1. Chapter 10 RWA
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2. Routing and Wavelength Assignment for Wavelength-Routed WDM Networks
Combined routing and wavelength assignment problem
Routing
static: ILP formulation
Incremental:
connection requests arrive sequentially a lightpath is established for each connection and the lightpath remains in the network indenitely
dynamic: on-line algorithms
a lightpath is set up for each connection request as it arrives and the lightpath is released after some finite amount of time
Wavelength assignment
static: graph coloring approach
dynamic: heuristics
A new wavelength assignment heuristic
First state the goal of this research is to write a tutorial for RWA. The new contribution is a wavelength assignment heuristic.
Problem statement : static vs dynamic
static: minimize the max flow on a link
dynamic: minimize the blocking probability of future connections
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3. Static Lightpath Establishment (SLE) problem
Static : The set of connections is known in advance Dynamic Lightpath Establishment (DLE) problem
Incremental : Connection requests arrive sequentially, a lightpath is established for each connection, and a lightpath remains in the network indefinitely
Dynamic : A lightpath is set up for each connection request as it arrives, and the lightpath is released after some finite amount of time
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4. RWA Problem statement Wavelength-continuity constraint
The SLE problem can be formulated as a mixed integer programming.
The work in proposed practical approximation algorithms to solve the SLE problem for large networks and graph –coloring problem.
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5. Combined Routing and Wavelength Assignment Problem
Goal:
minimize the max flow among all fiber links
Assumption:
wavelength-continuity constraint
Coverage:
Invariant- no lightpaths are assigned the same wavelength on the same fiber link
multi-equation
conservation of flows
Last requirement:
assume two connections between a source-destination pair take two different wavelengths - access station model
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6. Maximizing the number of established connection (fixed W)
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7. Routing - ILP Formulation
without wavelength continuity constraint
Assume at most one lightpath from any source to any destination.
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8. RWA with wavelength Conversion
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9. RWA with wavelength Conversion
Sparse location of wavelength converters in the network
Sharing of converters
Limited-range wavelength conversion
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10. Routing - Algorithms For Dynamic Traffic
Fixed routing (On/Off line)
Fixed-alternate routing (On/Off line)
Adaptive routing (On line)
adaptive shortest path routing
least congested path routing
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11. Fixed Routing Off-line calculation Shortest-path algorithm: Advantage:
Dijkstra’s or
Bellman-Ford algorithm
Advantage:
simple
Disadvantage:
high blocking probability and
unable to handle fault situation
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12. Fixed-Alternate Routing
Each node is required to maintain a routing table that contains an ordered list of a number of fixed routes to each destination node
A primary route between s-d is defined as the first route
An alternative route doesn’t share any links with the first route (link disjoint)
Advantage
Provide some degree of fault tolerance
Reduce the blocking probability compared to fixed routing
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13. Adaptive Routing
The route from a source node to a destination node is chosen dynamically, depending on the network state
Ex:
Shortest-cost-path routing
Each unused link has the cost of 1 unit;
used link ∞;
wavelength converter link c units.
Disadvantage: extensive updating routing tables
Advantage: lower blocking probability than fixed and fixed-alternate routing
Least-congestion-path routing (LCP)
Advantage
Lower connection blocking than fixed and fixed-alternate routing
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14. Consider fault-tolerant
Protection
Set up two link-disjoint lightpaths
Primary lightpath transmit data
Backup lightpath must be reserved
Fast but need reserve resource
Restoration
The backup path is determined dynamically after the failure has occurred
Slow but doesn't need reserve resource
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15. Wavelength Assignment
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16. Wavelength Assignment Heuristics
Random
First-Fit
Least-Used/SPREAD
Most-Used/PACK
Min-Product
Least Loaded
MAX-SUM
Relative Capacity Loss
Wavelength Reservation
Protecting Threshold
Explain R, FF.
will explain MS and RCL.
wavelength reservation and protecting threshold are not independent algorithms and must be combined with other WA algorithm.
will not explain LU, MU, MP and LL.
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17. Static Wavelength Assignment
Two lightpaths share the same physical link are assigned different wavelengths
Reduced to graph-coloring problem:
1.Construct a graph, such that each lightpath is represented by a node. There is one edge in between if two lightpaths share the same physical link.
2.Color the nodes such that no two adjacent nodes have the same colors.
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18. Static Wavelength-Assignment
Minimizes the number of wavelengths used under the wavelength-continuity constraint reduced to the graph coloring problem
Construct an auxiliary graph G(V,E)
Color the nodes of the graph G
Largest First
Smallest Last
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19. Static Wavelength-Assignment (cont.)
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20. example
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21. Largest First
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22. Smallest Last
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23. First-Fit First available wavelength is chosen
No global information needed
Proffered in practice because of its small overhead and low complexity
Perform well in terms of blocking probability and fairness
The idea behind is to pack all of the in-use wavelengths towards lower end and continuous longer paths towards higher end
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24. FF example λ0 will be assigned λ0 will also be assigned MP and LL
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25. Least-Used (LU) Wavelength Assignment
Least used in the network chosen first
Balance load through all the wavelength
Break the long wavelength path quickly
Worse than Random:
global information needed
additional storage and computation cost
not preferred in practice
Disadvantage
This scheme ends up breaking the long wavelength paths quickly
Additional communication overhead
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26. LU example λ0 ,λ1 ,λ3 are each used two links λ2 is used only one link
So LU will choose λ2
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27. Most-Used (MU) Assignment
Select the most-used wavelength in the network
Advantages:
-outperforms FF, doing better job of packing connection into fewer wavelength
-Conserving the spare capacity of less-used wavelength
Disadvantages:
-overhead, storage, computation cost are similar to those in LU
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28. MU example λ0 ,λ1 ,λ3 are each used two links λ2 is used only one link
So MU will choose one of λ0 ,λ1 ,λ3 with equal probability
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29. Notations
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30. Min-Product (MP) Used in multi-fiber network
The idea is to pack wavelength into fibers, minimizing the number of fibers in the network
∏ D lj
l є π(p)
for each wavelength j, 1≦j ≦W.
Chose a set of wavelength j minimizing the above value
Disadvantage: not better that multi-fiber version of FF
-introduce additional computation costs -
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31. MP example λ1 : 2*3*1*3*5=90 λ2 : 3*2*4*1*2=48 λ3 : 1*2*1*2*1=41 2 3 4 5
λ1=2
λ2=3
λ3=1
λ1=3
λ2=2
λ3=2
λ1=1
λ2=4
λ3=1
λ1=3
λ2=1
λ3=2
λ1=5
λ2=2
λ3=1
λ1 : 2*3*1*3*5=90
λ2 : 3*2*4*1*2=48
λ3 : 1*2*1*2*1=4
So choose λ3
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32. Least-Loaded (LL) Assignment
Multi-fiber network
Select the wavelength that the largest residual capacity in the most-loaded link along route p.
Advantage: outperforms MU and FF in terms of blocking probability
LL selects the minimum indexed wavelength j in Sp that achieves
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33. LL example Set up lightpath from 0 to 21 2 3 4 5
Assume 7 fibers per link
λ1=2(5)
λ2=3(4)
λ3=1(6)
λ1=3(4)
λ2=2(5)
λ3=2(5)
λ1=1(6)
λ2=4(3)
λ3=1(6)
λ1=3(4)
λ2=1(6)
λ3=2(5)
λ1=5(2)
λ2=2(5)
λ3=1(6)
Set up lightpath from 0 to 2
Choose λ3 Max(min(residual capacity))=5
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34. MAX-SUM Assignment Applied to multi-fiber and single-fiber also
Before lightpath establishment, the route is pre-selected;
After lightpath establishment, it attempts to maximize the remaining path capacity
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35. MAX-SUM Assignment (continued)
r(ψ, l, j) = Mj - D(ψ) lj
r(ψ, l, j):link capacity, the number of fibers on which wavelength j is unused on link l
r(ψ, p, j) = min r(ψ, l, j)
l є π(p)
r(ψ, p, j):the number of fibers on which wavelength j is available on the most-congested like along the path p
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36. MAX-SUM (MΣ)
MΣconsiders all possible paths in the network and attempts to maximize the remaining path capacities after lightpath establishment
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37. MAX-SUM Assignment (continued)w
R(ψ,p) = Σ min r(ψ, l, j)
j=1 l є π(p)
At last, chose the wavelength j that maximizes the quantity:
Σ R(ψ’(j) ,p)
pєP
ψ’(j) be the next state of the network if j is assigned
P is all the potential paths for the connection
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38. MΣexample
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39. Calculation of Max-Sum
wavelengths
P1:(2,4) 3 2 1
WPC:
Wavelength-path
Capacity 0 1 2 3 4 5 6
Show how to calculate the first row.
Wavelength
selected:
0, 1, or 3
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40. Relative Capacity Loss (RCL) Assignment
Chose wavelength j to minimize the relative capacity loss:
Σ (r(ψ, p, j) - r(ψ’(j), p, j))/ r(ψ, p, j)
pєP
Sometimes better than MAX-SUM
-MAX-SUM could cause blocking
Longer lightpaths have a higher block probability than shorter ones
Some schemes to protect longer paths:
Wavelength reservation (Rsv) and protesting threshold (Thr)
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41. Relative Capacity Loss (RCL)MΣ
RCL
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42. RCL example
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43. Illustrative Example 1 2 3 4 5 6
wavelengths
P1:(2,4) 3 2 1 0
Explain
bus
connections that are setup
Note: control network not shown. All wavelengths shown are for data traffic
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44. Calculation of Relative Capacity Loss
wavelengths
P1:(2,4) 3 2 1
Wavelength selected:
1 or 3 0 1 2 3 4 5 6
Show how to calculate the first row.
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45. Random Wavelength Assignment
Randomly chosen available wavelength
Uniform probability
No global information needed
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46. Connection management protocol: link-state
Simulation Network 2 1 2 1 1 3 1 1 1 1 5 4 2
Connection management protocol: link-state
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47. 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
Don’t explain. Say MS and RCL are expensive.
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48. Distributed Relative Capacity Loss (DRCL)
Speed up the wavelength-assignment procedure
each node stores information on the capacity loss on each wavelength
only table lookup
small amount of calculation are required upon the arrival of a connection request
Routing is implemented using the Bellman-Ford (each node exchange table with its neighboring nodes and updates its table)
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49. Distributed Relative Capacity Loss (DRCL) (cont.)
DRCL considers all of the paths from the source node of the arriving connection request to every other node ,excluding the destination node of the arriving connection request
DRCL choose the wavelength that minimize the sum of rcl(w,d) over all possible destination d
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50. DRCL example
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51. Distributed RCL Algorithm
P1:(2,4) 3 2 1 0 1 2 3 4 5 6 *
Wavelength
selected: 3
Why DRCL?
less info exchanged (only to neighbors)
Fast computation - only table lookup
adaptive routing (the performance of fixed routing is very limited)
Calculate the first row.
Drawback: no traffic information is considered. Might not work well with non-uniform traffic.
RCL table at Node 2
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52. 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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53. Simulation Network 2 1 2 1 1 1 3 1 1 1 5 4
For uniform traffic 2
Average propagation delay between two nodes: ms
Average hop distance: 1.53
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54. Simulation Results of Distributed RCL
Comparison of DRCL with adaptive routing and
RCL with fixed routing
No access station model.
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55. L: # of links, N: # of nodes, W: # of wavelengths
Conclusion for RWA
L: # of links, N: # of nodes, W: # of wavelengths
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56. 2019/5/9

57. Future Research Survivable wavelength-routed WDM networks
previous work: static traffic & single link failure [S. Ramamurthy 1998]
higher layer protection -logical topology design with bundle cut in mind
WDM layer protection - dynamic traffic
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58. Future Research (Cont’d)
Managing multicast connections in wavelength-routed WDM networks
KMB
Bellman-Ford
Chain
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59. Simulation Results
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60. Simulation Results (cont.)
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61. Simulation Results (cont.)
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62. Simulation Results (cont.)
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