Optical Networks - _Problems9_123

# B how do you know that your solution uses the minimum

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(b) How do you know that your solution uses the minimum possible number of wavelengths required to do this routing for any algorithm?

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620 WDM Network Design (c) How many ADMs are required at each node to support this traffic? (d) How many ADMs are required at each node if instead of fixed-wavelength routing, you decided to use point-to-point WDM links and receive and re- transmit all the wavelengths at each node? How many ADMs does wave- length routing eliminate? 10.3 Derive (10.1). What is the value when N is odd? 10.4 Derive (10.5). What is the value when N is odd? 10.5 Derive (10.8) for the case where there is one full-duplex lightpath between each pair of nodes. Hint: Use induction. Start with two nodes on the ring, and determine the number of wavelengths required. Add two more nodes so that they are diametrically opposite to each other on the ring and continue. 10.6 Show that when N is odd, (10.8) is modified to W = t N 1 N 2 1 8 . 10.7 Derive (10.9). What is the value when N is odd? 10.8 Develop other network designs besides the ones shown in Examples 10.2, 10.3, and 10.4, and compare the number of LTs and wavelengths required for these designs against these three examples. 10.9 Consider the LTD problem in Section 10.2.1 but with the following changes: There is a cost c i,j to set up a bidirectional lightpath between nodes i and j . The cost includes the cost of the transponders that terminate the lightpaths and any intermediate transponders and amplifiers. λ s,t is bidirectional traffic rate between source-destination pairs (s, t) . The bandwidth of a lightpath is r . The objective is now to minimize the total cost of the network. Give the MILP formulation for this LTD problem. 10.10 This problem illustrates the complexity of wavelength assignment in networks where the transmission is bidirectional over each fiber. Consider the two networks shown in Figure 10.21. In Figure 10.21(a), the network uses two fibers on each link, with two wavelengths and unidirectional transmission on each fiber. In Figure 10.21(b), the network uses one fiber on each link, with four wavelengths. Transmission is bidirec- tional on each fiber, with two wavelengths in one direction and two in the other. No wavelength conversion is allowed in either network. Both networks have the same nominal capacity (four wavelengths/link). Which network utilizes the capacity more efficiently?
Problems 621 (a) (b) λ 1 λ 2 λ 1 λ

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• Spring '09
• Boussert
• Wavelength, Shortest path problem, Standing wave, Network topology, Wavelength Assignment

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