The edge-disjoint path problem on random graphs by message-passing

We present a message-passing algorithm to solve the edge disjoint path problem (EDP) on graphs incorporating under a unique framework both traffic optimization and path length minimization. The min-sum equations for this problem present an exponential computational cost in the number of paths. To overcome this obstacle we propose an efficient implementation by mapping the equations onto a weighted combinatorial matching problem over an auxiliary graph. We perform extensive numerical simulations on random graphs of various types to test the performance both in terms of path length minimization and maximization of the number of accommodated paths. In addition, we test the performance on benchmark instances on various graphs by comparison with state-of-the-art algorithms and results found in the literature. Our message-passing algorithm always outperforms the others in terms of the number of accommodated paths when considering non trivial instances (otherwise it gives the same trivial results). Remarkably, the largest improvement in performance with respect to the other methods employed is found in the case of benchmarks with meshes, where the validity hypothesis behind message-passing is expected to worsen. In these cases, even though the exact message-passing equations do not converge, by introducing a reinforcement parameter to force convergence towards a sub optimal solution, we were able to always outperform the other algorithms with a peak of 27% performance improvement in terms of accommodated paths. On random graphs, we numerically observe two separated regimes: one in which all paths can be accommodated and one in which this is not possible. We also investigate the behaviour of both the number of paths to be accommodated and their minimum total length.Comment: 14 pages, 8 figure

Boltzmann meets Nash: Energy-efficient routing in optical networks under uncertainty

Motivated by the massive deployment of power-hungry data centers for service provisioning, we examine the problem of routing in optical networks with the aim of minimizing traffic-driven power consumption. To tackle this issue, routing must take into account energy efficiency as well as capacity considerations; moreover, in rapidly-varying network environments, this must be accomplished in a real-time, distributed manner that remains robust in the presence of random disturbances and noise. In view of this, we derive a pricing scheme whose Nash equilibria coincide with the network's socially optimum states, and we propose a distributed learning method based on the Boltzmann distribution of statistical mechanics. Using tools from stochastic calculus, we show that the resulting Boltzmann routing scheme exhibits remarkable convergence properties under uncertainty: specifically, the long-term average of the network's power consumption converges within $\varepsilon$ of its minimum value in time which is at most $\tilde O(1/\varepsilon^2)$, irrespective of the fluctuations' magnitude; additionally, if the network admits a strict, non-mixing optimum state, the algorithm converges to it - again, no matter the noise level. Our analysis is supplemented by extensive numerical simulations which show that Boltzmann routing can lead to a significant decrease in power consumption over basic, shortest-path routing schemes in realistic network conditions.Comment: 24 pages, 4 figure

A survey on OFDM-based elastic core optical networking

Orthogonal frequency-division multiplexing (OFDM) is a modulation technology that has been widely adopted in many new and emerging broadband wireless and wireline communication systems. Due to its capability to transmit a high-speed data stream using multiple spectral-overlapped lower-speed subcarriers, OFDM technology offers superior advantages of high spectrum efficiency, robustness against inter-carrier and inter-symbol interference, adaptability to server channel conditions, etc. In recent years, there have been intensive studies on optical OFDM (O-OFDM) transmission technologies, and it is considered a promising technology for future ultra-high-speed optical transmission. Based on O-OFDM technology, a novel elastic optical network architecture with immense flexibility and scalability in spectrum allocation and data rate accommodation could be built to support diverse services and the rapid growth of Internet traffic in the future. In this paper, we present a comprehensive survey on OFDM-based elastic optical network technologies, including basic principles of OFDM, O-OFDM technologies, the architectures of OFDM-based elastic core optical networks, and related key enabling technologies. The main advantages and issues of OFDM-based elastic core optical networks that are under research are also discussed

Resource Allocation in Survivable WDM Networks Under a Sliding Scheduled Traffic Model

In recent years there has been an increasing number of applications that require periodic use of lightpaths at predefined time intervals, such as database backup and on-line classes. A new traffic model, referred to as the scheduled traffic model, has been proposed to handle such scheduled lightpath demands. In this thesis we present two new integer linear program ( ILP) formulations for the more general sliding scheduled traffic model, where the setup and teardown times may vary within a specified range. We consider both wavelength convertible networks and networks without wavelength conversion capability. Our ILP formulations jointly optimize the problem of scheduling the demands ( in time) and allocating resources for the scheduled lightpaths. Simulation results show that our formulations are able to generate optimal solutions for practical sized networks. For larger networks, we have proposed a fast two-step heuristic to solve the demand scheduling problem and the RWA problem separately

Resource Management in Survivable Multi-Granular Optical Networks

The last decade witnessed a wild growth of the Internet traffic, promoted by bandwidth-hungry applications such as Youtube, P2P, and VoIP. This explosive increase is expected to proceed with an annual rate of 34% in the near future, which leads to a huge challenge to the Internet infrastructure. One foremost solution to this problem is advancing the optical networking and switching, by which abundant bandwidth can be provided in an energy-efficient manner. For instance, with Wavelength Division Multiplexing (WDM) technology, each fiber can carry a mass of wavelengths with bandwidth up to 100 Gbits/s or higher. To keep up with the traffic explosion, however, simply scaling the number of fibers and/or wavelengths per fiber results in the scalability issue in WDM networks. One major motivation of this dissertation is to address this issue in WDM networks with the idea of waveband switching (WBS). This work includes the author\u27s study on multiple aspects of waveband switching: how to address dynamic user demand, how to accommodate static user demand, and how to achieve a survivable WBS network. When combined together, the proposed approaches form a framework that enables an efficient WBS-based Internet in the near future or the middle term. As a long-term solution for the Internet backbone, the Spectrum Sliced Elastic Optical Path (SLICE) Networks recently attract significant interests. SLICE aims to provide abundant bandwidth by managing the spectrum resources as orthogonal sub-carriers, a finer granular than wavelengths of WDM networks. Another important component of this dissertation is the author\u27s timely study on this new frontier: particulary, how to efficiency accommodate the user demand in SLICE networks. We refer to the overall study as the resource management in multi-granular optical networks. In WBS networks, the multi-granularity includes the fiber, waveband, and wavelength. While in SLICE networks, the traffic granularity refers to the fiber, and the variety of the demand size (in terms of number of sub-carriers)