Optical Networks - _10_5 Maximum Load Dimensioning Models_121

# However such a scenario does not occur very often in

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However, such a scenario does not occur very often. In fact, [Tuc75] has shown that if no three lightpaths in a given traffic pattern cover the entire ring, then 3 2 L wavelengths are sufficient to perform the wavelength assignment. This is an example where the worst-case nonblocking model results in overdesigning the network. In order to support a few pathological patterns, we end up using approximately L 2 additional wavelengths. Let us see what can be gained by having wavelength conversion capabilities in a ring network. If we have full conversion capabilities at all the nodes, then we can support all lightpath requests with load L W . However, the same result can be achieved by providing much less conversion capabilities, as shown by the following results. Theorem 10.4 [RS97] Consider a ring network that has full wavelength con- version at one node and no wavelength conversion at the other nodes. This network can support all lightpath requests with load L W . The proof of this result is left as an exercise (Problem 10.19). Limited-wavelength conversion can help significantly in improving the load that can be supported in many network configurations. The detailed derivations of the results for this case are beyond the scope of this book. We summarize the key results here.

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614 WDM Network Design Fixed-wavelength converter WDM mux/demux Figure 10.20 A ring network with fixed-wavelength conversion at one node and no conversion at the others that is able to support lightpath requests with load L W 1 . One of the nodes is configured to convert wavelength i to wavelength (i + 1 ) mod W , and the other nodes provide no wavelength conversion. Theorem 10.5 [RS97] Consider the ring network shown in Figure 10.20, which has fixed-wavelength conversion at one node where wavelength i is con- verted to wavelength (i + 1 ) mod W , and no wavelength conversion at the other nodes. This network can support all lightpath requests with load L W 1 . By having d = 2 limited conversion at two nodes and no conversion at the others, it is possible to improve this result to L W [RS97], making such a network as good as a network with full wavelength conversion at each node. Other topologies such as star networks and tree networks have also been consid- ered in the literature. In star and tree networks, 3 2 L wavelengths are sufficient to do WA-NC [RU94]. In star networks, L wavelengths are sufficient for WA-FC [RS97]. The same result can be extended to arbitrary networks where lightpaths are at most two hops long. Table 10.3 summarizes the results to date on this problem. It is still a topic of intense research. Multifiber Rings The wavelength assignment problem in multifiber rings is considered in [LS00]. In a multifiber ring, each pair of adjacent nodes is connected by k > 1 fiber pairs: k > 1 fibers are used for each direction of transmission instead of 1 fiber. Recall that we are considering undirected edges and lightpaths, and each edge represents a pair of fibers, one for each direction of transmission. Thus, such a multifiber ring is represented by
10.5 Maximum Load Dimensioning Models 615 Table 10.3 Number of wavelengths required to perform ofﬂine wavelength as- signment as a function of the load L with and without wavelength converters. The

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• Spring '09
• Boussert
• Algorithms, Graph Theory, Computer network, Wavelength, Standing wave, wavelength conversion, lightpaths

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