Selforganizing systems Case study: peertopeer networks

1
Self-organizing systems Case study peer-to-peer
networks

• Maria Gradinariu
• IRISA - Université Rennes1

2
Self-organization where?

• Nature growing crystals, cells aggregation, ant
  colonies
• CS highly dynamic systems
• P2P, robots/nano-robots, ad-hoc or sensors
• Dynamic
• Frequent connections/disconnections
• Energy fluctuation
• Motion
• No centralized coordination authority

3
Self-organization - why?

• Infra-structures (overlays) P2P systems
• Better perfomances in look-up and routing
• Clustering/Coverings ad-hoc/ sensors
• Energy saving
• Geometric shapes robots/nano-robots
• Specific tasks

4
Self-organization

• Locality principal
• local interactions lead to global properties
• Entropy reduction (convergence)
• the entropy of the system progressively reduces
• Separation between the convergence and tolerance
  of transient faults

5
Self-organization our approach

• Evaluation criterion C 0,1- valued function
• C is a insensitive criterion
• P-stable configuration
• There is no neighbor of p that has a neighbor
  which improves C
• Local self-organization
• a system S locally self-organizes w.r.t. C in
  the neighborhood of p if S converges to a
  p-stable configuration

6
Self-organization logical overlay
7
Weak self-organization

• Definition based on the observation of the static
  fragments of an execution
• Weak Liveness ?e(f0,fi,,fj) ?fi,?fj,
  C(end(fj))gtC(begin(fj)) or ?p, begin(fj) is
  p-stable
• Safety ?e(f0,fi,) ?fi, C(end(fi))?C(begin(fi))
  

8
Weak self-organization

• Theorem S is weak self-organizing for a criteria
  C if for any processor p, S locally
  self-organizes in ps neighborhood

9
Self-organization

• Definition based on the observation of the static
  and dynamic fragments of an execution
• Liveness ?e(f0,fi,,fj) ?fi,?fj,
  C(end(fj))gtC(end(fi)) or ?p, begin(fj) is
  p-stable
• Safety ?e(f0,fi,) ?fi, C(end(fi))?C(begin(fi))
  

10
Strong self-organization

• Definition based on the observation of the static
  and dynamic fragments and the information stored
  in the system
• Kernel Preservation ?e(f0,fi,fi1), ?fi,fi1
  exists G, C(ProjG(end(fi))) C(ProjG(begin(fi1)
  )) where G is the common static core of end(fi)
  and begin(fi1)
• A system is strongly self-organizing if it is
  self-organizing and verifies the kernel
  preservation property

11
Self-organization Theorems

• Theorem (multi-criteria self-organization) Let S
  be a system and C1,,Cm a set of pair wise
  independent criteria. If S is self-organizing for
  each criteria Ci then S is self-organizing for
  C1? ?Cm
• Theorem (Self-organization Hierarchy)
• weak self-organization ? self-organization ?
  strong-self-organization

12
Self-organizing Lookup service
Lookup service
Logical Self-organized Layer
Load Balancing
Forwarding
Similarity
Physical P2P layer
13
Case study Pastrys self-organization

• Pastry 2001- A.Rowstron and P.Drushel
• Tree weak self-organizing tables
• Neighborhood set
• criteria - geographical proximity
• Leaf set
• criteria ids based similarity
• Routing table
• criteria covering the logical network (nodes
  that share a common prefix)
• Pastry is strong self-organizing when half of the
  tables are preserved after a dynamic period

14
Open problems

• Probabilistic extension of the model
• Defining the necessary and sufficient criteria in
  order to design self-organizing services
• Data lookup Publish/subscribe Group Membership
• Studying the self-organization in the context of
  sensors/robots/adhoc networks

15
Open problems

• Optimization of the social behavior of a
  self-organized group (Game Theory)
• Studying the relationship between the
  self-organization and super-stabilization
• Designing self-organizing systems that cope with
  severe faults (ex. byzantine or hybrid faults)