Broadcasting, Scalability, and Reconfigurability Aspects in an All-Optical Network Architecture

All-optical networks are a sound answer to the huge data traffic demand expected for the forthcoming information society. Interesting networking aspects are the broadcasting, scalability, and reconfiguration in an all-optical environment. These issues are addressed in the present article for an all-optical network called MATRIX, which is time slotted and uses packet switching. The architecture enables the all-optical interconnection of a large number of nodes with both a small number of wavelengths and wavelength continuity based on a consequent exploitation of wavelength-division multiplexing and space-division multiplexing (i.e., multiple fibers per cable are used). For an efficient use of the resources, each node is equipped with multiple transmitters and receivers, respectively. Two different broadcasting schemes are investigated. An analytical model is developed, and the corresponding simulation results are in good agreement. It is further shown how different networks of arbitrary size can be interconnected to larger all-optical network clusters, thereby providing scalability not only with respect to the number of nodes but also to the geographical extension. Finally, wavelength reassignments allow change of optical paths through the network in case of changing traffic patterns or network failures in order to best exploit the available network resources. The total number of possible configurations is determined by the theory of Latin Squares.     

Error estimates for the finite-element solution of an elliptic singularly perturbed problem

e-mail:ang{at}am.uni-erlangen.de The paper deals with an upwind discretization of finite-volume-typefor singularly perturbed elliptic boundary value problems. Stability,inverse monotonicity and convergence are considered. The mainobjective is to pursue the dependence of the error estimateon the perturbation parameter.     

An Existence Proof for a Boundary-Value Problem with Non-Smooth Boundary from the Theory of Water Waves

The generation of surface waves in a fluid caused by a partiallysubmerged body is modelled mathematically as a boundary-valueproblem for the Laplacian with Neumann data on the bottom ofthe fluid container and on the body, a linearized free-surfacecondition and a radiation condition at infinity. In the presentwork, existence of a unique solution of this problem is shownby integral-equation methods. Although corners and edges ofthe body and non-normal intersections of the body with the freesurface are allowed, the problem is reformulated as an integralequation in the space of continuous functions defined over thesubmerged portion of the body, on which Neumann data are given.This integral equation is uniquely solvable for all frequencies.