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Optical Switching Networks. Presentation by Joaquin Carbonara. References. Work by Ngo,Qiao,Pan, Anand, Yang Chu/Liu/Zhang Pippinger/Feldman/Friedman Winkler/Haxell/Rasala/Wilfong. Introduction. Statement of the Problem. About Optical Networks.

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optical switching networks

Optical Switching Networks

Presentation by

Joaquin Carbonara

references
References
  • Work by
    • Ngo,Qiao,Pan, Anand, Yang
    • Chu/Liu/Zhang
    • Pippinger/Feldman/Friedman
    • Winkler/Haxell/Rasala/Wilfong
introduction

Introduction

Statement of the Problem

about optical networks
About 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 networks5
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 networks6
About Optical Networks
  • Wavelength Continuity Constraint (which makes Optical nets different than circuit-switched telephone nets):Thustwo light paths that share a common fiber link should not be assigned the same wavelength.
  • Solution: Wavelength converters.
about optical networks7
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
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 --> RNB
design analysis9
Design 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 analysis10
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
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 tools12
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 tools13
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 activity
design tools14
Design Tools
  • Other tools include simulation and analysis (I will not talk about these tools).
optical network design

Optical Network Design

Definitions, Examples and Theoretical Results

components wavelength converters
Components: 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
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
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 M1
wxc rnb construction for m1 ngo pan qiao infocom 04
WXC-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]), fbn n-AWG,

fbn LWC([n],[bc,b(f+c)]), n multx,

nb nb-AWG, and f multx.

wxc rnb 1 means
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 requests will ask for the same input wavelength and fiber.
    • the number of requests asking for the same output fiber cannot exceed the fiber capacity.
wxc rnb 1 and gt
WXC-RNB-1 and GT
  • Konig’s 1916 Theorem: Let G(U,V;E) be a bipartite graph. Then: the maximum (vertex) degree equals the chromatic index.
  • Chromatic index= minimum number of colors needed to edge color G so that adjacent edges use different colors.
back to wxc rnb 1
Back to WXC-RNB-1...
  • Represent the network as a bipartite graph G(U,V;E) for the sole purpose of determining a non-blocking route for each request:
    • The set U corresponds to the set of input bands (there are fb of them)
    • The set V corresponds to the set of output fibers (there are f of them)
graph of wxc rnb 1
Graph of WXC-RNB-1
  • Represent the network as a bipartite graph G(U,V;E):
    • Request (p, Fq, Fj)  edge (ui,vj)

where i = qb+ p/n

  • By a simple variation of Konig’s theorem, the graph G is colorable with n x b colors (label each color with a tuple (c,d)), 1≤c ≤n and 1≤d ≤b, in such a way that edges sharing a vertex in U have different first color component.
routing in wxc rnb 1
Routing in WXC-RNB-1
  • The basic idea is this:

1. [request (p, Fq, Fj)] [edge (ui,vj)]  [color (c,d)]

2. Then Route p so that it ends up in the cthoutput line of its stage-1 AWGR.

3. Working from the other end, we want the request to end in Fj. There are b fibers demuxing to it. We can see that if the stage-2 LWC routes the wavelength to its dth line of its demuxer, the desired output is obtained.

routing in wxc rnb 127
Routing in WXC-RNB-1
  • The basic idea is this (cont.):

4. The properties of the coloring inherited from Konig’s theorem guaranteed non-blockiness.

other interesting results related to non blocking networks
Other interesting results related to non-blocking networks
  • Strictly non-blocking networks are highly desirable. It is difficult to build such networks that are cost efficient.
  • An interesting result (Ngo):

WXC-SNB-1 if and only if WXC-SNB-2

optical network complexity
Optical Network Complexity

Graph Theoretical representations, Bounds, minimizing the number of components. Examples and theoretical results.

complexity minimizing the number of lwc
Complexity: Minimizing the Number of LWC
  • Results related to using the least possible number of LWC on a uni/multicast network:
    • Define LWC(d) when LWC can convert i to j iff |i-j|≤d.
    • Consider Homogenous Model-2 of requests with w wavelengths and f fibers (HM2(w, f)).
    • Want to study statistic m1(w,f,d) = least number of LWC(d) needed if HM2(w, f) is SNB.
complexity size and depth using gt representation
Complexity: Size and Depth using GT representation
  • (Ngo) Using the DAG model (Directed Acyclic Graphs) we can establish a formal definition of size and depth of a network.
  • Size: number of edges in the graph
  • Depth: number of edges in the longest path.
complexity using graph theoretical representation
ComplexityUsingGraph/Theoretical Representation
  • (Ngo) Graph Theoretical representation.
  • a) Fiber-channels get replaced by vertices
  • b) Edges ~ capacity
complexity using graph theoretical representation example
ComplexityUsingGraph/Theoretical RepresentationExample
  • Size of the network is number of edges.
  • Depth is longest path.
  • It uses 2 2x2 AWG, 4 FWC 2 multiplexors and 2 demultiplexors
  • DAG=Directed Acyclic Graph
graph theoretical representation winkler haxell rasala wilfong dynamic bipartite graphs
Graph/Theoretical Representation(Winkler/Haxell/Rasala/Wilfong)Dynamic bipartite graphs
complexity using dag gt representation rigorous setting model 2
ComplexityUsingDAG GT RepresentationRigorous Setting Model-2
  • DAG model networks as follows:
    • (n1,n2)-network is a DAG N=(V,E;A,B)

V=vertices, E=edges, A=inputs, B=outputs,

n1= |A|, n2=|B|.

  • We can now define request, request frame, route, RNB/SNB/WSNB network.
  • Key idea: requests’ path must be disjoint to be (simultaneously) realizable.
complexity using graph theoretical representation rigorous setting model 1
ComplexityUsingGraph/Theoretical RepresentationRigorous Setting Model-1
  • DAG model networks as follows:
    • [w,f]-network is a DAG N=(V,E;A,B)

V=vertices, E=edges, A=inputs, B=outputs

|A|=|B|=wf and B=B1 B2 ... Bf

  • We can now define request, request frame, route, and RNB/SNB/WSNB [w,f]-network.
complexity dag size
Complexity: DAG size
  • Let an n-network be a Homogeneous Network with n inputs and outputs. If the output is further divided into f bands of size w (needed for M-2) we call it a [w,f]-network.
  • The smallest number of edges (size) for it to be SNB, RNB, and WSNB is sc2(w,f), rc2(w,f) and wc2(w,f) (Model 2), or sc1(n), rc1(n) and wc1(n) (Model 2).
  • rc1(n)≤wc1(n) ≤ sc1(n),
complexity results from dag model
Complexity:Results from DAG model
  • M1 is less restrictive than M2 since M2 requests specify an output wavelength. The following result shows that in the SNB case there is no difference in cost between models:
complexity rnb w f networks
Complexity:RNB [w,f]-networks
  • The size function has known estimates in this case:
complexity
Complexity
  • Advantages of having bounds:
    • Number of edges can be related to network cost
    • Theoretical results are often the only way to gain experience with abstract systems. Examples may be too poor or difficult to concoct.
complexity46
Complexity
  • Other results include different ways of create “atomic” networks, and operations to create larger networks from smalles
    • Left and right union
    • The -product
future work
Future Work
  • Expansion of current models using different models with the goal of eliminating blockiness while reducing cost.
  • Search for better bounds on the current statistics.
  • Search for new meaningful statistics (is size and depth the only ones that matter?) on GT representations.