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Wavelength Assignment in Optical Network Design

Team 6: Lisa Zhang (Mentor) Brendan Farrell, Yi Huang, Mark Iwen, Ting Wang, Jintong Zheng Progress Report Presenters: Mark Iwen. Wavelength Assignment in Optical Network Design. Wavelength Assignment. Motivated by WDM (wavelength division multiplexing) network optimization Input

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Wavelength Assignment in Optical Network Design

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  1. Team 6: Lisa Zhang (Mentor) Brendan Farrell, Yi Huang, Mark Iwen, Ting Wang, Jintong Zheng Progress Report Presenters: Mark Iwen Wavelength Assignment in Optical Network Design

  2. Wavelength Assignment Motivated by WDM (wavelength division multiplexing) network optimization Input • A network G=(V,E) • A set of demands with specified src, dest and routes • demand di = (si, ti, Ri) • WDM fibers • U: fiber capacity, number of wavelengths per fiber Output • Assign a wavelength for each demand route • Demand paths sharing same fiber have distinct wavelengths

  3. Example

  4. Model 1: Min conversion B A O converter C Fiber capacity u = 2 Demand routes: AOB, BOC, COA • Routes given • L(e): load on link e • u: fiber capacity • f(e) =  L(e) / u  • Deploy f(e) fibers on link e : no extra fibers • Use converters if necessary • Min number of converters

  5. Model 1: Min conversion Model 2: Min fiber converter • Routes given • L(e): load on link e • u: fiber capacity • f(e) =  L(e) / u  • Deploy f(e) fibers on link e : no extra fibers • Use converters if necessary • Min number of converters • Each demand path assigned one wavelength from src to dest – no conversion • Deploy extra fibers if necessary • Min total fibers

  6. Model 1: Min conversion Model 2: Min fiber Extra fiber converter • Routes given • L(e): load on link e • u: fiber capacity • f(e) =  L(e) / u  • Deploy f(e) fibers on link e : no extra fibers • Use converters if necessary • Min number of converters • Each demand path assigned one wavelength from src to dest – no conversion • Deploy extra fibers if necessary • Min total fibers

  7. Complexity Perspective of worst-case analysis NP hard • Cannot expect to find optimal solution efficiently for all instances Hard to approximate • Cannot approximate within any constant [AndrewsZhang] • For any algorithm, there exist instances for which the algo returns a solution more than any constant factor larger than the optimal.

  8. Heuristics Focus: • Simple/flexible/scalable heuristics • “Typical” input instances: not worst-case analysis A greedy heuristic • For every demand d in an ordered demand set: Choose a locally optimal solution for d

  9. Why greedy? Viable approach for many hard problems • Set Cover Problem (NP-hard) • SAT solving(NP-hard) • Planning Problems (PSPACE-hard) • Vertex Coloring (NP-hard) • …

  10. Vertex coloring: A closely related problem A classic problem from combinatorial optimization and graph theory Problem statement • Graph D • Color each vertex of D such that neighboring vertices have distinct colors • Minimize the total number of colors needed

  11. Connection to vertex coloring Create a demand graph D from wavelength assignment instance G: • One vertex for each demand • Two demands vertices adjacent iff demand routes share common link Demand graph D is u colorable iff wavelength assignment feasible with 0 extra fibers and 0 conversion.

  12. What we know about vertex coloring Complexity – worst case • NP-hard • Hard to approximate: cannot be approximated to within a factor of n1-e [FeigeKilian][KnotPonnuswami] Heuristic solutions – common cases • Greedy approaches extremely effective For vertex v in an ordering of vertices: Color v with smallest color not used by v’s neighbors • Example: Brelaz’s algorithm [Turner] gives priority to“most constrained” vertex

  13. Try greedy wavelength assignment For every demand d in an ordered demand set: Choose a locally optimal solution for d - Is there good ordering? - Is it easy to find a good ordering? - Local optimality is easy!

  14. Local optimality for model 1 : min conversion Starting at first link, assign wavelength available for greatest number of consecutive links. Convert and continue on a different wavelength until the entire demand path is assigned wavelength(s). Strategy locally optimal

  15. Local optimality for model 1 : min conversion Starting at first link, assign wavelength available for greatest number of consecutive links. Convert and continue on a different wavelength until the entire demand path is assigned wavelength(s). Strategy locally optimal

  16. Local optimality for model 2: Min fiber Choose wavelength w such that assigning w to demand d requires minimum number of extra fibers

  17. Local optimality for model 2: Min fiber Choose wavelength w such that assigning w to demand d requires minimum number of extra fibers Extra fiber on first link

  18. Ordering in Greedy approach Global ordering: Longest first : Order demands according to number of links each demand travels. Heaviest : Weigh each link according to the number of demands that traverse it. Sum the weights on each link of a demand. Ordering suggested by vertex coloring on demand graph Random sampling: choose a random permutation.

  19. Ordering in Greedy approach Local perturbation: d1, d2, d3, d4, … • Coin toss : • Reshuffle initial demand ordering by: • Flipping a coin for each entry in order • With a success, remove the demand and move it to new ordering 2. Top-n : • Reshuffle initial demand ordering by: • Randomly choosing a first n demands • Removing the demand to new ordering

  20. Iterative refinement Global ordering Greedy Local perturbation Greedy

  21. Generating instances Characteristics of network topology: • Sparse networks; average node degree < 3 • Planar • Small networks (~ 20 nodes) Large network (~ 50 nodes) Characteristics of traffic: • Fiber Capacity ~ [20,100] • Lightly loaded networks: 1 fiber per link, fibers half full • Heavily loaded networks: ~ 2 fibers per links

  22. Topologies of real networks

  23. Topologies of real networks

  24. Topologies of real networks

  25. Experimental data Group 1: real networks (light load)

  26. Experimental data Group 1: real networks (light load)

  27. Probability of No Wavelength Conflict vs. Link Load • O(log u) approx.: choose a wavelength uniformly at random for each demand • Birthday Paradox!

  28. Experimental data Group 2: simulated networks (heavy + small)

  29. Experimental data Group 2: simulated networks (heavy + small)

  30. Experimental data: Large Networks Group 3: simulated networks (heavy + large)

  31. Experimental data Group 3: simulated networks (heavy + large)

  32. Summary – Preliminary observations Small + light (real networks) • All greedy solutions close to optimal • Log approx behaves poorly Small + heavy • Random sampling has advantage • Longest/heaviest less meaningful for shortest paths in small networks Large + heavy • Longest/heaviest more meaningful

  33. Combined minimization New territory: • Ultimate cost optimization • Combined minimization of fiber and conversion Proposed approach • Compute a min fiber solution (x extra fibers) • From empty network, add one fiber at a time • Compute a min conversion solution for fixed additional fibers.

  34. Combined minimization

  35. QUESTIONS???

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