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Optical Networks: A Practical Perspective - Part 51

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Optical Networks: A Practical Perspective - Part 51. This book describes a revolution within a revolution, the opening up of the capacity of the now-familiar optical fiber to carry more messages, handle a wider variety of transmission types, and provide improved reliabilities and ease of use. In many places where fiber has been installed simply as a better form of copper, even the gigabit capacities that result have not proved adequate to keep up with the demand. The inborn human voracity for more and more bandwidth, plus the growing realization that there are other flexibilities to be had by imaginative use of the fiber, have led people. | 470 WDM Network Design 16 14 12 10 8 6 4 2 Full conversion o No conversion 10 wavelengths 16 32 64 128 Number of nodes Figure 8.18 Reuse factor plotted against the number of nodes for random graphs with average degree 4 with full wavelength conversion and no wavelength conversion from RS95 . converters the wavelength assignment algorithm assigns an arbitrary free wavelength on every link in the route to the lightpath thus we assume full wavelength conversion. In both cases if the wavelength assignment algorithm is unable to find a suitable wavelength the lightpath request is blocked. In order to compute the blocking probability for lightpath requests we make the simplifying assumption that the probability that a wavelength is used on a link is tt and that this event is independent of the use of other wavelengths on the same link and the use of the same and other wavelengths on other links. If the network has IV wavelengths on every link and a lightpath request chooses a route with H links the probability that it is blocked is given by Pb nc 1 - 1 - 7t H 8.12 when the network does not use wavelength converters. To see this note that the probability that a given wavelength is free on any given link is 1 it and thus the probability that it is free on all the H links in the route is 1 - tt h by the assumed independence of the use of a wavelength on each link. Therefore 1 1 rr H is the probability that a given wavelength is not free on some link of the route and since the use of each wavelength is assumed to be independent of the use of other 8.4 Statistical Dimensioning Models 471 wavelengths 1 1 tt z is the probability that all W wavelengths are not free on some link of the route that is Pb nc- When the network uses full wavelength conversion the probability that a lightpath request is blocked is given by w H . 8.13 The derivation of this equation using reasoning similar to that used in the derivation of 8.12 is left as an exercise Problem 8.23 . Given the blocking .