This paper investigates the problem of wavelength assignment in wavelength reusable multi-carrier distributed (WRMD) wavelength-division-multiplexing (WDM) ring networks. In conventional WDM ring networks, each edge node (EN) has its own light sources, and optical channels, called lightpaths, are established by using optical carriers generated from laser diodes (LDs) at the source EN. However, such networks will suffer from the need for complicated wavelength management (e.g., monitoring LDs, avoiding wavelength collision) in the future since each EN requires a large number of LDs to deal with the exponential increase in traffic. On the other hand, a WRMD ring network overcomes this problem. In this network, lightpaths between source and destination ENs are established by using carriers generated from a centralized multi-carrier light source. Moreover, the carrier regeneration technique is applied for the purpose of reducing the number of wavelengths used for lightpath establishment. Although optical carrier regeneration reduces the number of wavelengths, the quality of the regenerated carrier is slightly degraded after carrier regeneration. Therefore, in the WRMD network, the allowable number of carrier regenerations per wavelength must be limited in order to avoid communication error. This paper formulates the wavelength assignment problem, minimizing the number of wavelengths needed to establish all requested lightpaths, as the vertex coloring problem, and then an integer linear programming (ILP) solution is provided. Since ILP problems are non-deterministic polynomial-time- (NP-) complete, a heuristic algorithm is developed. Numerical results indicate that our developed algorithm performs well in our test cases. It is observed that one and two carrier regenerations per wavelength reduce the number of wavelengths for lightpath establishment by approximately 50% and 60%, respectively, compared to that without carrier regeneration. The results also show that regenerating carriers more than two times per wavelength has little effect on the required number of wavelengths regardless of the number of ENs.
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