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

C irculant - G raph- B ased F ault- T olerant R outing for A ll- O ptical WDM LAN s. Dexiang Wang and Janise McNair Wireless and Mobile Systems Laboratory. Introduction Exemplifying Application and Design Challenges Related Work and Contributions

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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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  1. www.wam.ece.ufl.edu Circulant-Graph-Based Fault-Tolerant Routing for All-Optical WDMLANs Dexiang Wang and Janise McNair Wireless and Mobile Systems Laboratory

  2. 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 www.wam.ece.ufl.edu outline

  3. 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 • 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) www.wam.ece.ufl.edu Introduction

  4. 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. www.wam.ece.ufl.edu Related Work

  5. 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 www.wam.ece.ufl.edu Contributions

  6. 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 www.wam.ece.ufl.edu CirculantNetwork Architecture 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

  7. 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 www.wam.ece.ufl.edu Node-Disjoint LightpathsSetup: Case 1 S=0 N-1 1 2 N-2 D=W N-W W+1 2W-1 2W

  8. 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 www.wam.ece.ufl.edu Node-Disjoint LightpathsSetup: Case 2 S=0 N-1 1 W N-W D-W D-1 D+W D>W D+1

  9. 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) www.wam.ece.ufl.edu Node-Disjoint LightpathsSetup: Case 3 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

  10. 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 www.wam.ece.ufl.edu Remaining Dpaths Setup: Scenarios I and II 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

  11. 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 www.wam.ece.ufl.edu Network Resource Utilization for D=W for D>W for D<W (scenario I) for D<W (scenario II)

  12. 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 www.wam.ece.ufl.edu Network Resource Utilization (cont.) Link utilization to varied destinations in C16({1,…,W}) Wavelength requirement for all-node simultaneous communications in C16({1,…,W})

  13. 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 www.wam.ece.ufl.edu Network Reliability Analysis 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

  14. 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 www.wam.ece.ufl.edu Network Reliability Analysis (cont.) Disconnection probability change with fL and fN for a s(0)-d(8) pair in the circulant network C16({1,2})

  15. 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. www.wam.ece.ufl.edu Network Reliability Analysis (cont.) 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}))

  16. www.wam.ece.ufl.edu • 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)} Conclusion and Future Work

  17. www.wam.ece.ufl.edu Questions & Answers Thanks for your attending and comments

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