Survivable Traffic Grooming in Elastic Optical Networks—Shared Protection

Power, routing, Modulation Level and Spectrum Assignment in all-optical and elastic networks

Elastic optical networks (EONs) have been receiving extensive attention because of their inherent flexibility and the efficiency with which they allocate fiber-bandwidth. For an EON, survivability is of crucial importance because of the very high bandwidth that it carries on each optical channel. In this article, we review the current state of the art of survivable EONs which reviews the literature to summarize the following aspects: (a) spectrum resource sharing among backup lightpaths, (b) sharing of high-speed optical transponders, (c) effect of spectrum conversion, (d) bandwidth squeezed restoration (BSR), (e) joint restoration by multiple sub-band optical channels, (f) multi-layer survivability, and (g) energy efficiency. Apart from a summary on the current research status, we also discuss open research issues which are important to survivable EONs from the perspectives of (a) impact of spectrum conversion, (b) impact of elastic optical transponder configuration, (c) impact of physical layer impairments and limitations, (d) protection-path-based spectrum defragmentation, and (e) network availability.

This paper analyses the viability in use a self-organizing metaheuristic known as Elastic Network to solve the Euclidean Traveling Salesman Problem (ETSP). We propose a new hybrid approach based on Elastic Networks associated with a convex hull algorithm to solve the ETSP. In order to analyze our hybrid algorithm, one of the best Elastic Networks versions was also implemented. Experimental results show the quality of our algorithm is good.KeywordsConvex HullTravel Salesman ProblemTravel Salesman ProblemCircular RingQuadratic Assignment ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

An Elastic Optical Network (EON) nowadays usually accommodates multiple Virtual Optical Networks (VON) by allocating orthogonal spectrum resources for them. A fixed resource allocation pattern may result in a low quality of service since data traffic on VONs may fluctuate with time. Spectrum trading (ST) among VONs could solve this problem by moving spectrum resources between them and blockchain-based ST has recently gained much interest since it avoids the traditional centralization concern. In this paper, we propose a smart contract based decentralized ST scheme for VONs. The system is built on a private blockchain which can be implemented with the off-shelf Ethereum platform at a low development cost. A frequency slot (FS) trading contract (FSTC) is designed to trade unoccupied spectrum resources among VONs. Compared with existing schemes, FSTC explicitly addresses the virtual link brokerage (VLB) problem by trading in the granularity of virtual links. Furthermore, FSTC ensures FS information authenticity and enables FS recyclability via mechanisms based on Ethereum smart contract features. We implement FSTC with Solidity and evaluate its costs which demonstrate the feasibility of the proposed solution.

To adapt to the network dynamics and support elastic network resource allocation in the future elastic optical networks, optical transmitter with flexibility and re-configurability in modulation formats becomes indispensable, offering network providers flexibility in transport bandwidth. In this paper, we discuss our proposed two flexible high-order quadrature amplitude modulation (QAM) transmitter schemes, including (i) a flexible transmitter based on tandem in-phase/quadrature (IQ) modulators for generating 16QAM, 32QAM, 64QAM signals; and (ii) a scheme based on monolithically-integrated quad-Mach-Zehnder IQ modulator (QMZ-IQ) with binary driving electronics for synthesizing minimum phase-shift keying (MSK), quadrature phase-shift-keying (QPSK), 8-ary phase-shift keying (8PSK), and 16QAM signals. These schemes provide different approaches to configure a flexible high-order QAM transmitter, either using cascaded off-the-shelf modulators, or via highly-integrated monolithic modulator. These flexible and reconfigurable transmitter schemes provide the network providers different flexible transmitter solutions suitable for different application scenarios in elastic optical networks.

Benefits of different channel grid configurations (ITU 50GHz grid, 12.5GHz grid, gridless) in an US network are analyzed for MLR/elastic networks, transparent network/network with high spectral efficiency, and for 2010/2020 traffic load scenarios. We show that elastic and MLR networks can achieve comparable performance levels using a 12.5 GHz grid.

We are fortunate to have three Research Spotlights articles, on a broad range of topics, in the current issue of SIAM Review. The first of these articles is “Flow and Elastic Networks on the $n$-Torus: Geometry, Analysis, and Computation." In it, authors Saber Jafarpour, Elizabeth Y. Huang, Kevin D. Smith, and Francesco Bullo explore a special case of network-based modeling. Instead of representing a physical quantity (e.g., density) or abstract quantity (e.g., opinions), in this regime the nodal variables represent phases (points on the circle) and the network state belongs to the $n$-torus instead of $R^{n}$. A flow network is described by a commodity (e.g., electricity) that is being exchanged between adjacent nodes and is defined in terms of its flow balance equation, flow equation, and angle constraint. The authors use AC power flow equations as an illustration of a flow network and explain how the general theoretical questions posed by the authors relate to important questions about stability of power supply. An elastic network is described via an interaction energy between adjacent nodes. For insight into this type of network model on the $n$-torus, the authors describe the model of collective motion in biological and engineering networks. To frame the balance of the paper, the authors enumerate five important theoretical questions they will address to greater or lesser extent. Since they prove early on that “any result about the flow network setting is directly applicable to the elastic network setting, and vice versa," the authors are free to focus only on the flow network setting in the remainder. What follows is the development of a rigorous graph-theoretic and geometric framework to study the solutions of flow network problems on the $n$-torus. Proofs are left to the appendices to enable the reader to better follow the stages of this development. Those whose interest is piqued by this line of research will find suggestions for further consideration and application in the final section of the paper. The topic of the second Research Spotlights article in this issue deals with, to quote the author, “one of the most fundamental matrices in applied mathematics," the discrete Fourier transform (DFT) matrix. In the article “How Exponentially Ill-Conditioned Are Contiguous Submatrices of the Fourier Matrix?" author Alex Barnett considers the conditioning of its $p \times q$ submatrices as functions of their scaled submatrix shape, where shape is defined by the pair ($p/N,q/N$), with $N$ denoting the DFT matrix dimension. The topic is of importance in many applications where the amplification of noise during the process must be avoided. Such applications, described in some level of detail in the introduction, include Fourier continuation, superresolution imaging, and coherent X-ray diffraction imaging. The paper focuses on finding good lower bounds on the condition number of a $p \times q$ submatrix in terms of $p$, $q$, and $N$. The author has chosen a creative presentation format. The three main theorems are presented immediately in section 1.1. The second of these largely supersedes the first, but, as the author notes, the first is included because “its prefactor is slightly stronger and, moreover, its elementary proof (section 2) is instructive." From there, the reader is presented with a discussion of previous work and an overview of the tools and techniques needed for the proofs presented in the following sections. With the background laid, each of the next three sections is devoted to a proof of one of three theorems. The interested reader might wonder about the sharpness of the bounds in practice, and indeed the discussion in section 5.1 addresses precisely this issue. Many open questions, such as upper bounds on the condition numbers, are described in the final section, leaving the curious reader with avenues for future research in this area. Our third article addresses a technique familiar to many of our RS readers: numerical quadrature. The article “Exactness of Quadrature Formulas," by Lloyd N. Trefethen, offers a survey and new results pertaining to four well-known quadrature rules. The jumping off point for the discussion is the concept of exactness, the principle around which quadrature rules are typically designed. A quadrature rule is said to be exact for a certain class of integrands---say, polynomials of degree less than or equal to $n-1$---if the rule returns the exact value of the integral for functions in this class. One point the paper drives home is the fact that “the exactness principle is not a reliable guide to the actual accuracy" of the rule. A simple but striking example of this fact lies in the author's comparison of the accuracy of an $n$-point Newton--Cotes for fixed $n$ on two polynomial classes of degree $n$ and higher. The error for the rule on the monomials remains small as the degree is slowly increased beyond $n$, an observation the author actually explains in terms of the exactness principle, while the accuracy for Chebyshev polynomials blows up almost immediately. In the case of the Gauss--Hermite quadrature rule, that the exactness principle leads to inefficiency and suboptimality in a practical sense is illustrated artfully in section 5. Here, the author also gives a theoretical result suggesting the preferred method for evaluating integrals of type (5.1) would be to instead truncate the interval to a finite length and then apply an unweighted rule like Gauss--Legendre. In another section, modifications to Gauss quadrature are derived that have a small potential gain in the convergence rate by taking factors other than exactness into consideration. The moral of the story woven together through survey and new results is, in the parting words of the author, “if you are told that a certain formula is optimal, do not assume this is the end of the discussion."

Rheological characteristics of commercial canola protein isolate–κ-carrageenan systems

Exceptionally recyclable, extremely tough, vitrimer-like polydimethylsiloxane elastomers via rational network design

We create variable-length pseudorandom permutations (PRPs) and strong PRPs (SPRPs) accepting any input length chosen from the range of b to 2b bits from fixed-length, b -bit PRPs. We utilize the elastic network that underlies the recently introduced concrete design of elastic block ciphers, exploiting it as a network of PRPs. We prove that three and four-round elastic networks are variable-length PRPs and five-round elastic networks are variable-length SPRPs, accepting any input length that is fixed in the range of b to 2b bits, when the round functions are independently chosen fixed-length PRPs on b bits. We also prove that these are the minimum number of rounds required.

We compare the cost-efficiency of optical networks based on mixed datarates (10, 40, 100Gb/s) and elastic technologies. We show elastic network bring up to 37% lower cost, in particular for high loads and dynamic scenarios.

We consider an elastic all-optical network, where each node is multicast-capable and does not support spectrum conversion. In such a network, for a given set of static multicast demands, we consider distance-adaptive spectrum resource allocation, and aim to optimize multicast routing, modulation, and spectrum assignment with shared protection in a way that minimizes the required spectrum resources for accommodating all multicast sessions. In our design, we provision each multicast demand by a light-tree where spectrum resources are allocated in all links included in the tree. We protect each light-tree from any single link failure in both directions by having a backup path that is link-disjoint to the path from the source to each destination on the primary tree. We reserve spectrum resources in the links that are not in the primary tree but in the backup paths between all source-destination pairs. The reserved spectrum resources can be shared to protect multiple light-trees as long as they do not fail simultaneously. For such a problem, we provide a mixed integer linear programming formulation. We also develop a scalable heuristic algorithm with an attribute that enables it to improve the quality of the results at the cost of longer running times. Numerical results for small problems show that the heuristic algorithm performs close to the optimum. In addition, we use a Markov chain simulation of the network to evaluate the performance of our proposed algorithm in terms of blocking probability in a dynamic environment, which demonstrates a significant improvement over straightforward approaches.

Elastic optical networks (EONs) have provision long transmission reach (TR) and high spectral-efficiency (SE). Hence, compared to fixed-grid optical networks, in EONs, managing resources and addressing network design poses complex challenges. In this work, we formulate a link-based mixed integer linear program (MILP) model which considers quality of transmission (QoT) while determining the route, modulation format/level (MF/ML) and spectrum allocation (SA) for every request. To improve SE, model chooses the highest ML; however, when QoT is considered, TR of path with highest ML is very limited. Hence, model finds trade-off between ML, number of required frequency slots (FSs), and TR, with the objective of minimising required amount of network FSs so as to admit all requests. Finally, we evaluate and analyse model's performance and show that for simplicity, existing schemes impractically assume single MF (i.e., higher SE and ML) compared to fixed-grid networks, thereby ignoring the flexible nature of EONs.

Ultra-low loss (ULL) fibers allow high-quality signal transmission and are expected to become important candidates for new deployment of fiber links in an optical network. In our previous study, we investigated strategies for selecting network links to be deployed with ULL fibers in a single stage, subject to an annual operational budget. As a step further, this study considers such deployment in multiple stages, which corresponds to a scheduling problem of ULL fiber deployment. To this end, we cannot simply adopt a repetition of our previous single-stage deployment approach since it cannot tell which set of links are to be deployed with ULL fibers in each stage. Rather, we need to jointly consider the set and the order of links to be deployed in each stage so as to get a maximum overall gain in terms of time-weighted frequency slot (FS) usage. Also, the time taken for deploying each fiber link and the interval between neighboring deployment stages should be considered. To achieve a global optimization, we develop a mixed integer linear programming (MILP) model and look at three scheduling strategies which are physical length (PL), shortest route traversed (SRT), and maximum deployment gain (MDG) based strategies. We evaluate the performance of these strategies through simulations and find that the proposed MDG strategy performs best in terms of the total time-weighted FS usage. Results also show that there is an optimal number of deployment stages which provides maximum gain of spectrum usage while requiring few network re-optimizations.

Presents corrections to the paper, “Multicast routing and distance-adaptive spectrum allocation in elastic optical networks with shared protection,” (Cai, A., et al), J. Lightw. Technol., vol. 34, no. 17, pp. 4076–4088, Sep. 2016.