The document discusses routing and wavelength assignment (RWA) in wavelength-division multiplexing (WDM) networks. It covers both static and dynamic RWA problems. For routing, it discusses integer linear programming formulations for static routing and online algorithms for dynamic routing. For wavelength assignment, it discusses graph coloring approaches for static assignment and heuristics like first-fit for dynamic assignment. Several heuristics for RWA are presented, along with their computational complexities and performance. Future research directions like survivable RWA and managing multicast connections are also outlined.

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)
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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
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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
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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
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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
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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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