Load-Optimal Local Fast Rerouting for Resilient Networks Yvonne-Anne - PowerPoint PPT Presentation

DSN, DENVER, 2017 – 06 - 28 Load-Optimal Local Fast Rerouting for Resilient Networks Yvonne-Anne Pignolet, ABB Corporate Research Stefan Schmid, University of Aalborg Gilles Trédan, LAAS-CNRS, Toulouse

Motivation – Critical infrastructure has high availability requirements – Industrial systems are more and more connected – Hard real-time requirements  How to provide dependability guarantee despite link failures in networks?  Possible without communication between nodes? And low load? Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan Slide 2 July 2, 2017

Local Fast Failover 1 2 6 Local failover @1: Traffic demand: Does not know {1,2,3}->6 failures downstream! 3 5 4 Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan Slide 3 July 2, 2017

Failover matrix: Local Fast Failover flow 1- >6: 2,3,4,5,… 1 2 6 Local failover @1: Reroute to 2! Traffic demand: {1,2,3}->6 3 5 4 Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan Slide 4 July 2, 2017

Local Fast Failover Failover matrix: flow 1- >6: 2,3,4,5,… 1 2 6 Local failover @1: Reroute to 2! But also from 2: Traffic demand: 6 not reachable. {1,2,3}->6 Next: 3. 3 5 4 Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan Slide 5 July 2, 2017

Local Fast Failover 1 Failover matrix: flow 1- >6: 2,3,4,5,… flow 2- >6: 3,4,5,… 2 6 flow 3- >6: 4,5,… Max load: Traffic demand: {1,2,3}->6 3  3 5 4 Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan Slide 6 July 2, 2017

Local Fast Failover Statically defined, no 1 global knowledge and no communication! 2 6 Failover matrix: flow 1- >6: 2,5, … flow 2- >6: 3,4,5,… flow 3- >6: 4,5,… A better solution: 3 5 load 2  4 Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan Slide 7 July 2, 2017

Local Fast Failover For load balance the 1 prefixes should differ 2 6 Failover matrix: flow 1- >6: 2,5, … flow 2- >6: 3,4,5,… flow 3- >6: 4,5,… A better solution: 3 5 load 2  4 Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan Slide 8 July 2, 2017

Problem statement Find a failover matrix M that needs many link failures for a high load Row i used for flow i, each row is a permutation, 1 2 3 4 5 6 source and destination are ignored 2 5 1 3 4 6 3 4 5 1 2 6 1: Upon receiving a packet of flow i at node v 4 1 2 5 3 6 2: If v != destination: 5 3 4 2 1 6 3: If (v,destination) available: forward to d 5 1 2 3 4 6 4: j = index of v in ith row, /*m_i,j = v*/ 5: While m_i,j = source or (v,m_i,j) unavailable 6: j = j+1 7: Forward to m_i,j Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan Slide 9 July 2, 2017

Good and bad news [BS,Opodis 2013] Lower bound: High load unavoidable even in well-connected residual networks: # failures φ can lead to load at least √ φ , even in highly connected networks Example: All-to-One Traffic Upper bound: Load √ φ generated with a failover matrix where each row is a random permutation needs at least Omega( φ /log n) failures. Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan Slide 10 July 2, 2017

Deterministic Failover Matrices 1 2 3 4 5 6 1 2 3 4 5 6 Construction goal: 2 3 4 5 1 6 2 5 1 3 4 6 Low intersection in short prefixes! 3 4 5 1 2 6 3 4 5 1 2 6 4 5 1 2 3 6 4 1 2 5 3 6 5 1 2 3 4 6 5 3 4 2 1 6 5 1 2 3 4 6 5 1 2 3 4 6 Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan Slide 11 July 2, 2017

Latin Squares with Low Intersection 1 4 12 9 3 5 If k < √ n a latin square failover matrix where the ... ... 3 12 4 5 6 8 intersection of two k-prefixes is at most 1 4 6 13 8 11 1 has load φ < k with Omega( φ ^2). load x x x x 4 13 x x x x x 9 4 Can we construct such matrices? n-k k Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan Slide 12 July 2, 2017

Ingredients: Design Theory and Graph Theory Symmetric Balanced Incomplete Block Designs 1,3,6 1,2,7 An (n, k, λ )-BIBD consists of 2,4,3 (7,3,1)-BIBD 2,5,6 - Set X with n elements {1,…,n} 3,5,7 1,4,5 - Blocks A1, …, An , containing k elements of X 4,7,6 - |Ai ∩ Aj| = λ Hall’s Marriage Theorem: 3-regular bipartite A d-regular graph contains d disjoint perfect matchings graph Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan Slide 13 July 2, 2017

Construction of k-prefix with low intersection 1 1, 4, 13 1 4 13 9 3 5 ... 3 12 4 5 6 8 2 12, 3, 4 ... ... ... 12 9, 1, 2 2 1 9 7 8 1 ... 13 8, 6, 12 12 8 6 3 13 10 n-k k Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan Slide 14 July 2, 2017

Results Theory: Deterministic BIBD-Failover Matrix achieves asymptotically optimal load Experiments: All-to-one routing and random failures Permutation routing and random failures Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan Slide 15 July 2, 2017

Conclusion and Future Work • Deterministic failover with load guarantees applying latin squares, BIBDs, matchings • BIBDs are a tool that can probably be used in many other contexts Next: Algorithms and improved bounds for sparse communication networks Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan Slide 16 July 2, 2017