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Traffic Grooming in WDM Ring Networks

Traffic Grooming in WDM Ring Networks. Presented by: Eshcar Hilel. Introduction. Optical Networks - A new generation of networks using optical fiber transmission Excellent medium, high BW, low error …

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Traffic Grooming in WDM Ring Networks

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  1. Traffic Grooming in WDM Ring Networks Presented by: Eshcar Hilel

  2. Introduction • Optical Networks - A new generation of networks using optical fiber transmission • Excellent medium, high BW, low error… • SONETring - synchronous optical network, currently the most widely deployed optical network infrastructure • WDMTechnology– wavelength-division multiplexing 236357 - Distributed Algorithms, Spring 2005

  3. Introduction – SONET Ring • SADM - SONET add/drop multiplexers can aggregate lower-rate signals into a single high-rate stream • SONET ring use one fiber pair (or two for protection) to connect SADMs in the source and destination nodes 236357 - Distributed Algorithms, Spring 2005

  4. Introduction – WDM • Increases the transmission capacity of optical fibers • Allows simultaneously transmission of multiple wavelengths (channels) within a single fiber • One wavelength may carry Internet traffic; another may carry voice or video 236357 - Distributed Algorithms, Spring 2005

  5. Introduction – SONET over WDM • Multiple SONET rings can be supported on a single fiber pair by using multiple wavelengths • The networks are limited by the processing capability of electronic switches, routers and multiplexers (not by transmission bandwidth) • New aim: overcoming the electronic bottleneck by providing optical bypass 236357 - Distributed Algorithms, Spring 2005

  6. Introduction – Optical bypass • WADM - WDM Add/Drop Multiplexer allows to drop (or add) only the wavelength that carries the traffic destined to (or originated from) the node • The dropped wavelength is electronically processed at the node • All the other wavelengths optically bypass the node 236357 - Distributed Algorithms, Spring 2005

  7. Introduction – WADM • More optical switches may be added to support more add-drop wavelengths 236357 - Distributed Algorithms, Spring 2005

  8. Introduction – Traffic Grooming • Every wavelength needs a SADM only at nodes where it is ended • Traffic typically require only a small fraction of the wavelength • Traffic grooming can be used in such a way that all of the traffic to and from the node is carried on minimum number of wavelength 236357 - Distributed Algorithms, Spring 2005

  9. Topics of Discussion • Traffic Grooming - Understanding the Problem • Single Exit Node Network • NP-complete problem • Special case: uniform traffic • Special case: minimum number of wavelengths • All-To-All Uniform Traffic Network 236357 - Distributed Algorithms, Spring 2005

  10. Traffic Grooming Understanding the problem

  11. What’s the Problem? • Unidirectional (clockwise) WDM ring • N nodes: 1,2,…,N • c– grooming factor • rij - number of low rate circuits from node i to node j • Objective: minimize total number of SADMs 236357 - Distributed Algorithms, Spring 2005

  12. Illustration • Unidirectional ring network: N = 4 • 6 pairs of nodes • rij = 8: 8 OC-3 circuits between each pair • c = 16: each wavelength supports an OC-48 ring • Total load: 6x8 OC-3 = 3 OC-48, requires 3 wavelengths 236357 - Distributed Algorithms, Spring 2005

  13. Illustration Traffic assignment: • 1: 1↔2, 3↔4 • 2: 1↔3, 2↔4 • 3: 1↔4, 2↔3 Total: 12 SADMs 236357 - Distributed Algorithms, Spring 2005

  14. Illustration Traffic assignment: • 1: 1↔2, 1↔3 • 2: 2↔3, 2↔4 • 3: 1↔4, 3↔4 Total: 9 SADMs 236357 - Distributed Algorithms, Spring 2005

  15. Goal – Traffic Grooming • Tradeoff between efficient use of fibers and the cost of electronic equipment • When no limitation on wavelengths – dedicated wavelength per connection, no multiplexing • Else design traffic grooming algorithms to • Minimize number of electronics (SADMs) • Minimize number of wavelengths (efficient use of wavelengths) 236357 - Distributed Algorithms, Spring 2005

  16. Single Exit Node Network E. Modiano, A. Chio, “Traffic Grooming Algorithms for Reducing Electronic Multiplexing Costs in WDM Ring Networks”

  17. Computational Complexity • Unidirectional ring • All the traffic on the ring is destined to a single exit node • Denote the exit node 0 • rij > 0, for j = 0 and i = 1,…,N • Note: maximum load Lmax = i=1..N ri0 and minimum wavelengths Wmin =  Lmax / c  Telephone company’s central office 236357 - Distributed Algorithms, Spring 2005

  18. Computational Complexity • Assume w.l.o.g. ri0<c for all i • Else fill  ri0/c  wavelengths with  ri0/c *c low rate circuits, and groom the remaining (<c)circuits • Theorem: The traffic grooming problem is NP-complete 236357 - Distributed Algorithms, Spring 2005

  19. Computational Complexity • Bin packing problem: What is the least number of bins (containers of fixed volume) needed to hold a set of objects (of different volumes)? • The bin packing problem is an NP-complete problem. 236357 - Distributed Algorithms, Spring 2005

  20. Computational Complexity • Claim: There exist an optimal solution such that no traffic from a node is split onto two rings • Proof: • Consider assignment where the traffic of some nodes is split onto 2 or more rings • Each such node have at least 2 SADMs • Accommodate the traffic on a separate wavelength • Requires at most 2 SADMs 236357 - Distributed Algorithms, Spring 2005

  21. Computational Complexity • Theorem Proof: • For any optimal solution with no split traffic: regular nodes - N SADMs; exit node - k SADMs, where k is the number of SONET rings • Problem reduced to minimizing total number of rings • Achieved by combining traffic from multiple nodes onto single ring (wavelength) • This is basically the Bin Packing problem! QED 236357 - Distributed Algorithms, Spring 2005

  22. Special Case: Uniform Traffic • ri0 = r • Optimal solution does not require split traffic • May groom traffic from at most c/r nodes on one SONET ring • Number of wavelengths: W = N/ c/r • Hence, minimum SADMs Mmin = N + W • Not the minimum number of wavelengths! 236357 - Distributed Algorithms, Spring 2005

  23. Special Case:Minimum Number of Wavelengths • Traffic from nodes may have to be split onto multiple rings, S - total number of traffic splits • Additional SADM per split • Hence, #SADMs M = N + Wmin + S, where Wmin =r*N/c • Objective: minimize the total number of splits 236357 - Distributed Algorithms, Spring 2005

  24. Special Case:Minimum Number of Wavelengths • Maximum load for ring with no split Lns = c/r*r • Wns Maximum number of rings with no split • Remaining rings contain at most c circuits: Wns *Lns + (Wmin- Wns)*c >= Lmax • Wns = min{Wmin , (c* Wmin–Lmax)/ (c-Lns)} 236357 - Distributed Algorithms, Spring 2005

  25. Iterative Algorithm • Initialization: c0 = c, N0 = N, r0 = r, W0 = W0min • Steps of loop i: • If Wins = Wimin then accommodate the remaining traffic without splitting - terminate • Fill Wi rings with unsplit traffic from ci /ri nodes • Remaining capacity is ci+1= ci - ci /ri*ri • Ni+1= Ni - ci /ri*Wi nodes needs to be assigned 236357 - Distributed Algorithms, Spring 2005

  26. Iterative Algorithm (cont) • Steps of loop i (cont): • Ni+1 = Ni - ci /ri*Wi nodes needs to be assigned • Fill remaining capacity ci+1 by traffic from Ni+1 nodes • Remaining traffic becomes ri+1= ri – ci+1 • Wi+1= Wi–Ni+1 • Continue to loop i+1 Ni+1<Wi 236357 - Distributed Algorithms, Spring 2005

  27. All-To-All Uniform Traffic Network J.C. Bermond, D. Coudert, “Traffic Grooming in Unidirectional WDM Ring Networks using Design Theory”

  28. All-To-All Uniform Traffic • We show the problem can be formulated in terms of graph partition into sub-graphs: • at most c edges and per sub-graph • minimize total number of vertices 236357 - Distributed Algorithms, Spring 2005

  29. Traffic Grooming:Reformulating the Problem • N nodes of unidirectional ring CN • R = N(N-1)/2 circles • c– grooming factor • KN - Complete graph on N vertices • Bλ denote a sub-graph of KN • V(Bλ) (resp E(Bλ)) denote its vertex (resp edge) set 236357 - Distributed Algorithms, Spring 2005

  30. Traffic Grooming:Reformulating the Problem • Bλ correspond to a wavelength • An edge of Bλ correspond to a circle in the ring • Bλ is viewed as a set of circles packed in a wavelength • |E(Bλ)| <= c • V(Bλ) correspond to the number of SADMs • A(c,N) denotes total number of SADMs 236357 - Distributed Algorithms, Spring 2005

  31. Traffic Grooming:Reformulating the Problem • Input: N and c • Output: partition of KNinto sub-graphs Bλ, λ = 1,…,W, such that |E(Bλ)| <= c • Objective: minimize ∑1<=λ<=W|V(Bλ)| 236357 - Distributed Algorithms, Spring 2005

  32. Lower Bound • ρ(Bλ) = |E(Bλ)|/|V(Bλ)| is the sub-graph ratio • ρ(m) maximum ratio of sub-graph with m edges • ρmax(c) = maxm<=c ρ(m) 236357 - Distributed Algorithms, Spring 2005

  33. Lower Bound • Theorem: any grooming of R circles with grooming factor c needs at least R/ρmax(c) SADMs • Proof: R = ∑Wλ=1|E(Bλ)| <= ρmax(c)* ∑Wλ=1|V(Bλ)| • Thus we have the lower bound: A(c,N) >= N(N-1) / ρmax(c)*2 236357 - Distributed Algorithms, Spring 2005

  34. Lower Bound • We compute ρmax(c) • Theorem: If k(k-1)/2<=c<=(k+1)(k-1)/2, then ρmax(c)=(k-1)/2 If (k+1)(k-1)/2<=c<=(k+1)k/2, then ρmax(c)=c/k+1 • Proof: on board 236357 - Distributed Algorithms, Spring 2005

  35. Lower Bound • Note: these sub-graphs do not have necessarily exactly c edges and so the minimum is not necessarily attained for W = Wmin • Example: N=13 and c=7 236357 - Distributed Algorithms, Spring 2005

  36. Discussion • My opinion of the subject • Your opinion of the subject (and presentation…) • That’s all folks! 236357 - Distributed Algorithms, Spring 2005

  37. References • J.C. Bermond, D. Coudert, “Traffic Grooming in Unidirectional WDM Ring Networks using Design Theory”, IEEE International Conference on Communications, May, 2003 • E. Modiano, A. Chio, “Traffic Grooming Algorithms for Reducing Electronic Multiplexing Costs in WDM Ring Networks”, IEEE J. Lightwave Tech., Jan. 2000 vol. 18(1) 236357 - Distributed Algorithms, Spring 2005

  38. References • E. Modiano, P. Lin, “Traffic Grooming in WDM Networks”, IEEE Communication Magazine, July 2001. 236357 - Distributed Algorithms, Spring 2005

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