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

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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 Trdan, LAAS-CNRS, Toulouse Motivation Critical infrastructure

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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

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July 2, 2017

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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

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1 2 3 4 6 5

Traffic demand: {1,2,3}->6

Local Fast Failover

Local failover @1: Does not know failures downstream!

July 2, 2017

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Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan

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1 2 3 4 6 5

Traffic demand: {1,2,3}->6

Local Fast Failover

Failover matrix: flow 1->6: 2,3,4,5,… Local failover @1: Reroute to 2!

July 2, 2017

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Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan

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1 2 3 4 6 5

Traffic demand: {1,2,3}->6

Local Fast Failover

Failover matrix: flow 1->6: 2,3,4,5,… Local failover @1: Reroute to 2! But also from 2: 6 not reachable. Next: 3.

July 2, 2017 Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan

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1 2 3 4 6 5

Traffic demand: {1,2,3}->6

Local Fast Failover

Failover matrix: flow 1->6: 2,3,4,5,… flow 2->6: 3,4,5,… flow 3->6: 4,5,…

Max load: 3 

July 2, 2017 Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan

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1 2 3 6 5

A better solution: load 2 

Local Fast Failover 4

Failover matrix: flow 1->6: 2,5, … flow 2->6: 3,4,5,… flow 3->6: 4,5,… Statically defined, no global knowledge and no communication!

July 2, 2017 Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan

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1 2 3 6 5

A better solution: load 2 

Local Fast Failover 4

Failover matrix: flow 1->6: 2,5, … flow 2->6: 3,4,5,… flow 3->6: 4,5,… For load balance the prefixes should differ

July 2, 2017 Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan

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Find a failover matrix M that needs many link failures for a high load

July 2, 2017 Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan

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Problem statement

1 2 3 4 5 6 2 5 1 3 4 6 3 4 5 1 2 6 4 1 2 5 3 6 5 3 4 2 1 6 5 1 2 3 4 6

1: Upon receiving a packet of flow i at node v 2: If v != destination: 3: If (v,destination) available: forward to d 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

Row i used for flow i, each row is a permutation, source and destination are ignored

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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.

July 2, 2017 Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan

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July 2, 2017 Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan

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Deterministic Failover Matrices

1 2 3 4 5 6 2 5 1 3 4 6 3 4 5 1 2 6 4 1 2 5 3 6 5 3 4 2 1 6 5 1 2 3 4 6 1 2 3 4 5 6 2 3 4 5 1 6 3 4 5 1 2 6 4 5 1 2 3 6 5 1 2 3 4 6 5 1 2 3 4 6

Construction goal: Low intersection in short prefixes!

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July 2, 2017 Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan

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Latin Squares with Low Intersection

k n-k

load

1 4 12 9 3 5 3 12 4 5 6 8 4 6 13 8 11 1 x x x x 4 13 x x x x x 9

... ...

If k < √n a latin square failover matrix where the intersection of two k-prefixes is at most 1 has load φ < k with Omega(φ^2). Can we construct such matrices?

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Symmetric Balanced Incomplete Block Designs An (n, k, λ)-BIBD consists of

Set X with n elements {1,…,n}
Blocks A1, …, An, containing k elements of X
|Ai ∩ Aj| = λ

Hall’s Marriage Theorem: A d-regular graph contains d disjoint perfect matchings

July 2, 2017 Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan

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Ingredients: Design Theory and Graph Theory

1,3,6 2,5,6 1,4,5 1,2,7 2,4,3 3,5,7 4,7,6

(7,3,1)-BIBD 3-regular bipartite graph

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July 2, 2017 Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan

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Construction of k-prefix with low intersection

1, 4, 13 12, 3, 4 9, 1, 2 8, 6, 12 1 2 12 13

1 4 13 9 3 5 3 12 4 5 6 8 2 1 9 7 8 1 12 8 6 3 13 10

... ... ... ... ... k n-k

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July 2, 2017 Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan

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Results

Theory: Deterministic BIBD-Failover Matrix achieves asymptotically optimal load Experiments:

Permutation routing and random failures All-to-one routing and random failures

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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

July 2, 2017 Yvonne-Anne Pignolet, Stefan Schmid, Gilles Trédan

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Conclusion and Future Work

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