Optical Switching NetworksReferencesIntroductionAbout Optical NetworksAbout Optical networksSlide 6Slide 7Design analysisDesign AnalysisSlide 10Design toolsSlide 12Slide 13Design ToolsOptical Network DesignHeterogeneous WDM Cross-ConnectComponents: Wavelength ConvertersComponents: AWGRRequest Model (understanding Nets blocking properties)WXC-RNB construction for M1 (Ngo/Pan/Qiao infocom ‘04)WXC-RNB-1 means ...WXC-RNB-1 and GTAbout Konig’s TheoremBack to WXC-RNB-1...Graph of WXC-RNB-1Routing in WXC-RNB-1Slide 27Example (Ngo/Pan/Qiao): WXC-RNB in Model-2Other interesting results related to non-blocking networksHaxel/Rasala/Wilfong/Winkler’s work on WDM Cross-connectsOn the news...Optical Network ComplexityComplexity: Minimizing the Number of LWCComplexity of WDM networks (unicast) m1(w,f,d) even w (Ngo/Pan/Yang)Complexity of WDM networks (unicast) m1(w,f,d) odd w (Ngo/Pan/Yang)Complexity: Size and Depth using GT representationComplexity Using Graph/Theoretical RepresentationComplexity Using Graph/Theoretical Representation ExampleGraph/Theoretical Representation (Winkler/Haxell/Rasala/Wilfong) Dynamic bipartite graphsComplexity Using DAG GT Representation Rigorous Setting Model-2Complexity Using Graph/Theoretical Representation Rigorous Setting Model-1Complexity: DAG sizeComplexity: Results from DAG modelComplexity: RNB [w,f]-networksComplexitySlide 46Future WorkOptical Switching NetworksPresentation byJoaquin CarbonaraReferences•Work by–Ngo,Qiao,Pan, Anand, Yang–Chu/Liu/Zhang–Pippinger/Feldman/Friedman–Winkler/Haxell/Rasala/WilfongIntroductionStatement of the ProblemAbout Optical Networks•Wavelength-routed all-optical WDM networks are considered to be candidates for the next generation wide-area Backbone networks [Chlamtac,Ganz and Karmi, 1992 and Mukherjee, 2000]•Wavelength Routed Network: wavelength routers connected by fiber links (each being able to support wavelength channels by supporting WDM)•WXC can be uni/multicast. OXC can be used between processors in a parallel or distributed system.About Optical networks•In a dynamic wavelength-routed WDM network, limitations of the network may result in some light-paths requests not being satisfied.•Goal: design all-optical networks that minimizes blocking.About Optical Networks•Wavelength Continuity Constraint (which makes Optical nets different than circuit-switched telephone nets): Thus two light paths that share a common fiber link should not be assigned the same wavelength.•Solution: Wavelength converters.About Optical Networks•Switching speed is the bottleneck at the core of the optical network infrastructure [Singhal and Jain, 2002]•Goal: design cost-effective WXC that are fast and easily scalable.Design analysis•RNB (rearrangeable non-blocking): a set of requests submitted at once can be satisfied by the network.•SNB (Strictly non-blocking): a new request can be satisfied without changing current request paths.•WSNB (Wide sense non-blocking): a new request can be satisfied using an (on-line) algorithm.•SNB --> WSNO --> RNBDesign Analysis•Cost of components is important.•Number of different components:–(de)multiplexors (MUX/DEMUX)–Wavelenght converters (full-FWC or limited-LWC)–Semiconductor Optical Amplifiers (SOA)–Optical add-drop multiplexors (OADM)–Arrayed Waveguide Grating Routers (AWGR)Design Analysis•Theoretical results help understand and design networks–Complexity is important (as a function of size)•Size: number of edges in graph theoretical representation•Depth: number of edges in longest path of graph theoretical representation.Design tools•Mathematical modeling–Graph Theory; Theory of Discrete Mathematics/Combinatorics; Functions (Real/Integer valued, one or more variables); Linear/Multilinear Algebra.•In mathematics you don't understand things. You just get used to them. von Neumann, Johann (1903 - 1957)•Mathematicians are a species of Frenchmen: if you say something to them they translate it into their own language and presto! it is something entirely different. Goethe (German writer), Maxims and Reflexions, (1829)Design tools•Advantages of mathematical modeling:–Many tools available since Mathematics is an old and well established discipline–True statements are backed by proofs (100% guaranteed--if used properly). –Math language is practically universal. This guarantees a larger audience .–Math organizes knowledge extremely well.Design tools•Disadvantages of Mathematical modeling–It is hard to fit reality into a “nice” Theory–Theory requires organized abstract thinking--not a very popular activityDesign Tools•Other tools include simulation and analysis (I will not talk about these tools).Optical Network DesignDefinitions, Examples and Theoretical ResultsHeterogeneous WDM Cross-ConnectComponents: Wavelength Converters•Wavelength converters: take as input wavelengths coming on different fibers and can be programmed to modify the wavelength and output modified wavelength.•To reduce cost, researchers have–Used Limited Range Wavelength converters (LWC) instead of Full Range Wavelength converters (FWC)–Share wavelength converters among fiber links.•Notation: LWC(A,B) takes inputs from set A and produces outputs from set B.Components:AWGR•Arrayed Waveguide Grating Routers: –Passive devices: reroute channels inside fibers–Easily available and inexpensive–Take m inputs and have m outputs fibers–Process wavelengths 0 to m-1–Wavelength i at input fiber j gets routed to the same wavelength at output fiber (i-j)mod m.Request Model(understanding Nets blocking properties)•Model 1 -- (, F, F): Requests are of the form (i, Fj, Fj  ) where i is a wavelength, Fj is an input fiber and Fj  is an output fiber. Requests requires only an given output fiber, but do not specify the output wavelength.•Model 2 -- (, F, , F): More restrictive than Model 1 since output wavelength is also requested.•Note: If N satisfies M2 then it satisfies M1WXC-RNB construction for M1(Ngo/Pan/Qiao infocom ‘04)•Components: Let f=2, b=3, n=4. Then it has f demultx, fbn LWC(Bi,[n]), fb n  n-AWG, fbn LWC([n],[bc,b(f+c)]), n multx, nb  nb-AWG, and f multx.WXC-RNB-1 means ...•RNB means that any set S of valid requests will not be blocked in the network N. While in transit inside the network, the Wavelength Continuity Constrain must be satisfied. •Valid request means–no two