Optical Switching Networks

1
Optical Switching Networks

• Presentation by
• Joaquin Carbonara

2
References

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

3
Introduction

• Statement of the Problem

4
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.

5
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.

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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.

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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.

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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 --gt WSNO --gt RNB

9
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)

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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.

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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)

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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.

13
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

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Design Tools

• Other tools include simulation and analysis (I
  will not talk about these tools).

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Optical Network Design

• Definitions, Examples and Theoretical Results

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Heterogeneous WDM Cross-Connect
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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.

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ComponentsAWGR

• 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.

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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

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WXC-RNB construction for M1(Ngo/Pan/Qiao infocom
04)

• Components Let f2, b3, n4. Then it has
• f demultx, fbn LWC(Bi,n), fb n ? n-AWG,
• fbn LWC(n,bc,b(fc)), n multx,
• nb ? nb-AWG, and f multx.

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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.

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WXC-RNB-1 and GT

• Konigs 1916 Theorem Let G(U,VE) 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.

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About Konigs Theorem
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Back to WXC-RNB-1...

• Represent the network as a bipartite graph
  G(U,VE) 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)

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Graph of WXC-RNB-1

• Represent the network as a bipartite graph
  G(U,VE)
• Request (?p, Fq, Fj) ? edge (ui,vj)
• where i qb ?p/n?
• By a simple variation of Konigs theorem, the
  graph G is colorable with n x b colors (label
  each color with a tuple (c,d)), 1c n and 1d
  b, in such a way that edges sharing a vertex in
  U have different first color component.

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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 cth
  output 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.

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Routing in WXC-RNB-1

• The basic idea is this (cont.)
• 4. The properties of the coloring inherited from
  Konigs theorem guaranteed non-blockiness.

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Example (Ngo/Pan/Qiao) WXC-RNB in Model-2
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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

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Haxel/Rasala/Wilfong/Winklers work on WDM
Cross-connects
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On the news...
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Optical Network Complexity

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

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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-jd.
• 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.

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Complexity of WDM networks(unicast) m1(w,f,d)
even w (Ngo/Pan/Yang)
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Complexity of WDM networks (unicast) m1(w,f,d)
odd w (Ngo/Pan/Yang)
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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.

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ComplexityUsing Graph/Theoretical Representation

• (Ngo) Graph Theoretical representation.
• a) Fiber-channels get replaced by vertices
• b) Edges capacity

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ComplexityUsing Graph/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
• DAGDirected Acyclic Graph

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Graph/Theoretical Representation(Winkler/Haxell/R
asala/Wilfong)Dynamic bipartite graphs
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ComplexityUsing DAG GT RepresentationRigorous
Setting Model-2

• DAG model networks as follows
• (n1,n2)-network is a DAG N(V,EA,B)
• Vvertices, Eedges, Ainputs, Boutputs,
• n1 A, n2B.
• We can now define request, request frame, route,
  RNB/SNB/WSNB network.
• Key idea requests path must be disjoint to be
  (simultaneously) realizable.

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ComplexityUsing Graph/Theoretical
RepresentationRigorous Setting Model-1

• DAG model networks as follows
• w,f-network is a DAG N(V,EA,B)
• Vvertices, Eedges, Ainputs, Boutputs
• ABwf and BB1 B2 ... Bf
• We can now define request, request frame, route,
  and RNB/SNB/WSNB w,f-network.

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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),

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ComplexityResults 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

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ComplexityRNB w,f-networks

• The size function has known estimates in this
  case

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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.

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Complexity

• Other results include different ways of create
  atomic networks, and operations to create
  larger networks from smalles
• Left and right union
• The ??-product

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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.