Algorithms for Allocating Wavelength Converters in All-Optical Networks Authors: Goaxi Xiao and Yiu-Wing Leung

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Algorithms for Allocating Wavelength Converters
in All-Optical NetworksAuthors Goaxi Xiao and
Yiu-Wing Leung

• Presented by Douglas L. Potts
• CEG 790 Summer 2003
• From IEEE/ACM Transactions on Networking, Vol. ,
  No. 4, Aug. 1999
• Authors Goaxi Xiao and Yiu-Wing Leung

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Overview

• Wavelength Converters background
• Converter Placement a study, a algorithm
  proposal
• Simulations to determine worth
• Conclusions

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Wavelength Converters background

• What are they?
• Distinction in terminology
• Why?

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Wavelength Converters background What are
they?

• In Wavelength Division Multiplexing (WDM) divides
  bandwidth across multiple wavelength channels
• On multiple hop lightpaths, it is difficult to
  reserve a single wavelength for all hops
  (Wavelength Continuity Constraint)
• For high network load, need a way to get around
  the Wavelength Continuity Constraint
• Mechanism for converting one fiber optic signals
  light wavelength to another light wavelength

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Wavelength Converters background Distinction
in Terminology

• Full Range Wavelength Converter (FWC)
• Converts incoming wavelength to any outgoing
  wavelength
• Limited Range Wavelength Converter
• Converts incoming wavelength to a subset of
  outgoing wavelengths

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Wavelength Converters background Distinction
in Terminology

• Complete Wavelength Conversion
• When number of FWCs in a node is equal to total
  number of outgoing wavelength channels of this
  node
• Partial Wavelength Conversion
• As Complete Wavelength Conversion has a high cost
  using fewer FWCs per node.

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Wavelength Converters background Why use them?

• To resolve wavelength conflicts on a particular
  hop
• Which reduces blocking probability.

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Wavelength Converters background Why not?

• Costly (in terms of cost, but also in time
  delay for conversion and signal degradation)
• Introduces complexity in Route-Wavelength
  Allocation (RWA)

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Converter Placement converters for all

• Previous studies looked at putting a FWC at each
  node
• Results were that blocking probability is
  drastically reduced, but at great cost (and an
  unrealistic assumption)

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Converter Placement example node
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Converter Placement Choosy allocation

• Paper looks at a method for optimizing FWC
  placement to reduce total number of wavelength
  converters
• Goals for allocation
• Reduce overall blocking probability (better mean
  quality of service)
• Maximum of the blocking probabilities experienced
  at all the source nodes (better fairness)

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Converter Placement Choosy allocation

• Want to minimize blocking probability
• Blocking probability is available via
• Analysis
• Simulation

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Converter Placement Choosy allocation

• Blocking probability by analysis is only
  available by making some simplifying assumptions
• specific traffic models or
• specific routing and wavelength assignment
  methods
• Therefore simulation approach chosen

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Converter Placement Choosy allocation

• Main Idea Simulate a complete wavelength
  conversion network and analyze the utilization
  matrix of the nodes FWCs, optimize converter
  allocation based on this utilization matrix
• Optimized allocation does alter utilization
  matrix for the network, but authors claim that
  the estimated utilization (i.e. that based on
  complete conversion) is good because for a
  well-engineered network the traffic load
  handled by each node should not approach or
  exceed its capacity.

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Converter Placement Choosy allocation

• It is because of the only slight change to the
  utilization matrix when fewer FWCs are used that
  network performance is maintained.

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Converter Placement RWA Algorithm

• Previous work based on two extremes of wavelength
  conversion
• No Wavelength Conversion
• Complete Wavelength Conversion
• Authors needed to come up with a new allocation
  algorithm

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Converter Placement RWA Algorithm

• Critical problem that algorithm needs to solve
  when a certain no. of FWCs have been allocated
  to each node, how should the tuning nodes (i.e.
  nodes with wavelength converters) be selected

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Converter Placement RWA Algorithm

• Main ideas for solving the problem
• Once a request arrives, select the set of tuning
  nodes such that required number of FWCs is
  minimized
• When more than one choice, select the one that
  maximizes the min. no. of free FWCs in each
  tuning node of src. to dest. path
• When more than one choice, select one that has
  max. no. of FWCs installed on the critical node

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Converter Placement RWA Algorithm

• Resulting algorithm
• Check if there is at least one clear channel on
  source-to-destination path. If one exists,
  assign this clear channel to the transmission
  request if there is more than one channel,
  select one of them on a first-fit basis if there
  is none, go to step 2.
• If there is at least one free wavelength channel
  (at any wavelength) on every hop of the
  source-to-destination path, execute
• Construct a directed graph in a manner similar to
  that in the Conflict Resolution Algorithm. For
  each free wavelength channel on every hop, the
  weight of the corresponding edge is M. On every
  intermediate node l, the weight of the edge
  between the node vi(?i, l) and node vo(?o, l) is
• c(?i, ?o, l) M S, if ?i ? ?o or 0, if ?i
  ?o
• where
• SM/(Nt(l) Na(l)) (1 Na(l)/Nt(l)), if
  Nt(l) gt Na(l) or 8, if Nt(l) Na(l)

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Converter Placement RWA Algorithm
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Converter Placement RWA Algorithm

• Resulting algorithm (cont.)
• Apply in the Conflict Resolution Algorithm to
  find the shortest path from the source to the
  destination
• Determine the set of tuning nodes and increment
  Na(l) of each tuning node by 1.
• Otherwise, the transmission request is blocked.

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Numerical Results

• Simulations used to evaluate performance of the
  proposed allocation method, with the steps
• Conduct simulation for any given network with
  complete wavelength conversion and any given
  traffic load and pattern. During simulation,
  record utilization matrix.
• Based on recorded utilization matrix, execute
  Optimization Algorithm to optimize allocation of
  FWCs.
• Conduct another simulation for the same network
  with the FWC allocation being that determined by
  the Optimization Algorithm. During simulation,
  execute the RWA Algorithm to perform routing and
  wavelength assignment and record blocking
  probability.

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Numerical Results

• Extensive Simulations conducted on regular and
  irregular networks, considering both uniform and
  non-uniform traffic
• Regular network 11x11 torus mesh network with
  121 nodes
• Irregular network generated randomly, starting
  from a 10x10 mesh network with 100 nodes and 180
  bi-directional links
• Randomly delete 20 links, while ensuring that
  resulting network is not disconnected
• Randomly add 30 links to the network for the
  j1th node on the i1th row and j2th node on the
  i2th row, define the distance as
• d(i1,j1),(i2,j2) sqrt((i1-i2)2(j1j2)2)

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Simulations Results

• Fig. 7a, 7b, 8a, and 8b

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Simulations Results

• Fig. 9a, 9b, 10a, and 10b

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Simulations Results

• Fig 11a, 11b, 12a, and 12b

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Summary

• Wavelength Converters why and why not
• Converter Placement all nodes, select nodes
• Simulations indicate Proposed allocation matching
  Complete wavelength conversion within a small
  margin

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Conclusions

• Utilizing Wavelength Converters in a Optical WDM
  Network drastically reduces blocking probability
• Wavelength Converters are expensive, so ideal
  situation is to use small number of converters
  while maintaining performance
• By using a simulation-based optimization
  approach, it is possible to collect utilization
  statistics, upon which converter allocation is
  based
• It is possible to use the optimized converter
  allocation to significantly reduce the number of
  converters required, and achieve blocking
  probabilities which are roughly those of Complete
  Wavelength Conversion