Routing and Wavelength Assignment in Wavelength Routing Networks

1. Routing and Wavelength Assignment in Wavelength Routing Networks

2. 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

3. 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

4. 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

5. 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

6. 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

7. Reduce Wavelength Assignment to Graph Coloring

8. 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.

9. 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

10. 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

11. 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