1. DISA under NSA-LUCITE Contract
Preserving Survivability During Logical Topology Reconfiguration in WDM Ring Networks
Hwajung Lee, Hongsik Choi,
Suresh Subramaniam,
and Hyeong-Ah Choi
The George Washington University
Supported in part by
DARPA under grant #N
(Co-funded by NSA)
DISA under NSA-LUCITE Contract
NSF under grant ANI
My name is Hwajung Lee from the George Washington University. This work is collaborated with others.
Today, I’ll present about “Reconfiguration of Survivable Logical Topologies in WDM Optical Ring Networks”.

2. Outline Introduction – Network Survivability Motivation
Problem Formulation
Problem Complexity
Simple Reconfiguration Approach
& its Limitation
MinCostReconfiguration Algorithm
Concluding Remarks
In the Introduction, I’ll briefly mention what the network survivability is.
Then, motivation of this work, Problem Formulation, and Problem Complexity will be discussed.
As a solution, Reconfiguration Algorithm will be provided. And Limitation of Reconfiguration algorithm will be mentioned.
Concluding remarks will be the last part of my presentation.

3. Network Survivability
Introduction
Network Survivability
To guarantee for users to use the network service without any interruption.
Each layer has its own fault recovery functions.
Fault propagation
ATM IP
WDM Optical Network
Physical Fiber Plant
SONET/
SDH
Network Survivability is an effort to guarantee for users to use the network service without any interruption.
If we use some protocol stack, for example like this,
to support network Survivability, each layers have their own fault recovery functions.
Sometimes, a single fault of a lower layer can propagate into a multiple failures of an upper layer so that the upper layer topology can be disconnected into at least two part, which can damage the fault recovery function of the upper layer. So careful mapping from an upper layer to a lower layer is necessary to minimize the impact of the fault propagation.

4. Survivable Logical Topology
Introduction
Survivable Logical Topology
Logical topology (Upper Layer) is called survivable if it remains connected in the presence of a single optical link failure.
Faulty Model : Single optical link failure.
So, if the upper layer is still connected from the impact of the fault propagation, we can call the upper layer of the mapping survivable.

5. Survivable Logical Topology
Introduction
Survivable Logical Topology
Survivable
Electronic layer is connected
even when a single optical link fails 1
Optical Layer
= Physical Topo.
Upper Layer
= Logical Topology 5 2
Not Survivable
Desirable! 1 3 4 3 4 1 2 5
Now, what I mean by mapping is this.
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This example shows that if you do not carefully map a logical topology to a physical topology, you might not have a survivable logical topology.
Suppose the left topology is a logical topology and each edge represents a connection request between two electronic devices. And the right topology is a physical topology of optical devices.
For each connection request of the logical topology, we establish a lightpath over the physical topology.
For example, for (0,1), a lightpath (0,1) is established. And (0,4) is embedded on the lightpath (0,4) and so on.
Both physical rings are identical except a lightpath (2,5) embedding.
Now, if the link (0,1) is failed, three lightpaths are broken so that the shown edges of the logical links are failed. At this moment, we can see that all the devices in the logical topology are still connected each other.
Whereas, in the case of the second embedding, if the link (0,1) is failed, four lightpaths are broken so that the shown edges of the logical links are failed. At this moment, we can see that the logical topology is divided into two parts so that there is no way to deliver data from the left to the right vice versa.
Map each connection request
to an optical lightpath. 2 5 3 4

6. Survivable Logical Topology
Introduction
Survivable Logical Topology
Sometimes, there is no way to have a Survivable
Logical Topology Embedding
on a Physical Topology.
Optical Layer
= Physical Topo.
Electronic Layer
= Logical Topology e1 … d b c a b a … …
In this slide, I would like to show that, sometimes, there is no way to have a Survivable Logical Topology Embedding on a Physical Topology.
If we have a logical topology which is 2-edge connected, the logical topology can not be survivable if (a,b) and (c,d) are located as shown. What I mean by 2-edge connected is that, if we delete two edges e1 and e2, the topology will be divided into two components. Both e1 and e2 are failed by a physical link fault.
Here is the example of the Survivable Logical Topology for the logical topology in the left side. Please note that the node location.
As long as all the edge cuts, e1 and e2, are not overlapped on one optical link, the Logical Topology can have a survivable embedding.
Thus, we observe that, depending the node embedding, it is possible not to have a Survivable Logical Topology. e2 c d
2-Edge Connected

7. Survivable Logical Topology Design Problem (SLTDP)
Introduction
Survivable Logical Topology Design Problem (SLTDP)
Given
a physical topology, and
a logical topology = a set of connection requests.
Objectives
Find a route of lightpath for each connection request, such that the logical topology remains connected after a single link failure if possible.
Otherwise, determine and embed the minimum number of additional lightpaths to make the logical topology survivable.
Now, here is the summary of our objectives.
Given a physical topology and a logical topology, we first try to find a route for each logical link and, if it is the case that we can not have a survivable logical topology no matter how we try to, we add the a few additional lightpaths based on our algorithm.

8. Survivable LT design possible
Introduction
H. Lee, H. Choi, S. Subramaniam, and H.-A. Choi, “Survivable Logical Topology Design in WDM Optical Ring Networks,” The 39th Annual Allerton Conference, October 2001, Invited Paper
Survivable LT design possible
Completely connected (i.e., (n-1)-edge connected)
NO survivable LT design when logical topology G is
2-edge connected
3-edge connected
4-edged connected
Degree Constraints
Survivable LT design possible when min. degree >=
No survivable LT design for min. degree <= ( )
Experimental Results – Near Optimal
Here is the summary of the results of the Survivable Logical Topology Design Problem. We have a near optimal solution, which is presented in Allerton Conference.
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Let’s look into the edge-connectivity first. In case of 2, 3, 4, and up to (n/2)-1 edge connected logical topology, we can NOT guarantee to have a survivable logical topology whereas the completely connected logical topology always have a SURVIVABLE logical topology. Each case will be shown briefly from the next slide.
Currently, we are working on tightening this gap between those two groups to find the value k of k-connectivity which always guarantees to have a SURVIVABLE logical topology.
Now, let’s consider with the degree constraints. We find out that we can guarantee to have a SURVIVABLE logical topology if the minimum degree of the logical topology is greater than equal to (2n)/3. And we can NOT guarantee the SURVIVABILITY of the logical topology if the minimum degree of the logical topology is less than equal to (n/2)-1. 2n 3 n 2

9. Reconfiguration of Survivable Logical Topologies
Motivation
Reconfiguration of Survivable Logical Topologies
What if # of Wavelength < 3 or # of Ports < 3
Survivable Logical Topology = G1
Survivable Logical Topology = G2 1 1 3 2 3 2
Physical Topology = Gp
# of Ports = 3
# of Wavelength = 3
Now, let’s think about the reconfiguration.
Suppose we have a logical topology, a physical topology, and a survivable mapping from the two topologies. While time passed, the connection requests can be modified so that the logical topology can be changed.
Therefore, we need to reconfigure the current mapping to support the new logical topology
with holding the survivability of the logical topology
throughout all the reconfiguration steps.
If we don’t have any restriction, we can easily add all the new connection requests and then delete all the old ones.
Let me briefly introduce two terms. First one is # of port of a node which is the number of points that lightpaths can arrive at and depart from.
Second one is # of wavelength of a link which is the number of lightpaths that pass on the link.
If we have some restrictions on the # of port and # of wavelength, the reconfiguration is more complicated.
=======
As long as the logical topology is connected, there is a way to transfer data from any node to any other node.
Add G2\G1
to form G1  G2 1 3 2
Delete G1\G2

10. Reconfiguration of Survivable Logical Topologies
Problem Formulation
Reconfiguration of Survivable Logical Topologies
Given
Two Survivable Logical Topology G1 and G2
on a physical topology Gp
Constraints
the number of port p, the number of wavelength W
Objectives
During the entire period of reconfiguration,
The logical topology remains survivable
The port p and wavelength W constraints are satisfied.
This is the problem formulation of the reconfiguration issue.
What we want to do is, during the entire period of reconfiguration,
to guarantee that the logical topology remains survivable and the port and wavelength constraints are satisfied.

11. Problem Complexity If no p or W constraint exists,
In General, the problem can be solved by
Add G2\G1 to form G1  G2.
Delete G1\G2.
Except CASE 1 in the next slide.
If the port and/or wavelength constraints exist(s),
more Complicated.
CASE 2 and CASE 3.
Now, let’s talk how hard this problem is.
We have three cases to show the problem complexity.

12. CASE 1 Problem Complexity
Need to change the directions of some lightpaths in G1  G2.
Physical topology
Logical topologies 6 6 1 5 1 5 1 6 2 5
isolated
isolated 3 4 2 4 2 4 3 3
Survivable
Survivable 1 6 1 6 2 5 2 5 3 4 3 4

13. CASE 3 CASE 2 Problem Complexity
Need to temporarily add some lightpaths not in G1  G2 to guarantee the survivability and delete later.
CASE 3
CASE 2
Need to temporarily delete and re-establish some lightpaths
in G1  G2 due to Wavelength Constraints. 3 1 2 4 5 6
Logical
topologies
Physical
topology !
Yes !
(W = 3) ?
No !
(W = 4) 1 1 6 6 2 5 2 5 3 3 4 4
W = 3, p = 4 .

14. Simple Reconfiguration Approach
Reconfiguration Algorithm
Simple Reconfiguration Approach
If the current lightpath setup uses W-1 wavelength
in each optical link and upto p-2 ports at each node,
add a lightpath btw each pair of adjacent nodes,
delete all lightpaths in G1 except the above, and
establish all lightpaths in G2 based on its survivable embedding. 1 6 2 5
By using one more wavelength, we can a good benefit which is reconfiguration.
With going one step further, this algorithm can be expend to the mapping which uses W wavelengths if we can have an algorithm to modify the mapping with using only W-1 wavelength.
We found out a certain condition to guarantee that except the following cases. 3 4
W = 4, p = 6

15. Limitation of Simple Reconfiguration Approach
Reconfiguration Algorithm
Limitation of Simple Reconfiguration Approach
W = k + 1
The intermediate nodes between n and n-k connect to the nodes n and n-k only. Thus, no lightpath can be removed without violating the survivability. In the green box, each node is connected to its adjacent node only. You can have as many nodes as you want in the green box.
So, we are finalizing the conditions to cover this case too.

16. Reconfiguration Algorithm
Algorithm MinCostReconfiguration Cost = # of add * UnitCostadd + # of delete * UnitCostdelete
Given Input : M1, M2, Gp
Output : Wadd,
Wadd = Wreconfig – max{WM1, WM2}
Constraints
the number of port p, the number of wavelength W
Objectives
To minimize Wreconfig while reconfiguration cost is preserved minimum.
During the entire period of reconfiguration,
The logical topology remains survivable
The port p and wavelength W constraints are satisfied.
This is the problem formulation of the reconfiguration issue.
What we want to do is, during the entire period of reconfiguration,
to guarantee that the logical topology remains survivable and the port and wavelength constraints are satisfied.

17. Wreconfig = max{ML1, ML2}
= 4 (= Winitial )
From To
ML1 = 4
ML2 = 3

18. Wreconfig = 4 1 7 2 6 3 5 4

19. Wreconfig = 4 1 7 2 6 3 5 4

20. Wreconfig = 4

21. Wreconfig = 4 1 7 2 6 3 5 4

22. Wreconfig = 5

23. Wreconfig = 5

24. Wreconfig = 5
Wadd = Wreconfig - Winitial
= 5 – 4 = 1

25. Numerical Results # of Simulations per each case = 500 n = 8

26. Numerical Results # of Simulations per each case = 500 n = 16

27. Numerical Results # of Simulations per each case = 500 n = 32

28. Numerical Results DiffFactor = 2(|E(G1)-E(G2)|+|E(G2)-E(G1)|)/n(n-1)

29. Concluding Remarks Develop Algorithms to guarantee min # of Wavelength
to find a proper compromising point of reconfiguration cost and the best number of wavelength under the reconfiguration cost constraint and the number of wavelength constraint.