Wavelength Conversion

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Chapter 11

• Wavelength Conversion

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Wavelength Conversion

• To establish a lightpath, we require that the
  same wavelength be allocated on all the links in
  the path.
• This requirement is known as the
  wavelength-continuity constraint (e.g., see
  BaMu96).
• This constraint distinguishes the
  wavelength-routed network from a circuit-switched
  network which blocks calls only when there is no
  capacity along any of the links in the path.
  assigned to the call.

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Wavelength conversion

• wavelength conversion
• It is easy to eliminate the wavelength-continuity
  constraint, if we were able to convert the data
  arriving on one wavelength along a link into
  another wavelength at an intermediate node and
  forward it along the next link.
• a single lightpath in such a wavelength-convertibl
  e network can use a different wavelength along
  each of the links in its path.
• Thus, wavelength conversion may improve the
  efficiency in the network by resolving the
  wavelength conflicts of the lightpaths.

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Wavelength converter
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Characteristics of WC

• transparency to bit rates and signal formats,
• fast setup time of output wavelength,
• conversion to both shorter and longer
  wavelengths,
• moderate input power levels,
• possibility for same input and output wavelengths
  (i.e., no conversion),
• insensitivity to input signal polarization,
• low-chirp output signal with high extinction
  ratio7 and large signal-to-noise ratio, and
• simple implementation.

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Wavelength Conversion Technologies

• Wavelength conversion techniques can be broadly
  classified into two types
• opto-electronic wavelength conversion the
  optical signal must first be converted into an
  electronic signal and
• all-optical wavelength conversion the signal
  remains in the optical domain.
• coherent effects
• cross modulation.

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Wavelength Conversion in Switches

• Where do we place them in the network? switches
  (crossconnects)
• A possible architecture of such a
  wavelength-convertible switching node is the
  dedicated wavelength-convertible switch (from
  LeLi93). (wavelength interchanging crossconnect
  (WIXC)),.
• Each wavelength along each output link in a
  switch has a dedicated wavelength converter i.e.,
  an M x M switch in an N-wavelength system
  requires M x N converters.

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• The incoming optical signal from a link at the
  switch is first wavelength demultiplexed into
  separate wavelengths.
• Each wavelength is switched to the desired output
  port by the nonblocking optical switch.
• The output signal may have its wavelength
  changed by its wavelength converter.
• Finally, various wavelengths combine to form an
  aggregate signal coupled to an outbound fiber.

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Wavelength Conversion in Switches
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Switch sharing converter

• the dedicated wavelength-convertible switch is
  not very cost efficient since all of its
  converters may not be required all the time
  InMu96.
• An effective method to cut costs is to share the
  converters.
• Two architectures
• shareper-node structure
• share-per-link structure

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shareper-node structure

• All the converters at the switching node are
  collected in a converter bank.
• A converter bank is a collection of a few
  wavelength converters.
• This bank can be accessed by any wavelength on
  any incoming fiber by appropriately configuring
  the larger optical switch.
• In this architecture, only the wavelengths which
  require conversion are directed to the converter
  bank.
• The converted wavelengths are then switched to
  the appropriate outbound fiber link by the second
  optical switch.

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Share-per-Node WC
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Share-per-link structure

• Each outgoing fiber link is provided with a
  dedicated converter bank which can be accessed
  only by those lightpaths traveling on that
  particular outbound link.
• The optical switch can be configured
  appropriately to direct wavelengths to-ward a
  particular link, either with conversion or
  without conversion.

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Share-per-link structure
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11.3 network design

• Network designs must evolve to incorporate
  wavelength conversion effectively.
• Network designers must choose not only among the
  various conversion techniques but also among the
  several switch architectures described.
• An important challenge in the design is to
  overcome the limitations in using wavelength
  conversion technology.
• These limitations fall into the following three
  categories
• Limited availability of wavelength converters at
  the nodes.
• Sharing of converters.
• Limited-range wavelength conversion.

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Limited availability of wavelength converters at
the nodes.

• As long as wavelength converters remain expensive
  Yoo96, it may not be economically viable to
  equip all the nodes in a WDM network with them.
• Some effects of sparse conversion (i.e., having
  only a few converting switches in the network)
  have been examined SuAS96.
• An interesting question which has not been
  answered is where (optimally?) to place these few
  converters in the network.

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Sharing of converters.

• Even among the switches capable of wavelength
  conversion, it may not be cost effective to equip
  all the output ports of a switch with this
  capability.
• Designs of switch architectures have been
  proposed which allow sharing of converters among
  the various signals at a switch.
• It has been shown in LeLi93 that the
  performance of such a network saturates when the
  number of converters at a switch increases beyond
  a certain threshold.
• An interesting problem is to quantify the
  dependence of this threshold on the routing
  algorithm used and the blocking probability
  desired.

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Limited-range wavelength conversion.

• Four-wave-mixing-based alloptical wavelength
  converters provide only a limited-range
  conversion capability.
• If the range is limited to k, then an input
  wavelength ?i can only be converted to
  wavelengths ?max(i-k,1)through ?max(ik,N)
• where N is the number of wavelengths in the
  system (indexed 1 through N).
• Analysis shows that networks employing such
  devices, however, compare favorably with those
  utilizing converters with full-range capability,
  under certain conditions.

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Network Control

• Control algorithms are required in a network to
  manage its resources effectively.
• An important task of the control mechanism is to
  provide routes to the lightpath requests while
  maximizing a desired system parameter, e.g.,
  throughput.
• Such routing schemes can be classified into
  static and dynamic categories depending on
  whether the lightpath requests are known a priori
  or not.

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Dynamic Routing

• In a wavelength-routed optical network, lightpath
  requests arrive at random between
  source-destination pairs and each lightpath has a
  random holding time after which it is torn down.
• These lightpaths need to be set up dynamically
  between source-destination pairs by determining a
  route through the network connecting the source
  to the destination and assigning a free
  wavelength along this path.
• Two lightpaths which have at least a link in
  common cannot use the same wavelength. Moreover,
  the same wavelength has to be assigned to a path
  on all of its links. This is the
  wavelength-continuity constraint described in
  Section 11.1.
• This routing and wavelength assignment (RWA)
  problem

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Dynamic Routing

• However, if all switches in the network have full
  wavelength conversion, the network becomes
  equivalent to a circuitswitched telephone
  network RaSi95.
• Routing algorithms have been proposed for use in
  wavelength-convertible networks. In LeLi93, the
  routing algorithm approximates the cost function
  of routing as the sum of individual costs due to
  using channels and wavelength converters.
• For this purpose, an auxiliary graph is created
  BaSB91 and the shortestpath algorithm is
  applied on the graph to determine the route.
• In ChFZ96, an algorithm with provably optimal
  running time has been provided for such a
  technique.

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Dynamic Routing

• Algorithms have also been studied which use a
  fixed path or deterministic routing RaSi95.
• In such a scheme, there is a fixed path between
  every source-destination pair in the network.
• Several RWA heuristics have been designed based
  on which wavelength to assign to a lightpath
  along the fixed path BaSB91, MoAz96a, MoAz96b
  and which, if any, lightpaths to block
  selectively.
• However, design of efficient routing algorithms
  which incorporate the limitations in Section
  11.3.1 still remains an open problem.

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Static Routing

• Static RWA problem assumes that all the
  lightpaths that are to be set up in the network
  are known initially.
• The objective is to maximize the total throughput
  in the network, i.e., the total number of
  light-paths which can be established
  simultaneously in the network.
• An upper bound on the carried traffic per
  available wavelength has been obtained (for a
  network with and without wavelength conversion)
  by relaxing the corresponding integer linear
  program (ILP) RaSi95.
• Several heuristicbased approaches have been
  proposed for solving the static RWA problem in a
  network without wavelength conversion ChBa96.
• Again, efficient algorithms which incorporate the
  limitations in Section 11.3.1 for a
  wavelength-convertible network are still
  unavailable.

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Network Management

• Issues arise in network management regarding the
  use of wavelength conversion to promote
  interoperability across sub-networks managed by
  independent operators.
• Wavelength conversion supports the distribution
  of network control and management functionalities
  into smaller sub-networks by allowing flexible
  wavelength assignments within each sub-network
  Yoo96.

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Related Issue

• RWA on wavelength convertible WDM
• Converter placement problem
• Converter allocation problem

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RWA on wavelength convertible WDM

• Graph model
• Layered graph
• WS (wavelength selected)
• WC (wavelength convertible)
• Node
• Vertical edge
• Horizontal edge
• M(NK) nodes

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Example

• Book in p. 115

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Converter placement problem

• Given k number of converters, how can the mean
  blocking probability in a network be computed?
• Is it possible to achieve performance close to
  the best achievement with only a few converters?
• What is the effect of network topology on the
  number of converter required?
• Given k number of converters, how can the best k
  nodes be chosen to place them, to achieve optimal
  performance?

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Converter allocation problem

• Allocating Wavelength Convertersin All-Optical
  Networks
• WCs can be distinguished into two types
• a full-range wavelength converter (FWC) can
  convert an incoming wavelength to any outgoing
  wavelength and
• a limited range wavelength converter can convert
  an incoming wavelength to a subset of the
  outgoing wavelengths.

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Types

• When the number of FWCs in a node is equal to
  the total number of outgoing wavelength channels
  of this node (which is equal to the number of
  outgoing fibers times the number of wavelength
  channels per fiber), FWCs are always available
  when they are needed. We call this scenario a
  complete wavelength conversion.
• It may be more cost-effective to use a fewer
  number of FWCs this scenario is called partial
  wavelength conversion. Given a limited number of
  FWCs, it is necessary to allocate these FWCs to
  the node.

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• With the above idea, we divide the problem into
  thefollowing two subproblems.
• 1) Record the utilization matrix via computer
  simulations.
• 2) Based on the utilization matrix, optimize the
  allocations of the FWCs.

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Recording Utilization Matrix

• We record the utilization matrix via simulation
  experiments.
• One important issue is that, when there is
  wavelength conflict,we need to determine where
  we should perform wavelengthconversion.
• Different methods can lead to different
  utilizationmatrices.
• In our study, we design and adopt one
  possiblemethod to resolve wavelength conflict
  that gives good results.
• However, our simulation-based optimization
  methodology isalso applicable to any other
  conflict resolution method.
• For any given call duration statistics, we can
  generate theduration for each transmission.

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Recording Algorithm
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Recording Algorithm
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Conflict Resolution Algorithm

• The main idea is to transform the problem of
  resolving wavelength conflict into an equivalent
  shortest path problem in a directed graph, where
  the length of a path in the directed graph is
  determined by
• 1) the total number of FWCs used and
• 2) the maximum number of FWCs being used on
  every node of the source-to-destination path.
• By determining the shortest path in this directed
  graph, we can fulfill both of our objectives.
• .
• Along the source-to-destination path in the
  network, the intermediate nodes (excluding the
  source and destination nodes) are indexed from 1
  to L.
• Let W(L) denotes the number of FWCs being used
  on the the intermediate node.
• Auxiliary graph construction
• Minimum-Cost Path Selected

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Auxiliary graph construction
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Conflict Resolution Algorithm
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Allocating FWCs

• In this subsection, we optimize the allocations
  of a given number of FWCs based on the
  utilization matrix .
• After allocating a certain number of FWCs to a
  node, we can get from the percentage of time that
  this node has sufficient FWCs to serve the
  transmission.
• For convenience, we call this quantity the total
  utilization.

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Three different objectives

• Maximize the sum of total utilizations of all the
  nodes, so that the overall utilization of FWCs
  can be improved. As a result, the overall
  blocking probability can be smaller and, hence,
  the mean quality of service is better.
• Maximize the product of the total utilizations of
  all the nodes. In this manner, the overall
  utilization of FWCs can be improved (i.e.,
  better mean quality of service) and the
  allocation of FWCs to the nodes can be more
  fair.
• Maximize the minimum value of total utilization
  of the nodes, so that the allocation of FWCs to
  the nodes can be more fair.

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Maximize the sum of total utilizations of all the
nodes
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Maximize the product of the total utilizations of
all the nodes
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Maximize the minimum value of total utilization
of the nodes