
N
r
k
: The number of member nodes in session r
k
and
N
r
k
= |M
r
k
|.
T
r
k
: The session size indicator of r
k
and T
r
k
=
(N
r
k
−1)·b
r
k
Ψ
.
S
r
k
: The number of subsessions divided from session
r
k
; S
r
k
= N
r
k
/
Ψ
b
r
k
, which ensures that a simple cir-
cle aggregates traffic flows for each subsession.
N
r
i
k
: The number of member nodes in the ith subsession
r
i
k
of session r
k
;1≤ N
r
i
k
≤
Ψ
b
r
k
and 1 ≤ i ≤ S
r
k
.
lp
λ
i,j
: The lightpath built from node i ∈ N to a different
node j ∈ N, where the wavelength λ ∈ W is occupied.
LT
λ
i,k
: The light-tree built for subsession r
i
k
on wavelength
λ ∈ W .
4) Other notations unrelated to ILP
rlp
λ
i,j
: The residual bandwidth of the lightpath lp
λ
i,j
.
TR
m
: The number of consumed transponders at node m ∈
N.
f
i
: The number of times that node i ∈ N is shared by
sessions.
π: The set of established lightpaths in the network.
5) Decision variables
η
r
k
:IfT
r
k
≤ 1, this variable should be equal to 1 and we
should serve r
k
through a simple lightpath cycle; other-
wise, the value is set to 0 and we should serve r
k
through
simple cycles and small trees.