584
WDM Network Design
0
5
10
15
20
25
30
35
40
0
2
4
6
8
10
Traffic,
t
Single hub
Fully optical
PWDM
Lower bound
Number of wavelengths
Figure 10.8
Number of wavelengths required for the different designs of Examples
10.2–10.4, for a ring with
N
=
8
nodes. The lower bound from (10.10) is also shown.
or PWDM architectures. If
t
is close to one unit, then the best solution may be to
have another direct lightpath between them.
Overall, we have learned that it is possible to save significantly in higherlayer
(IP or SONET) equipment costs by providing networking functions (routing and
switching of wavelengths) within the optical layer.
10.2
LTD and RWA Problems
The general approach of dividing the wavelengthrouting network design problem
into that of an LTD problem and an RWA problem, which we employed above in
the threenode linear network and the ring network, is a good heuristic for practical
problems because solving the two problems in a combined fashion is quite hard. In
both the examples, we considered a few different lightpath topologies and examined
the RWA problem for each of them. This clarified the cost tradeoffs among the
different designs. In practice, each lightpath topology together with its realization
in the optical layer (the solution of the RWA problem) would result in a net, real
(monetary) cost. We can then pick the design that results in the lowest cost. We will
consider one such example in Chapter 13. We will now examine the two component
problems, LTD and RWA, in greater detail.
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10.2
LTD and RWA Problems
585
10.2.1
Lightpath Topology Design
We now consider a specific, though rather simplified, lightpath topology design
problem and examine how it can be solved. We will assume that no constraints are
imposed by the underlying fiber topology or the optical layer. (Examples of such
constraints are a limit on the length of a lightpath and a limit on the number of
lightpaths traversing a link.)
We assume that all lightpaths are bidirectional (see Section 10.2.2); that is, if we
use a lightpath from node
i
to node
j
, then we also use a lightpath from node
j
to node
i
. This is the case that most frequently occurs in practice since almost all
higherlayer protocols, including IP and SONET, assume bidirectional physical layer
links.
One constraint is that at each node we use an IP router with at most
ports
connecting it to other IP routers. (In addition, each router would have local interfaces
to Ethernet switches and the like.) This constrains the maximum number of ports
per router to
and thus indirectly constrains the cost of the IP routers. This also
constrains the number of lightpaths in the network to
n
, where
n
is the number of
nodes in the network, since each lightpath starts and ends at an IP router port. This
constraint is equivalent to a constraint on the lightpath costs if we assume that the
tariff for a lightpath is the same regardless of its end points. This is an assumption
that would not hold in a widearea environment where we expect longer lightpaths
to be more expensive than shorter ones. However, it may hold in a regional network.
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 Spring '09
 Boussert
 Optimization, Wavelength, Standing wave, Network topology, RWA

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