Shortest Path versus Multi-Hub Routing in Networks with Uncertain Demand

We study a class of robust network design problems motivated by the need to scale core networks to meet increasingly dynamic capacity demands. Past work has focused on designing the network to support all hose matrices (all matrices not exceeding marginal bounds at the nodes). This model may be too conservative if additional information on traffic patterns is available. Another extreme is the fixed demand model, where one designs the network to support peak point-to-point demands. We introduce a capped hose model to explore a broader range of traffic matrices which includes the above two as special cases. It is known that optimal designs for the hose model are always determined by single-hub routing, and for the fixed- demand model are based on shortest-path routing. We shed light on the wider space of capped hose matrices in order to see which traffic models are more shortest path-like as opposed to hub-like. To address the space in between, we use hierarchical multi-hub routing templates, a generalization of hub and tree routing. In particular, we show that by adding peak capacities into the hose model, the single-hub tree-routing template is no longer cost-effective. This initiates the study of a class of robust network design (RND) problems restricted to these templates. Our empirical analysis is based on a heuristic for this new hierarchical RND problem. We also propose that it is possible to define a routing indicator that accounts for the strengths of the marginals and peak demands and use this information to choose the appropriate routing template. We benchmark our approach against other well-known routing templates, using representative carrier networks and a variety of different capped hose traffic demands, parameterized by the relative importance of their marginals as opposed to their point-to-point peak demands

Calculation of Mutual Information for Partially Coherent Gaussian Channels with Applications to Fiber Optics

The mutual information between a complex-valued channel input and its complex-valued output is decomposed into four parts based on polar coordinates: an amplitude term, a phase term, and two mixed terms. Numerical results for the additive white Gaussian noise (AWGN) channel with various inputs show that, at high signal-to-noise ratio (SNR), the amplitude and phase terms dominate the mixed terms. For the AWGN channel with a Gaussian input, analytical expressions are derived for high SNR. The decomposition method is applied to partially coherent channels and a property of such channels called "spectral loss" is developed. Spectral loss occurs in nonlinear fiber-optic channels and it may be one effect that needs to be taken into account to explain the behavior of the capacity of nonlinear fiber-optic channels presented in recent studies.Comment: 30 pages, 9 figures, accepted for publication in IEEE Transactions on Information Theor

A universal specification for multicore fiber crosstalk

© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.In order to transition multi-core fiber (MCF) technologies from their research state to volume production, the key design specifications have to be broadly agreed upon, first and foremost an acceptable level of inter-core crosstalk per unit length. Against common belief, we show that MCF crosstalk requirements per unit length are fairly independent of transmission distance in the context of modern coherent optical communication systems. As a consequence, a single value for the tolerable inter-core crosstalk per unit length can be used to specify MCFs, valid from metropolitan (~100 km) to trans-pacific (~10 000 km) deployment scenarios. The notion of a universal inter-core crosstalk specification allows for application-independent MCF designs (including a distance-independent optimum core density) and will facilitate the standardization and volume manufacturing of MCF.Peer ReviewedPostprint (author's final draft

Nonlinear propagation equations in fibers with multiple modes—Transitions between representation bases

The transverse pattern of the field that propagates in a fiber supporting multiple modes can always be described as a superposition of the patterns of the individual fiber modes. Yet, the use of other bases is often found to be more convenient, with the most famous example being that of linearly polarized modes in weakly guiding fibers. The nonlinear propagation equations contain coefficients that involve overlap integrals between the lateral profiles of multiple propagation modes. A fundamental question that has been raised in this context is whether it is legitimate to compute these coefficients from the overlap integrals between elements of alternative bases for the field representation. In this paper, we show that the answer to this question is positive in the most general sense. This result is significant in the context of space-division multiplexed transmission in multi-mode and multi-core fibers.The transverse pattern of the field that propagates in a fiber supporting multiple modes can always be described as a superposition of the patterns of the individual fiber modes. Yet, the use of other bases is often found to be more convenient, with the most famous example being that of linearly polarized modes in weakly guiding fibers. The nonlinear propagation equations contain coefficients that involve overlap integrals between the lateral profiles of multiple propagation modes. A fundamental question that has been raised in this context is whether it is legitimate to compute these coefficients from the overlap integrals between elements of alternative bases for the field representation. In this paper, we show that the answer to this question is positive in the most general sense. This result is significant in the context of space-division multiplexed transmission in multi-mode and multi-core fibers

Stokes-space analysis of modal dispersion in fibers with multiple mode transmission

Modal dispersion (MD) in a multimode fiber may be considered as a generalized form of polarization mode dispersion (PMD) in single mode fibers. Using this analogy, we extend the formalism developed for PMD to characterize MD in fibers with multiple spatial modes. We introduce a MD vector defined in a D-dimensional extended Stokes space whose square length is the sum of the square group delays of the generalized principal states. For strong mode coupling, the MD vector undertakes a D-dimensional isotropic random walk, so that the distribution of its length is a chi distribution with D degrees of freedom. We also characterize the largest differential group delay, that is the difference between the delays of the fastest and the slowest principal states, and show that it too is very well approximated by a chi distribution, although in general with a smaller number of degrees of freedom. Finally, we study the spectral properties of MD in terms of the frequency autocorrelation functions of the MD vector, of the square modulus of the MD vector, and of the largest differential group delay. The analytical results are supported by extensive numerical simulations

Random coupling between groups of degenerate fiber modes in mode multiplexed transmission.

We study random coupling induced crosstalk between groups of degenerate modes in spatially multiplexed optical transmission. Our analysis shows that the average crosstalk is primarily determined by the wavenumber mismatch, by the correlation length of the random perturbations, and by the coherence length of the degenerate modes, whereas the effect of a deterministic group velocity difference is negligible. The standard deviation of the crosstalk is shown to be comparable to its average value, implying that crosstalk measurements are inherently noisy

Modeling and performance metrics of MIMO-SDM systems with different amplification schemes in the presence of mode-dependent loss.

Mode-dependent loss (MDL) is a major factor limiting the achievable information rate in multiple-input multiple-output space-division multiplexed systems. In this paper we show that its impact on system performance, which we quantify in terms of the capacity reduction relative to a reference MDL-free system, may depend strongly on the operation of the inline optical amplifiers. This dependency is particularly strong in low mode-count systems. In addition, we discuss ways in which the signal-to-noise ratio of the MDL-free reference system can be defined and quantify the differences in the predicted capacity loss. Finally, we stress the importance of correctly accounting for the effect of MDL on the accumulation of amplification noise

LuxS-independent formation of AI-2 from ribulose-5-phosphate

<p>Abstract</p> <p>Background</p> <p>In many bacteria, the signal molecule AI-2 is generated from its precursor <it>S</it>-ribosyl-L-homocysteine in a reaction catalysed by the enzyme LuxS. However, generation of AI-2-like activity has also been reported for organisms lacking the <it>luxS </it>gene and the existence of alternative pathways for AI-2 formation in <it>Escherichia coli </it>has recently been predicted by stochastic modelling. Here, we investigate the possibility that spontaneous conversion of ribulose-5-phosphate could be responsible for AI-2 generation in the absence of <it>luxS</it>.</p> <p>Results</p> <p>Buffered solutions of ribulose-5-phosphate, but not ribose-5-phosphate, were found to contain high levels of AI-2 activity following incubation at concentrations similar to those reported <it>in vivo</it>. To test whether this process contributes to AI-2 formation by bacterial cells <it>in vivo</it>, an improved <it>Vibrio harveyi </it>bioassay was used. In agreement with previous studies, culture supernatants of <it>E. coli </it>and <it>Staphylococcus aureus luxS </it>mutants were found not to contain detectable levels of AI-2 activity. However, low activities were detected in an <it>E. coli pgi-eda-edd-luxS </it>mutant, a strain which degrades glucose entirely via the oxidative pentose phosphate pathway, with ribulose-5-phosphate as an obligatory intermediate.</p> <p>Conclusion</p> <p>Our results suggest that LuxS-independent formation of AI-2, via spontaneous conversion of ribulose-5-phosphate, may indeed occur <it>in vivo</it>. It does not contribute to AI-2 formation in wildtype <it>E. coli </it>and <it>S. aureus </it>under the conditions tested, but may be responsible for the AI-2-like activities reported for other organisms lacking the <it>luxS </it>gene.</p

AI-2 does not function as a quorum sensing molecule in Campylobacter jejuni during exponential growth in vitro

<p>Abstract</p> <p>Background</p> <p><it>Campylobacter jejuni </it>contains a homologue of the <it>luxS </it>gene shown to be responsible for the production of the signalling molecule autoinducer-2 (AI-2) in <it>Vibrio harveyi </it>and <it>Vibrio cholerae</it>. The aim of this study was to determine whether AI-2 acted as a diffusible quorum sensing signal controlling <it>C. jejuni </it>gene expression when it is produced at high levels during mid exponential growth phase.</p> <p>Results</p> <p>AI-2 activity was produced by the parental strain NCTC 11168 when grown in rich Mueller-Hinton broth (MHB) as expected, but interestingly was not present in defined Modified Eagles Medium (MEM-α). Consistent with previous studies, the <it>luxS </it>mutant showed comparable growth rates to the parental strain and exhibited decreased motility halos in both MEM-α and MHB. Microarray analysis of genes differentially expressed in wild type and <it>luxS </it>mutant strains showed that many effects on mRNA transcript abundance were dependent on the growth medium and linked to metabolic functions including methionine metabolism. Addition of exogenously produced AI-2 to the wild type and the <it>luxS </it>mutant, growing exponentially in either MHB or MEM-α did not induce any transcriptional changes as analysed by microarray.</p> <p>Conclusion</p> <p>Taken together these results led us to conclude that there is no evidence for the role of AI-2 in cell-to-cell communication in <it>C. jejuni </it>strain NCTC 11168 under the growth conditions used, and that the effects of the <it>luxS </it>mutation on the transcriptome are related to the consequential loss of function in the activated methyl cycle.</p