Photon Netw Commun (2012) 24:177–186 DOI 10.1007/s11107-012-0378-7 Modeling the routing and spectrum allocation problem for flexgrid optical networks L. Velasco · M. Klinkowski · M. Ruiz · J. Comellas Received: 20 February 2012 / Accepted: 12 April 2012 / Published online: 27 April 2012 © Springer Science+Business Media, LLC 2012 Abstract Flexgrid optical networks are attracting huge interest due to their higher spectrum efficiency and flexibil- ity in comparison with traditional wavelength switched opti- cal networks based on the wavelength division multiplexing technology. To properly analyze, design, plan, and operate flexible and elastic networks, efficient methods are required for the routing and spectrum allocation (RSA) problem. Spe- cifically, the allocated spectral resources must be, in absence of spectrum converters, the same along the links in the route (the continuity constraint) and contiguous in the spectrum (the contiguity constraint). In light of the fact that the conti- guity constraint adds huge complexity to the RSA problem, we introduce the concept of channels for the representation of contiguous spectral resources. In this paper, we show that the use of a pre-computed set of channels allows considerably reducing the problem complexity. In our study, we address an off-line RSA problem in which enough spectrum needs to be allocated for each demand of a given traffic matrix. To this end, we present novel integer lineal programming (ILP) formulations of RSA that are based on the assignment of channels. The evaluation results reveal that the proposed approach allows solving the RSA problem much more effi- ciently than previously proposed ILP-based methods and it can be applied even for realistic problem instances, contrary to previous ILP formulations. Keywords Flexgrid optical networks · Off-line routing · Spectrum allocation L. Velasco (B ) · M. Ruiz · J. Comellas Universitat Politècnica de Catalunya (UPC), Barcelona, Spain e-mail: lvelasco@ac.upc.edu M. Klinkowski National Institute of Telecommunications (NIT), Warsaw, Poland 1 Introduction Spectrum-sliced flexgrid optical networks are gaining great momentum as a consequence of both the expected better spectrum efficiency and flexibility compared with the rigid spectrum grid networks implementing the traditional WDM technology, and the maturity of the technology enabling their development [1, 2]. In flexgrid optical networks, the available optical spec- trum, for example, C-band, is divided into frequency slots of a fixed (finer) spectral width in comparison with the current ITU-T WDM rigid frequency grid (50 GHz) [3]. Current pro- posals for the slot size are 25, 12.5 GHz, and even 6.25 GHz. Optical connections have allocated a number of these slots, which is a function of the requested capacity, the modulation technique applied, and the slot width. As an analogy to the off-line routing and wavelength assignment (RWA) problem in WSON, the off-line rout- ing and spectrum assignment (RSA) problem appears when designing or planning flexgrid optical networks. The RSA problem was proved to be NP-complete in [4] and [5]. In the RSA problem, in addition to the spectrum continuity along the links of a given routing path where the same slots must be used in all links of the path, the spectrum contiguity must be also guaranteed, which means that the allocated slots must be contiguous in the spectrum. As a consequence, it is crucial that efficient methods are available to allow solving realistic problem instances in practical times. For illustrative purposes, Fig. 1a shows an example of the optical spectrum divided into frequency slots, each hav- ing same width. A guard band may be introduced to sepa- rate two spectrum adjacent connections in any optical link (Fig. 1b). We assume that once the requested frequency resources have been allocated, the optical connection can be used to convey single-carrier or multi-carrier modulated 123