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Optical Networks - _10_2 LTD and RWA Problems_118

Optical Networks - _10_2 LTD and RWA Problems_118 - 584 WDM...

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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 higher-layer (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 wavelength-routing network design problem into that of an LTD problem and an RWA problem, which we employed above in the three-node 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 trade-offs 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 higher-layer 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 wide-area 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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