On solving the capacitated routing and spectrum allocation problem for flexgrid optical networks
Introduction
Due to the increasing data traffic demand in global communication network, the optical networks can be considered one of the pillars of the digital age, being able to cope with the constant demand for high transmission rates. In fact, the annual global IP traffic is estimated to reach 3.3 ZB per year by 2021 [1].
The traditional WDM (Wavelength-division Modulation) technologies for optical networks have a large transmission capacity [2]. The WDM technique splits the optical spectrum into static intervals of frequency. Each interval is used as a transmission channel. Channels are assigned to meet connection demands with different band requirements. Each connection demand may entirely or partially use the channel transmission rate. The latter case implies in wasting the optical resource, as it is not possible to assign the unused portion of the spectrum to allocate another demand.
To deal with heterogeneous band demands, one needs to resort to technologies capable of providing scalable and flexible allocation. The elastic optical networks approach consists in splitting the spectrum into small transmission bands (subcarriers or slots) that can be aggregated to a combined signal. Different techniques and architectures were proposed to generate and manipulate the slots in elastic optical networks [3].
The SLICE architecture (Spectrum-sliced Elastic Optical Path) [4] uses variable band transponders to generate a single signal of orthogonality modulated slots. The OFDM (Orthogonal Frequency-division Multiplexing) technology was recently introduced to optical domain and it was called CO-OFDM (Coherent Optical OFDM) [5]. The SLICE architecture allows for sub-wavelengths and super-wavelengths generation, which provides flexibility and elasticity to the channels, as shown in Fig. 1.
This paper introduces a novel ILP (Integer Linear Programming) model the capacitated version of the RSA (Routing and Spectrum Allocation) problem in the context of elastic optical networks. We also implement and a simple yet efficient load balancing procedure to generate promising paths to be used in a path-based formulation from the literature. Although limiting the number of paths (variables) may potentially prevent one to find the optimal solution for the problem, such formulation may be used in practice to find very good heuristic solutions, given that one provides a subset of suitable paths. In contrast to existing models for this version of the RSA problem, the proposed ILP formulation relies on the flow conservation principle, whereas the load balancing approach is based to enhance the effectiveness of an ILP model from the literature in find high quality solutions but without ensuring their optimality. Computational experiments revealed that the newly proposed model could solve more instances to optimality when compared with the existing model specifically proposed for the problem. Moreover, the load balancing procedure enabled the formulation from the literature to find high quality solutions, with average gaps smaller than 1%.
The remainder of the paper is structured as follows. Section 2 presents the version of the RSA problem addressed in this paper, as well as the related work and the so-called LP-CA (Link-Path Channel Assignment) ILP formulation from the literature. Section 3 introduces the proposed flow conservation-based ILP model for the problem. Section 4 describes the load balancing approach. Section 5 contains the results of the computational experiments. Finally, Section 6 concludes.
Section snippets
The RSA problem
The RSA problem, which is known to be -hard [6], [7], aims at determining an efficient spectrum assignment given an elastic optical network topology with an associated set of traffic demands [8]. For each demand, one must try to assign a route and a spectrum allocation setup, which means a set of subcarriers (slots) to carry the optical signal.
The offline version of the RSA problem addressed in this paper, known as capacitated RSA, was introduced in [9] and has the following input data.
- •
An
Proposed formulation
Given the limitation of the LP-CA model discussed in the previous section, we introduce a novel ILP formulation for the capacitated RSA in elastic optimal networks. The proposed model, here denoted as MCF (Multi-commodity Flow), does not rely on precomputed routes, but it still makes use of the channel concept employed in the LP-CA model. In our case, each “commodity” (which is the usual term adopted for this type of network flow-based formulation) is associated with a demand. We remark that
A load balancing approach
Because the capacitated RSA problem is -hard, its exact solution may turn out to be extremely challenging. Therefore, we decided to implement a simple load balancing procedure to provide promising paths to the LP-CA model. In this case, the performance of the method depends on the number of precomputed routes for each demand. Smaller values for the parameter could improve the performance of the algorithm in terms of CPU time but at the expense of losing an optimal solution, whereas larger
Computational experiments
The models and algorithms were coded in C++ and they were executed on an Intel® Core™ i7-3770 3.40 GHz with 16 GB of RAM running Linux Ubuntu 16.04 LTS. The ILP models were solved using IBM CPLEX 12.6.
For all cases the demands were randomly generated and the size of the requisitions were allowed take one of the following values: 10, 40 and 100 Gb/s (1, 2 and 4, slots of 12,5 GHz, respectively). In addition, we assume that as in [9]. It is worth mentioning that the guard band was considered
Concluding remarks
This paper dealt with the capacitated RSA problem in elastic optical networks. In order to solve it, we presented a novel multi-commodity flow ILP formulation and a load balancing procedure to generate promising paths to be used in the so-called LP-CA model [9]. Extensive computational experiments were performed on hundreds of instances based on different real world topologies. The results obtained showed that the proposed formulation yielded, on average, superior results than the LP-CA model,
CRediT authorship contribution statement
Carlos M. Araújo: Methodology, Investigation, Data curation, Software, Writing - original draft, Visualization. João Marcos P. Silva: Investigation, Data curation, Validation, Formal analysis, Writing - original draft, Visualization. Anand Subramanian: Methodology, Supervision, Resources, Writing - review & editing. Iguatemi E. Fonseca: Conceptualization, Resources, Writing - review & editing, Supervision, Project Administration.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This research was partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), grants 307843/2018-1 and 311419/2019-4, and by Comissão de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) – Finance Code 001.
Carlos M. Araújo was born in João Pessoa, Brazil, in 1990. He received his B.Sc. degree in Computer Science from the Universidade Federal da Paraíba in 2015, Brazil and his M.Sc. degree in Informatics in 2018 from the same institution. Currently, he works as a software development at VSoft. His research interests include computer networks and combinatorial optimization.
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Carlos M. Araújo was born in João Pessoa, Brazil, in 1990. He received his B.Sc. degree in Computer Science from the Universidade Federal da Paraíba in 2015, Brazil and his M.Sc. degree in Informatics in 2018 from the same institution. Currently, he works as a software development at VSoft. His research interests include computer networks and combinatorial optimization.
João Marcos P. Silva was born in Caririaçu, Brazil, in 1993. He received his B.Sc. degree in Mechanical Production Engineering from the Universidade Regional do Cariri in 2016, Brazil and his M.Sc. degree in Production Engineering from the Universidade Federal da Paraíba in 2019, Brazil. Currently, he is a Ph.D. candidate at the Universidade Federal Fluminense. His research interests include combinatorial optimization, integer programming and metaheuristics.
Anand Subramanian was born in João Pessoa, Brazil, in 1983. He received his B.Sc. degree in Mechanical Production Engineering from the Universidade Federal da Paraíba (UFPB), Brazil, in 2006 and his M.Sc. degree in Production Engineering in 2008 from the same institution. He obtained his D.Sc. degree in Computing in 2012 from the Universidade Federal Fluminense, Brazil. His D.Sc. thesis was selected as one of the top 3 of Brazil in the field of Computer Science and he received an Honorable Mention award from the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), on behalf of the Brazilian Ministry of Education. He is currently an Associate Professor at the Departamento de Sistemas de Computação, UFPB, Brazil. He is an author of more than 40 articles published in highly-ranked international journals. He works mainly on heuristic, exact and hybrid algorithms for combinatorial optimization problems. In 2016 he received the highly cited research award from Elsevier for the paper “A hybrid algorithm for a class of vehicle routing problems”, as one of the top 5 most cited papers in Computer & Operations Research (C&OR) during the period of 2014–2016. He is a member of the Editorial Advisory of Board of C&OR since 2019.
Iguatemi E. Fonseca was born in Nova Floresta, Brazil, in 1974. He received the electronics engineering degree from the Federal University of Campina Grande (UFCG), Campina Grande, PB, Brazil, in 1999, and the M.Sc. and Ph.D. degrees from the State University of Campinas (Unicamp), Campinas, SP, Brazil, in 2001 and 2005, respectively, specializing in nonlinear fiber optics and its applications, optical network design with physical-layer impairments and Impairment-Aware RWA. He is currently an associate professor at the Departamento de Sistemas de Computação, UFPB, Brazil. His current research interests include areas of the Electrical Engineering and Computer Science as: i) Communications Networks (Optical Networks, Wireless Sensor Networks, Mobile Networks and IP Networks), working on topics as identification/models of traffic in computer networks, techniques for identification and mitigation of denial of service attacks, algorithms and protocols in Industrial Wireless Sensor Networks, WDM and elastic optical networks with QoS requirements, and design and simulation of photonic devices; ii) Design of simulators in virtual reality with applications in industry sectors, as energy sector.