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 v k+1,..., v n have been selected, choose v k so that the degree of v k in the subgraph induced by V - {v k+1,..., v n } 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