Supriya Krishnamurthy, SICS and KTH

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SP3 Overlay Networks and ServicesWP3n
Analytical Study of the effects of Churn and
Maintenance

• Supriya Krishnamurthy, SICS and KTH
• Partners EPFL
• Zurich, March 5-6, 2007

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Goal Understanding the Competing Effects of a
Dynamic environment and Maintenance on Overlays

• Churn causes degradation of performance loss of
  availability of data, large lookup
  costs,degradation of network structure, etc
• Maintenance strategies try to remedy this. But
  the outcome depends on the strategy used.
• In WP3n, we have tried to analytically understand
  the full interplay of churn and maintenance, in
  order to compare different strategies and to
  device better ones.

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Methods and Motivation

• Earlier studies have either been empirical
• ( Li et al, IPTPS 2004Rhea et al, USENIX
  2004,
• Castro et al, DSN 2004) or via theoretical
  bounds
• (Liben-Nowell et al, PODC 2002 Aspnes et al,
• PODC 2002).
• By taking into account the full time-evolution
  of the system, we can predict most quantities
  to better than 1 accuracy, for the full range
  of system parameters.
• The analysis can take into account fine details
  such as
• how new joiners construct a routing table.
  But also
• broader aspects such as how different
  maintenance
• strategies affect system performance.

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Defining the System and Parameters

• periodic maintenance
• Rate of periodically checking a 'successor' or
  a 'finger'
• ParametersN, K, r

• reactive maintenance
• Rate of periodically checking a successor
• Rate of sending messages once an error is found

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Results Behaviour Under Churn

• Accurate determination of functional form of
  Lookup cost as a function of churn. L A (1f3
  )
• This is useful for
• i) Evaluating level of churn from a lookup
  measurement
• ii) Evaluating lookup cost for varying routing
  table sizes
• iii) Comparing different maintenance
  strategies

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Results Comparing Maintenance Strategies

• We theoretically compare the lookup cost for two
  maintenance strategies
• i) Nodes periodically trigger a repair action
• ii) Nodes periodically only check their
  immediate neighbour. On finding an incorrect or
  failed link, they inform all the affected nodes.
• We generalize the master-equation based approach
  to analyse ii).
• We have completed a preliminary analysis for some
  values of the system parameters

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Results Comparing different Maintenance
schemes and different routing table sizes

• Lookup latency vs. maintenance rate

• Lookup latency vs. maintenance rate

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Results Effect of Churn and Maintenance on
Content Storage

• System studied
• P2P storage systems based on erasure codes under
  churn
• Theory
• Closed-loop, discrete-time model
• Markovian behaviour
• CS approach for repairing
• Self-organized fragment sampling
• adapted to churn rate
• Resilience of the storage system
• Strategy-A Deterministic procrastination
• Strategy-B Randomized subset sampling (our
  idea)
• IEEE P2P06 Internet-scale storage systems
  under churn - A study of the steady-state using
  Markov models

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Plans for 2007

• Accounting for link delays and comparing
  different maintenance strategies with this
  extended model
• We have taken the rates of different processes
  into account. But what about the time they take?
• How do different maintenance strategies,
  including gossip-based ones, compare in this case
  ?
• Analytical model considering peer churn rate and
  uptime distribution
• How can we take advantage of node uptime
  heterogeneity?
• What is the trade-off between maintenance and
  routing performance ?