Kalman Graffi - IEEE NetSys 2013 - Ca-Re-Chord - A Churn Resistant Self-stabilizing Chord Overlay...

Markus Benter, Mohammad Divband, Sebastian Kniesburges, Andreas Koutsopoulos, Kalman Graffi

University of Paderborn 1

Ca-Re-ChordA Churn Resistant Self-stabilizing Chord Overlay Network

Networked Systems 2013



1. Chord

2. Re-Chord

3. Ca-Re-Chord

4. Evaluation

5. Conclusion

Overview



Chord[Stoica et al., 2001]



• DHT (Distributed Hash Table)• Node degree: O(log(n))• Routing performance: O(log(n))

Chord



• Chord network partitioned (due to churn)• E.g. two Chord rings• Successors and predecessors locally consistent• Cannot be detected

Chord: Inconsistency Issue



Re-Chord[Kniesburges et al., 2011]



Re-Chord: Self-Stabilizing Chord



• Each node has identifier in interval [0,1)• Fingers: virtual nodes do the same as fingers in Chord

• Node joins network several times• Virtual Nodes are

Re-Chord: State



• Edges:• Each node has successor and predeccessor• Each real node has real right neighbor and real left neighbor

Re-Chord: State



Example: route from to

Re-Chord: State



In stable state, Chord is subgraph of Re-Chord

Re-Chord: State



Six stabilization rules are necessary:

1. Create and Delete Virtual Nodes

2. Overlapping Neighborhood

3. Closest Real Neighbor

4. Linearization

5. Ring Edge

6. Connection Edges

Provable: Network is weakly connected then eventually be in stable state after finite number of steps

Re-Chord: Stabilization Rules



• Virtual nodes are • Do not create nodes in interval ( is real right neighbor of )• They are not necessary (routing via real right neighbor of )

• Rules:• Create all nodes according to (but without • Delete all nodes in interval

1. Create and Delete Virtual Nodes



Rules:• Left real neighbor and right real neighbor recalculated every step

• = left real neighbor = real neighbor with lower identifier• = right real neighbor = real neighbor with higher identifier

• All nodes in interval [ , ] are notified• Can find new real neighbor as well




• Theorem: Can be found in O(log(n)) steps• Each node has O(log(n)) virtual nodes• Number of virtual nodes between two real nodes O(log(n))• Worst-Case is O(„number of contiguous virtual nodes“)

• Analysis in paper




• Rule: Propagate all edges (but the two closest neighbors)• Provable: Graph becomes a line after O(n) steps

4. Linearization



• Each nodes that think its the node with biggest (smallest) identifier in the network, creates a ring edge

• Rules:• No neighbor with higher identifier => Tell node with smallest identfier to

create ringe edge • Node propdates ring edge to node with smaller identifer if possible: remove

and create

5. Ring Edge



• Weakly connected graph: stable after O(n log(n)) rounds • Node joins: stable after O(log2(n)) rounds • Node leaves: stable after O(log(n)) rounds

Re-Chord: Analysis

Too slow in contiguous churn szenarios

Ca-Re-ChordChurn Aware Re-Chord



• Each real node stores up to right real neighbors• Each virtual node stores up to right real neighbors• Node leaves: Quickfix instead of self-stabilization• Up to contiguous nodes can fail

Ca-Re-Chord: Idea



• Send find successor messages with time-to-live • Time-to-live descreased by 1 each hop• Successor reply messages indicates found successor• Datatrucuture updated

Ca-Re-Chord: Build up



• Apply quick-fixing in two situations• Ping fails• Message transmission fails (re-transmit)

• Quickfix can fix...• The embedded Chord ring (applied on real nodes)• The finger representations (applied on virtual nodes)

• Quickfixing can improve two things• Speed-up self-stabilization• Improve message delivery directly (message re-transmission)

• How to choose k? Should depend on...• Node failure rate • Desired robustness against churn (increases with k)• Acceptable message overhead (increases with k)

Ca-Re-Chord: Properties



• Assume that each node fails with propability• Then probability that contiguous nodes fail is • Value should be small constant (often )

Ca-Re-Chord: Churn resistance



Evaluation



• PeerfactSim.KOM• Realistic P2P network simulator

• Implementation of ...• Chord• Re-Chord• Ca-Re-Chord

• Settings• Initial Network Size: 1000 Nodes• Successors k=3• Drop packet after 50 hops

• Exponential churn• Mean session length = 60 min• Adjustable churn factor (?)• Let nodes join (60 min), churn after stabilization (1400 min)

Ca-Re-Chord: Evaluation



Ca-Re-Chord: Evaluation (churn factor ???)

axis



Ca-Re-Chord: Evaluation



Ca-Re-Chord: Evaluation (Unklar)



Conclusion



• Re-Chord • Self-stabilizing: Recover from every weakly connected graph• Not robust against churn • Stabilization too slow

• Ca-Re-Chord• Extends Re-Chord• Goal: churn resilience• Apply k-successor quickfixing before stabilization• Disadvantage: additional traffic (maintaining k links)

• Evaluation: Ca-Re-Chord as good as Chord

Conclusion



Tank you for your attention

Kalman Graffi - IEEE NetSys 2013 - Ca-Re-Chord - A Churn Resistant Self-stabilizing Chord Overlay...

Education

Transcript of Kalman Graffi - IEEE NetSys 2013 - Ca-Re-Chord - A Churn Resistant Self-stabilizing Chord Overlay...