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C irculant - G raph- B ased F ault- T olerant R outing for A ll- O ptical WDM LAN s

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Circulant-Graph-Based Fault-Tolerant Routing for All-Optical WDMLANs

Dexiang Wang and Janise McNair

Wireless and Mobile Systems Laboratory

- Introduction
- Exemplifying Application and Design Challenges

- Related Work and Contributions
- Proposed Circulant-Graph-Based Node-Disjoint Routing
- Network Architecture
- Node-Disjoint Lightpaths Setup

- Network Resource Utilization
- Network Reliability Analysis
- Conclusion and Future Work

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- Exemplifying Application
- Avionic onboard communications using WDM LAN technologies
- Design an optical backbone network architecture that is able to carry time-critical data communications and meanwhile tolerate a certain number of critical link or node failures without loss of data

- Solution: multi-disjoint-lightpaths communication

- Avionic onboard communications using WDM LAN technologies
- Design Challenges
- Choice of topology
- Flexibility of Connectivity
- Network scalability

- Fault-tolerant routing
- Number of tolerable critical faults
- Algorithm to find disjoint lightpaths

- Efficient resource utilization
- Link utilization (depending on fault-tolerant routing)
- Wavelength utilization (depending on wavelength assignment scheme)

- Choice of topology

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- Wen, Y.; Chan, V.W.S., "Ultra-reliable communication over unreliable optical networks via lightpath diversity: system characterization and optimization,“ GLOBECOM 2003
- Weichenberg, G.; Chan, V.W.S.; Medard, M., "High-reliability topological architectures for networks under stress, “ JSAC 2004
- The former proposes a redundant lightpaths protection scheme and the latter develops a reliability analysis model. Concluded is that circulant graph can be a good fault-tolerant candidate topology. However, no routing issue is discussed.

- Wang, D.; Kumar, A.; Sivakumar, M.; McNair, J. Y., "A Fault-Tolerant Backbone Network Architecture Targeting Time-Critical Communication for Avionic WDM LANs, " ICC 2009
- Proposes a 4-way redundant lightpaths protection scheme in the 2-D torus

- S. C. Liaw, G. J. Chang, F. Cao, and D. F. "Fault-tolerant routing in circulant networks and cycle prefix networks," Annals of Combinatorics 1998
- Proposes a fault-tolerant routing scheme for a circulant graph Cd^n({1,d,…,dn-1}), in which d≥2 and n ≥ 1. However, the scheme only works for limited choices of number of supported nodes (dn) and network connectivity. Besides, it works only on directed circulant graph.

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- Propose a circulant-gragh-based all-optical WDM LAN architecture
- Develop a fault-tolerant routing algorithm that works for any number of nodes and arbitrary network connectivity via setting up a maximum number of node-disjoint lightpaths
- Instead of directed graph, we base the fault-tolerant routing on undirected graph such that network connectivity and fault tolerance capacity are doubled by simply adding a “reverse” link for each directed link in the directed circulant graph

- Analytically calculate network resource utilization that is measured by the number of required optical links and wavelengths
- Derive a reliability model combining both node and link failure effects

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S

1

11

2

10

D

9

4

8

5

7

6

0

1

11

2

10

3

9

4

8

5

7

6

S

S

1

11

D

11

2

10

2

10

3

3

9

9

4

8

4

8

5

7

5

7

D

6

- A circulant graph CN(A) is a graph of N vertices, indexed from 0 to N-1, in which vertex i is adjacent to vertices i+j and i-j (modulo) for each j in set A
- Circulant-graph-based all-optical architecture
- Fix the offset A={1,…,W} for any possible W (depending on fault tolerance requirement)
- Replace all vertices with data delivery/switching/reception nodes
- Replace all edges by two unidirectional optical fibers in opposite directions

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Exemplifying topology and fault-tolerant routing for 3 cases of destination locations

C12({1,2,3})

Fault-tolerant routing: Case 1

Case 2

Case 3

- The goal is to setup a maximum number of lightpaths (2W) for any S-D pair
- WLOG, fix source at node 0 and vary destination node from 1 to floor(N/2)
- According to positional relationship between destination node D and node W, there are 3 different cases of fault-tolerant routing
- Case 1: D=W
- First W node-disjoint lightpaths (clockwise)
0→1→D, 0→2→D, …, 0→W-1→D, 0→D

- Other W node-disjoint lightpaths (counter-clockwise)
0→N-1→N-1-W→…→ →W

0→N-2→N-2-W→…→ →W

…

0→N-W→N-W-W→…→ →W

- First W node-disjoint lightpaths (clockwise)

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S=0

N-1

1

2

N-2

D=W

N-W

W+1

2W-1

2W

- Case 2: W<D≤
- First W node-disjoint lightpaths (clockwise)
0→1→1+W→…→ →D

0→2→2+W→…→ →D

…

0→W→W+W→…→ →D

- Other W node-disjoint lightpaths (counter-clockwise)
0→N-1→N-1-W→…→ →D

0→N-2→N-2-W→…→ →D

…

0→N-W→N-W-W→…→ →D

- First W node-disjoint lightpaths (clockwise)

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S=0

N-1

1

W

N-W

D-W

D-1

D+W

D>W

D+1

- Case 3: 0<D<W
- First 2W-D node-disjoint lightpaths
D purely clockwise routed lightpaths

0→1→D, 0→2→D, …, 0→D,

W-D clockwise/counter-clockwise routed lightpaths

0→D+1→D, …, 0→W →D,

W-D counter-clockwise/clockwise routed lightpaths

0→N-1→D, …, 0→N-(W-D)→D

- Development of remaining D node-disjoint lightpaths falls into 2 scenarios depending on the overlapping relation between the D lightpaths and the group of nodes indexed from W+1 to W+D.
- Heading lightpath: the lightpath taking biggest stride (W) in its first hop (counter-clockwise)
- Tailing lightpath: the lightpath taking stride (W-D) in its first hop (counter-clockwise)

- First 2W-D node-disjoint lightpaths

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S=0

1

N-1

N-W+D

D<W

N-W+D-1

D

W-1

W

N-W

W+1

D

W+D

- Scenario I
0→N-W+D-1→… → →W+D→D

0→N-W+D-2→… → →W+D-1→D

…

0→N-W→… →

→W+D-1→D

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S=0

- Scenario II
0→N-W+D-1→… → →W+T→D

…

0→N-W+D-T→… → →W+1→D

- 0→N-W+D-T-1→… → →W+D→D
…

0→ N-W → … →

→W+T+1→D

W

D<W

N-W+D-1

D

N-W

W+1

D

D

W

S=0

W+D

W

W

D

N-W+D-1

H

D<W

D

D

W

N-W

W+1

D

W+D

D

W

T

D

W

- Number of links utilized for 2W lightpaths setup for a S-D pair
- For a non-complete CN({1, …, W})
- For a complete CN({1, …, W})
- Wavelengths required for all-node communication given wavelength conversion is offered

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for D=W

for D>W

for D<W (scenario I)

for D<W (scenario II)

- Link requirement distribution is fairly flat across varied destinations except for those index-close to the source
- Link utilization increase with W is comparably slow to increase of W itself (due to larger stride that the source can take to route towards destination)
- Resulted in is the wavelength requirement decrease for all-node communication with W, which help reduce the complexity of node MUX/DEMUX/switching structure

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Link utilization to varied destinations in C16({1,…,W})

Wavelength requirement for all-node simultaneous communications in C16({1,…,W})

- Model the networks faults via associating a failure probability fN to each node and fL to each link
- Assume all nodes and links fail in an independent fashion
- A node failure will block all incoming and outgoing communications

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P(S/D disconnection) = P(S/D disconnection | no fault on S and D) ∙ P(no fault on S and D)

+ P(S/D disconnection | faulty S or D) ∙ P(faulty S or D)

P(S/D disconnection | no fault on S and D) =

Disconnection probability for an S-D pair

P(no fault on S and D) =

Expressions of the 4 items of right-hand side above

P(faulty S or D) =

P(S/D disconnection | faulty S or D) = 1.0

- fN plays a bigger role since disconnection probability grows faster with fN than with fL
- This is because both source and destination nodes are subject to failures while the pressure of link failures is mitigated by multiple disjoint lightpaths

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Disconnection probability change with fL and fN for a s(0)-d(8) pair in the circulant network C16({1,2})

- Effect of W: disconnection probability decreases almost proportionally to increase of W in logarithmic scale, which demonstrates vast fault-tolerance improvement via increasing network connectivity
- Distribution of disconnection probability: destinations index-closer to source are of higher connection reliabilities because they can be routed to through more 2-hop lightpaths and hence require a lower number of links.

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Effect of different W on disconnection probability (fN=0, N=16, S=0, D=8)

Disconnection probability distribution across the network (fL=0.1, fN=0, C16({1,2}))

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- Circulant-graph-based all-optical WDM LAN architecture can provide good flexibility in number of supported nodes (N) and capacity of fault tolerance (W)
- There exists a node-disjoint routing scheme that fully leverages connectivity of circulant graph to offer maximum fault tolerance design
- In future, we plan to study the two following problems:
- Assign wavelengths to the lightpaths developed in this paper under wavelength continuity constraint with goal of minimizing wavelength utilization
- Optimize the choice of offset A in CN(A) with goal of either maximizing connection reliability or minimizing link resource utilization by relaxing the elements of A to take on any integers in {1, floor(N/2)}

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Thanks for your attending and comments