Optical Networks - _10_4 Statistical Dimensioning Models_120

Optical Networks - _10_4 Statistical Dimensioning...

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10.4 Statistical Dimensioning Models 599 We can view the above approach of forecasting a fixed traffic matrix and di- mensioning the network to support the forecasted traffic as using a “deterministic” traffic model. This is because the variations in traffic are not explicitly accounted for during the design phase, though the use of crossconnects in the network enables some of these variations to be handled at the time of actually setting up the light- paths. Another approach to capacity planning is through the use of statistical traffic models, which we will discuss in Section 10.4. In a wavelength-routing network, if the nodes have full conversion capability, the situation is the same as in classical circuit-switched telephone networks: a lightpath is equivalent to a phone call and must be assigned one circuit on each of the links it traverses. Another approach studied extensively by researchers is to dimension optical networks with no or limited conversion capabilities and to support the same traffic that would be supported using full conversion within the optical layer. We discuss these methods in Section 10.5. In this case, as well as in the case of statis- tical models, we consider only the RWA problem and not the LTD problem. Thus, grooming issues that are part of the LTD problem are not discussed. The problem of determining the location of regenerators is also outside the scope of our discussion. 10.4 Statistical Dimensioning Models Two classes of statistical traffic models can be used in solving the dimensioning problem. These models differ in their assumptions regarding what is known about the set or sets of lightpaths that must be supported. In some cases, these models also assume that each link supports the same number (and set) of wavelengths, but this may not always be appropriate. 1. First-passage model: In this model, the network is assumed to start with no lightpaths at all. Lightpaths arrive randomly according to a statistical model and have to be set up on the optical layer. Some lightpaths may depart as well, but it is assumed that, on average, the number of lightpaths will keep increasing and eventually we will have to reject a lightpath request. (Thus the rate of arrival of lightpath requests exceeds the rate of termination of lightpaths, and the network is not in equilibrium.) We are interested in dimensioning the WDM links so that the first lightpath request rejection will occur, with high probability, after a specified period of time, T . This is a reasonable model today since lightpaths are long lived. This longevity, combined with the cost of a high-bandwidth lightpath today, means that network operators are unlikely to reject a lightpath request. Rather, they would like to upgrade their network by the addition of more capacity on existing links, or by the addition of more links, in order to accommodate the
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600 WDM Network Design lightpath request. The time period T corresponds approximately to the time by
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Optical Networks - _10_4 Statistical Dimensioning...

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