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
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2. RWA
Problem statement
Wavelength-continuity constraint
ECS 259 -- H. Zang and B. Mukherjee, UC Davis
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3. Combined Routing and Wavelength
Assignment Problem
ECS 259 -- H. Zang and B. Mukherjee, UC Davis
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4. Routing - ILP Formulation
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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20. Future Research (Cont’d)
Managing multicast connections in
wavelength-routed WDM networks
x KMB
x Bellman-Ford
x Chain
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