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Routing and Wavelength Assignment for
Wavelength-Routed WDM Networks
   Combined routing and wavelength assignment problem
   Routing
    x static: ILP formulation

    x dynamic: on-line algorithms

   Wavelength assignment
    x static: graph coloring approach

    x dynamic: heuristics

   A new wavelength assignment heuristic
              ECS 259 -- H. Zang and B. Mukherjee, UC Davis
                                                              1
RWA
 Problem statement
 Wavelength-continuity constraint




            ECS 259 -- H. Zang and B. Mukherjee, UC Davis
                                                            2
Combined Routing and Wavelength
Assignment Problem




          ECS 259 -- H. Zang and B. Mukherjee, UC Davis
                                                          3
Routing - ILP Formulation




           ECS 259 -- H. Zang and B. Mukherjee, UC Davis
                                                           4
Routing - Algorithms For Dynamic Traffic
   Fixed routing (On/Off line)
   Fixed-alternate routing (On/Off line)
   Adaptive routing (On line)
    x adaptive shortest path routing

    x least congested path routing




               ECS 259 -- H. Zang and B. Mukherjee, UC Davis
                                                               5
Wavelength Assignment with Known
Lightpaths and Routes - Graph Coloring
   Construct an auxiliary graph G(V,E)
   Color the nodes of the graph G such
   that no two adjacent nodes have the
   same color
   Sequential graph coloring approaches




              ECS 259 -- H. Zang and B. Mukherjee, UC Davis
                                                              6
Wavelength Assignment Heuristics
  Random                                   Least Loaded
  First-Fit                                MAX-SUM
  Least-Used/SPREAD                        Relative Capacity Loss
  Most-Used/PACK                           Wavelength Reservation
  Min-Product                              Protecting Threshold




             ECS 259 -- H. Zang and B. Mukherjee, UC Davis
                                                                    7
Illustrative Example
        wavelengths              P1:(2,4)
            λ3

            λ2

            λ1

            λ0

                 0     1        2           3       4        5        6


Note: control network not shown. All wavelengths shown are for data traffic
                      ECS 259 -- H. Zang and B. Mukherjee, UC Davis
                                                                              8
Calculation of Max-Sum
 wavelengths           P1:(2,4)
     λ3

     λ2

     λ1
                                                                      WPC:
     λ0                                                               Wavelength-path
          0    1       2          3      4         5       6          Capacity

 wavelengths WPC loss of each path on each λ                      Total WPC
                                                                     loss
                   P2:(1,5)       P3:(3,6)       P4:(0,3)
          λ3          1              0              0                   1      Wavelength
          λ2          1              1              0                   2       selected:
          λ1          0              1              0                   1      λ0, λ1, or λ3
          λ0          0              0              1                   1
                      ECS 259 -- H. Zang and B. Mukherjee, UC Davis
                                                                                           9
Calculation of Relative Capacity Loss
 wavelengths            P1:(2,4)
     λ3

     λ2

     λ1
                                                                    Wavelength selected:
     λ0                                                                  λ1 or λ3
          0    1       2           3      4         5       6

wavelengths          RCL of each path on each λ                        Total RCL
                   P2:(1,5) P3:(3,6)     P4:(0,3)
     λ3              0.5        0           0                              0.5
     λ2              0.5       0.5          0                               1
     λ1               0        0.5          0                              0.5
     λ0               0         0           1                               1
                    ECS 259 -- H. Zang and B. Mukherjee, UC Davis
                                                                                           10
Simulation Network
                                   2
                       1                          2
         1                                                      1

    0              1                                  1             3

         1                                                      1
                       5                          4
                                   2
  Connection management protocol: link-state
                ECS 259 -- H. Zang and B. Mukherjee, UC Davis
                                                                        11
Results from Others’ Publication
        Source: S. Subramaniam and R. A. Barry, “Wavelength assignment in fixed
          routing WDM networks,” Proc. ICC'97 - International Conference on
          Communications, Montreal, Canada, vol. 1, pp. 406-410, June 1997.



                                                                                      5x5
20-node
                                                                                      bidirectional
unidirectional                                                               R
                                                                                      mesh-torus,
ring, load/W                              R
                                                                             FF, MU   load/W
= 1 Erlang
                                                                                      = 25 Erlangs
                                          FF                                MS

                                                                            WC
                               WC     MU, MS

                       # of wavelengths                  # of wavelengths
                            (a)                                 (b)
                           ECS 259 -- H. Zang and B. Mukherjee, UC Davis
                                                                                                      12
Computational Complexity
   Wavelength reservation & Protecting threshold -
   constant
   Random & First-Fit - O(W)
   Min-Product & Least-Loaded - O(NW)
   Least-Used & Most-Used - O(LW)
   Max-Sum & Relative Capacity Loss - O(WN3)
   where W - # of wavelengths, N - # of nodes, L - # of
   links
               ECS 259 -- H. Zang and B. Mukherjee, UC Davis
                                                               13
Distributed RCL Algorithm
                                                   P1:(2,4)
                            λ3

                            λ2

                            λ1

                            λ0

                                 0   1         2          3       4         5        6
      Wavelength                 0   1         2          3       4        5         6   Subtotal

                                                                                                    Wavelength
                       λ3
RCL table at Node 2




                                 0   1/3       0        1/4     1/4       1/3        0   11/12 *    selected: λ3

                       λ2        0   1/3       0        1/4     1/4       1/3       1/2 17/12
                       λ1        0   0         0        1/4     1/4       1/3       1/2 13/12
                       λ0        1   1/3       0        1/4     1/4        0         0   19/12
                                         ECS 259 -- H. Zang and B. Mukherjee, UC Davis
                                                                                                              14
Characteristics of Distributed RCL
   Less state information is exchanged
   Faster computation of wavelength assignment
   upon a connection request
   Can be combined with adaptive routing




              ECS 259 -- H. Zang and B. Mukherjee, UC Davis
                                                              15
Simulation Network
                               2
                  1                          2
       1                                                    1

   0          1                                  1              3

       1                                                    1
                  5                          4
                        2
       Average propagation delay between two
       nodes: 0.107 ms
       Average hop distance: 1.53
            ECS 259 -- H. Zang and B. Mukherjee, UC Davis
                                                                    16
Simulation Results of Distributed RCL

                                                   Comparison of
                                                   DRCL with adaptive
                                                   routing and
                                                   RCL with
                                                   fixed routing




            ECS 259 -- H. Zang and B. Mukherjee, UC Davis
                                                                        17
Conclusion for RWA
         Heuristics              Complexity                Performance
Least Used                      O(LW)                     Ordered in
Random                          O(W)                      increasing
                                                          order
Min-Product                     O(NW)
First-Fit                       O(W)
Most-Used                       O(NW)
Least-Loaded                    O(LW)
Max-Sum                         O(WN3)
Relative Capacity Loss          O(WN3)

         L: # of links, N: # of nodes, W: # of wavelengths
               ECS 259 -- H. Zang and B. Mukherjee, UC Davis
                                                                         18
Future Research

   Survivable wavelength-routed WDM networks
    x previous work: static traffic & single link failure
      [S. Ramamurthy 1998]
    x higher layer protection -logical topology design
      with bundle cut in mind
    x WDM layer protection - dynamic traffic




                ECS 259 -- H. Zang and B. Mukherjee, UC Davis
                                                                19
Future Research (Cont’d)
   Managing multicast connections in
   wavelength-routed WDM networks
    x KMB

    x Bellman-Ford

    x Chain




              ECS 259 -- H. Zang and B. Mukherjee, UC Davis
                                                              20

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Lecture5c

  • 1. Routing and Wavelength Assignment for Wavelength-Routed WDM Networks Combined routing and wavelength assignment problem Routing x static: ILP formulation x dynamic: on-line algorithms Wavelength assignment x static: graph coloring approach x dynamic: heuristics A new wavelength assignment heuristic ECS 259 -- H. Zang and B. Mukherjee, UC Davis 1
  • 2. RWA Problem statement Wavelength-continuity constraint ECS 259 -- H. Zang and B. Mukherjee, UC Davis 2
  • 3. Combined Routing and Wavelength Assignment Problem ECS 259 -- H. Zang and B. Mukherjee, UC Davis 3
  • 4. Routing - ILP Formulation ECS 259 -- H. Zang and B. Mukherjee, UC Davis 4
  • 5. Routing - Algorithms For Dynamic Traffic Fixed routing (On/Off line) Fixed-alternate routing (On/Off line) Adaptive routing (On line) x adaptive shortest path routing x least congested path routing ECS 259 -- H. Zang and B. Mukherjee, UC Davis 5
  • 6. Wavelength Assignment with Known Lightpaths and Routes - Graph Coloring Construct an auxiliary graph G(V,E) Color the nodes of the graph G such that no two adjacent nodes have the same color Sequential graph coloring approaches ECS 259 -- H. Zang and B. Mukherjee, UC Davis 6
  • 7. Wavelength Assignment Heuristics Random Least Loaded First-Fit MAX-SUM Least-Used/SPREAD Relative Capacity Loss Most-Used/PACK Wavelength Reservation Min-Product Protecting Threshold ECS 259 -- H. Zang and B. Mukherjee, UC Davis 7
  • 8. Illustrative Example wavelengths P1:(2,4) λ3 λ2 λ1 λ0 0 1 2 3 4 5 6 Note: control network not shown. All wavelengths shown are for data traffic ECS 259 -- H. Zang and B. Mukherjee, UC Davis 8
  • 9. Calculation of Max-Sum wavelengths P1:(2,4) λ3 λ2 λ1 WPC: λ0 Wavelength-path 0 1 2 3 4 5 6 Capacity wavelengths WPC loss of each path on each λ Total WPC loss P2:(1,5) P3:(3,6) P4:(0,3) λ3 1 0 0 1 Wavelength λ2 1 1 0 2 selected: λ1 0 1 0 1 λ0, λ1, or λ3 λ0 0 0 1 1 ECS 259 -- H. Zang and B. Mukherjee, UC Davis 9
  • 10. Calculation of Relative Capacity Loss wavelengths P1:(2,4) λ3 λ2 λ1 Wavelength selected: λ0 λ1 or λ3 0 1 2 3 4 5 6 wavelengths RCL of each path on each λ Total RCL P2:(1,5) P3:(3,6) P4:(0,3) λ3 0.5 0 0 0.5 λ2 0.5 0.5 0 1 λ1 0 0.5 0 0.5 λ0 0 0 1 1 ECS 259 -- H. Zang and B. Mukherjee, UC Davis 10
  • 11. Simulation Network 2 1 2 1 1 0 1 1 3 1 1 5 4 2 Connection management protocol: link-state ECS 259 -- H. Zang and B. Mukherjee, UC Davis 11
  • 12. Results from Others’ Publication Source: S. Subramaniam and R. A. Barry, “Wavelength assignment in fixed routing WDM networks,” Proc. ICC'97 - International Conference on Communications, Montreal, Canada, vol. 1, pp. 406-410, June 1997. 5x5 20-node bidirectional unidirectional R mesh-torus, ring, load/W R FF, MU load/W = 1 Erlang = 25 Erlangs FF MS WC WC MU, MS # of wavelengths # of wavelengths (a) (b) ECS 259 -- H. Zang and B. Mukherjee, UC Davis 12
  • 13. Computational Complexity Wavelength reservation & Protecting threshold - constant Random & First-Fit - O(W) Min-Product & Least-Loaded - O(NW) Least-Used & Most-Used - O(LW) Max-Sum & Relative Capacity Loss - O(WN3) where W - # of wavelengths, N - # of nodes, L - # of links ECS 259 -- H. Zang and B. Mukherjee, UC Davis 13
  • 14. Distributed RCL Algorithm P1:(2,4) λ3 λ2 λ1 λ0 0 1 2 3 4 5 6 Wavelength 0 1 2 3 4 5 6 Subtotal Wavelength λ3 RCL table at Node 2 0 1/3 0 1/4 1/4 1/3 0 11/12 * selected: λ3 λ2 0 1/3 0 1/4 1/4 1/3 1/2 17/12 λ1 0 0 0 1/4 1/4 1/3 1/2 13/12 λ0 1 1/3 0 1/4 1/4 0 0 19/12 ECS 259 -- H. Zang and B. Mukherjee, UC Davis 14
  • 15. Characteristics of Distributed RCL Less state information is exchanged Faster computation of wavelength assignment upon a connection request Can be combined with adaptive routing ECS 259 -- H. Zang and B. Mukherjee, UC Davis 15
  • 16. Simulation Network 2 1 2 1 1 0 1 1 3 1 1 5 4 2 Average propagation delay between two nodes: 0.107 ms Average hop distance: 1.53 ECS 259 -- H. Zang and B. Mukherjee, UC Davis 16
  • 17. Simulation Results of Distributed RCL Comparison of DRCL with adaptive routing and RCL with fixed routing ECS 259 -- H. Zang and B. Mukherjee, UC Davis 17
  • 18. Conclusion for RWA Heuristics Complexity Performance Least Used O(LW) Ordered in Random O(W) increasing order Min-Product O(NW) First-Fit O(W) Most-Used O(NW) Least-Loaded O(LW) Max-Sum O(WN3) Relative Capacity Loss O(WN3) L: # of links, N: # of nodes, W: # of wavelengths ECS 259 -- H. Zang and B. Mukherjee, UC Davis 18
  • 19. Future Research Survivable wavelength-routed WDM networks x previous work: static traffic & single link failure [S. Ramamurthy 1998] x higher layer protection -logical topology design with bundle cut in mind x WDM layer protection - dynamic traffic ECS 259 -- H. Zang and B. Mukherjee, UC Davis 19
  • 20. Future Research (Cont’d) Managing multicast connections in wavelength-routed WDM networks x KMB x Bellman-Ford x Chain ECS 259 -- H. Zang and B. Mukherjee, UC Davis 20