1020 W. Hou et al. / Optik 122 (2011) 1019–1029
1.1. Related work
With the number of wavelengths in a fiber increases, ordinary
OXCs that only switch wavelength-granularity demands require
a large number of transmitting ports, which results in increasing
cost and control complexity. MG-OXC is the foremost solution due
to its small scale modularity, crosstalk and complexity reduction.
The authors in Refs. [6,7] proposed the use of MG-OXC without
any other additional function matrixes. But recently, the concept
of using sub-wavelength, wavelength, waveband and even fiber
switches in a hierarchical manner has received growing attention,
and then the authors in Refs. [8,9] provided MG-PXC that contains
a three-layer MG-OXC with the function of converting wavelength
or waveband and a OEO traffic grooming unit used to support mul-
tiplexing LRSs. Since the joint routing algorithm and the integrated
grooming policy based on MG-PXC was not considered in Ref. [9],
the proposed MG-PXC was lack of the necessary policy control
plane and improvements for decreasing the overall cost of the IP
over WDM network system.
On the other hand, an integrated auxiliary graph was pre-
sented in Ref. [10] to compute the route and assign the wavelength
for lightpath synchronously with constrained transceivers in a
dynamic environment. Based on that integrated auxiliary graph,
the authors proposed an algorithm called IGA to obtain lower
blocking probability followed by multi-hop grooming since it can
perform full-wavelength conversion on each node. But the prob-
lem here is that, the full-wavelength conversion may consume a
large number of OEO ports inevitably. In addition, IGA and other
traditional traffic grooming algorithms choose route for lightpath
in wavelength-routed manner. If the lightpath has no available
bandwidth for LRSs, we will compute another wavelength-route
for establishing new lightpath with two same end nodes, and that
new wavelength-route also consumes transmitting ports at inter-
mediate nodes, which is not desirable. Waveband switching can
save additional consumption of transmitting ports because it can
bind several wavelength-routes into a waveband tunnel as a sin-
gle entity. The WBS algorithms and several WM-strategies were
introduced in Refs. [11–17], among which, the authors in Ref. [16]
described a new dynamic WBS algorithm called RA-IAG followed
by sub-path merging strategy, compared to the other WBS algo-
rithms followed by end-to-end merging strategy, it can save more
OOO transmitting ports. But RA-IAG did not have the function of
traffic grooming and also performed full-wavelength conversion
in each node. The additional consumption of OEO ports has not
still been solved. A practical way to solve this problem is to pay
attention on sparse placement of a limited number of wavelength
converters or limited-range wavelength converters. The authors in
Ref. [17] proposed a waveband switching algorithm with consid-
ering the intra-band wavelength conversion technology, where a
wavelength can only be converted to any other wavelengths within
the same waveband. Intra-band wavelength conversion technology
has an ability of reducing the times of converting wavelengths so
that it can save the consumed OEO ports. However, the authors in
Ref. [17] only considered the wavelength-granularity demands and
ignored the sub-wavelength-granularity demands, i.e., LRSs. More-
over, although the idea of integrating the advantages of traditional
traffic grooming and waveband switching was first presented in
Ref. [9], how to perform the multi-granularity traffic grooming was
not described in this paper. Therefore, the multi-granularity traffic
grooming is an interesting and challenging problem we face in IP
over WDM networks.
1.2. Our contribution
As mentioned above, some wavelength-convertible traffic
grooming algorithms can attain low blocking probability by incor-
porating wavelength conversion capability at all of the nodes.
However, as the number of active wavelengths in a fiber increases,
the solution of multiplexing several LRSs into the high-capacity
lightpaths, whose consumed wavelengths are different from each
other, followed by full-wavelength conversion technology may
cost a large number of expensive OEO ports and also may require
many transceivers if most of lightpaths are set up anew since each
new lightpath will consume transceivers on its two end nodes.
The idea of implementing with the limited wavelength conversion
technology to save OEO ports by decreasing the times of wave-
length conversion is readily necessary. Therefore, the intra-band
wavelength conversion is conceivably of interest to us. In addi-
tion, the waveband switching wherein several wavelengths can be
grouped into a waveband and be switched as a single entity can save
more all optical transmitting ports than other technologies using
wavelength routing switches at intermediate nodes. Therefore, in
our opinion, the intra-band wavelength conversion and waveband
switching are both practical and should be considered when solving
the multi-granularity traffic grooming problem.
In this paper, we devise an identified structure of MG-PXC
and the new integrated grooming policy (IGP) that contains three
WG-schemes and two WM-strategies, introduce three important
technologies including multi-hop grooming, intra-band wave-
length conversion and waveband switching, and present the
mathematical model for calculating the number of consumed ports.
Since the traffic grooming problem is the NP-hard [18], we pro-
pose a new heuristic joint routing algorithm MGIAG for routing
traffic with different granularities starting from sub-wavelength
granularity (i.e., LRSs) to individual wavelength granularity and
then to waveband granularity. Finally, to support our algorithm
MGIAG, we employ a novel graph model called IAG. The algorithm
MGIAG is developed based on the auxiliary graph IAG and applies
the least-cost-path routing algorithm in that auxiliary graph for
each traffic demand and updates that auxiliary graph accordingly.
Our proposed MGIAG can integrate the advantages of traditional
traffic grooming using multi-hop grooming scheme and waveband
switching using sub-path waveband merging strategy effectively to
save OOO ports and obtain low blocking probability. On the other
hand, MGIAG can reduce a large number of OEO ports by using the
intra-band wavelength conversion.
This paper is organized as follows. In Section 2, we firstly intro-
duce the identified structure of MG-PXC, the multi-hop grooming,
the intra-band wavelength conversion and the waveband switch-
ing technologies in our proposed mechanism, and then we present
the integrated grooming policy and demonstrate how to calculate
consumed ports by using our proposed mathematical model. In
Section 3, we construct an integrated auxiliary graph according to
the network state. Based on that auxiliary graph, we proposed the
joint routing algorithm MGIAG in Section 4, and give an illustrative
example to explain the routing and wavelength/waveband assign-
ment in MGIAG in Section 5. In Section 6, we make the simulation
and performance analysis. Section 7 concludes this paper.
2. Problem statement
2.1. Network model
The physical network topology can be denoted as PNT (N, L,
B, W, T, G), where N is the set of physical nodes, L is the set
of fiber links, B is the set of active wavebands per fiber link, W
is the set of active wavelengths per fiber link (i.e., fiber capac-
ity), T is the set of tunable transceivers per physical node and
G is waveband granularity, in this work, we ensure
W
=
B
×
G. The set of wavelengths in a waveband is specified before-
hand. Each waveband B
y
(1 ≤ y ≤
B
) consists of G contiguous