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The most important thing in all optical networks is to reduce the cost of using the network in electronic processing equipment, along with wavelength division multiplexing (WDM) technology are increasingly improved. Add-drop multiplexer (ADM) is not only the most important equipment but also the most basic equipment using the point difference in all-optical networks. The function of the ADM processing device ,is a separation or insert the desired wavelength to networks. The key to reducing the cost is to reduce the number of ADM uses and minimize the number of ADMs. Traffic grooming problem is an important generalization of the ADM minimization problem, which is NP-hard. The specific way is to effectively package the number of available wavelengths ADMS on low speed traffic streams by requiring the number of wavelength per fiber and the required network, so as to reduce the network cost as much as possible. Synchronous optical network (SONET), which is a fiber-optic network for high-speed data communications transmission network .This paper mainly use the algorithm GROOMBYSC(k) to solve the traffic grooming problems in bi-directional interconnected SONET/WDM rings networks. The algorithm analysis shows that the algorithm has a better approximation ratio. We further improve the algorithm by computational analysis. We obtain a similar result by using the algorithm, and the approximation ratio is 2 ln (ln ) g o g  , where g is the grooming factor. Algorithm analysis shows that the grooming factor smaller than its approximation ratio of the approximation algorithm, the better the performance of the algorithm can be seen, what’s more we can obtain proved a general of the approximation algorithm.

The analysis of Grooming Factor on Optimization Algorithms in All-optical Network