Transcript Document

Routing and Wavelength
Assignment in Wavelength
Routing Networks
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Routing and Wavelength
Assignment (RWA) Problem
• Given a set of connections, set up lightpaths by
routing and assigning a wavelength to each
connection
• Two constraints
– Wavelength continuity constraint: a lightpath must use
the same wavelength on all the links along its path
– Distinct wavelength constraint: all lightpaths using the
same link must be allocated distinct wavelengths
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Two Versions of RWA
• Static RWA
– Set of connections known in advance
– Goal is to minimize the number of wavelengths used
• Dynamic RWA
– Connection requests arrive sequentially.
– Setup a lightpath when a connection request arrives and
teardown the lightpath after a finite amount of time
– Goal is to minimize connection blocking
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Static RWA
• An ILP (see handout)
– Solve routing and wavelength assignment jointly
– Objective: minimize the maximum flow (flow = #
lightpaths passing through a link)
• Use the ILP to obtain the min number of
wavelengths required:
– Pick a certain number of wavelengths, see if a solution
can be found
– No - increase the number of wavelengths until a
solution can be found.
– Yes - decrease the number of wavelengths until a
solution can’t be found
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Static RWA
• Decompose into two sub-problems
– Routing
• Formulated as ILP
• Objective: minimize the maximum number of
lightpaths on any link
– Wavelength assignment
• Reduce to graph coloring problem
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Static Wavelength Assignment
Problem
• Given a set of lightpaths and their routes, assign a
wavelength to each lightpath
– Constraint: any two lightpaths sharing the same
physical link are assigned different wavelengths
– Objective: minimize the number of wavelengths used
• Problem can be reduced to graph coloring
– Construct a graph G where nodes represents lightpaths,
an edge exists between two nodes if the corresponding
lightpaths pass through a common physical link
– Color the nodes in G such that no two adjacent nodes
have the same color
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Reduce Wavelength Assignment
to Graph Coloring
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Graph Coloring
• NP-complete
• Sequential graph-coloring heuristic
– Vertices sequentially added to the portion of the graph
already colored
– When add a vertex, assign it the smallest color not
used by any of its neighbors
• Smallest-last ordering: assuming that the vertices
vk+1, ..., vn have been selected, choose vk so that
the degree of vk in the subgraph induced by V {vk+1, ..., vn} is minimal.
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Wavelength Converters
• Wavelength converter: convert the wavelength of
an input signal to a different wavelength
• Degree of Wavelength Conversion
– Full wavelength conversion: any input wavelength can
be converted to any other wavelength
– Fixed wavelength conversion: an input wavelength can
be converted to exactly one other wavelength
– Limited wavelength conversion: an input wavelength
can be converted to a subset of the available
wavelengths
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Static RWA with Wavelength
Conversion
• If each node has full wavelength conversion
capability
– Only need solve routing problem
– Minimizing the maximum flow will minimize
the number of wavelengths used
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Static RWA: a Layered Graph
Approach
• Route and assign wavelength to each connection
one by one
• Use layered graph to deal with wavelength
continuity constraint
– Create W copies of the network graph, W = number of
wavelengths in a fiber
– RWA is solved by finding a path in one copy of the
network graph
• Limited/fixed conversion: add links between
layers
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