Routing and wavelength assignment in wavelength routing networks
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Routing and Wavelength Assignment in Wavelength Routing Networks. 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

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Routing and wavelength assignment rwa problem
Routing and Wavelength Assignment (RWA) Problem Networks

  • 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


Two versions of rwa
Two Versions of RWA Networks

  • 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


Static rwa
Static RWA Networks

  • 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


Static rwa1
Static RWA Networks

  • 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


Static wavelength assignment problem
Static Wavelength Assignment Problem Networks

  • 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



Graph coloring
Graph Coloring Networks

  • 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.


Wavelength converters
Wavelength Converters Networks

  • 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


Static rwa with wavelength conversion
Static RWA with Wavelength Conversion Networks

  • If each node has full wavelength conversion capability

    • Only need solve routing problem

    • Minimizing the maximum flow will minimize the number of wavelengths used


Static rwa a layered graph approach
Static RWA: a Layered Graph Approach Networks

  • 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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