Spectrum-switched optical networks (SSONs) are an attractive solution for core networks. With respect to wavelength-switched optical networks (WSONs), they achieve a higher spectrum efficiency thanks to the use of a flexible grid, instead of a fixed one. In SSONs, the well-known wavelength assignment (WA) problem of WSONs becomes a spectrum assignment (SA) problem. The SA problem aims at assigning a portion of the spectrum (called a frequency slot) to lightpaths. The width of the frequency slot depends on the requested bit rate and the modulation format adopted for the lightpath, and it is a multiple of the minimum bandwidth granularity, referred to as frequency slice. Thus, differently from WA, which assigns a single wavelength (or color) to each lightpath, SA assigns a set of colors (i.e., a set of frequency slices) to the lightpath. The shift from WA to SA introduces an additional constraint, which is related to the spectral adjacency of such frequency slices. This paper proves that the adjacency constraint in SA is not required and that by solving the WA problem (or the coloring problem) it is possible to derive a solution with spectrally adjacent slices in polynomial time. Based on such results, an integer linear programming formulation (ILP) for the optimal SA in a SSON with multi modulation formats and multi line rates (MMF/MLR) is presented for minimizing the network cost. The total cost of the network comprises the spectrum cost and the transponder card cost. Optimal results are presented for a MMF/MLR-SSON ring and show the amount of total occupied bandwidth and the network costs for different loads and ring lengths. Optimal selection of the modulation format and line rate is driven by the slice cost and the transponder card cost. Result comparison indicates that support of MMF and MLR is especially effective for improving spectrum utilization and allows spectrum saving up to 20% with respect to an SSON ring with single modulation format and line rate.
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