GS3: Scalable Self-configuration and Self-healing in Wireless Networks

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GS3 Scalable Self-configuration and Self-healing
in Wireless Networks

• BY
• Hongwei Zhang and Anish Arora

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• GS3 , a distributed, scalable, self-sonfiguration
  and self-healing algorithm for multi-hop wireless
  networks.
• Enables network nodes to configure themselves
  into Cellular hexagonal structure.
• Structure self healing under
• various perturbations.

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• Scalability in Large scale multi-hop wireless
  networks achieved by divide and conquer strategy.
• Clustering can be used for this purpose.
• In this model, the clustering criteria,
  Geographic radius , is taken into consideration
  which many previous works didnt. (If not many
  factors will be implicitly neglected, like energy
  dissipated, efficiency of local coordination
  functions,quality of communications and so on)

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• Contributions of the Paper.
• Present the GS3 algorithm.
• Each cell has a radius which is tightly bounded
  with respect to a given value R(ideal cluster
  radius), and no overlapping with other cells.
• Each cell has a head(a node in the cell).
• All the heads form a Head graph, whose root is
  the big node which is one of the heads of the
  cell.
• Algorithm makes a self healing system.(ie. Stable
  in presence of various perturbations).

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• What is Self healing?
• Masking of unanticipated node leaves within a
  cell.
• In case of a number of deaths at the same time, a
  shift
• of the cell helps in maintaining relative
  locations.
• When big node moves a distance d, only a part of
  graph
• within sqrt(3)d/2 radius ?? from the root needs
  to be
• changed.
• GS3 also scalable in 3 respects.
• 1.Local knowledge.
• 2.Local self healing
• 3.Local coordinations.

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• Local Knowledge allows node to keep minimum
  information about its neighbours.
• Local self healing guarantees that all
  perturbations are dealt with in a tightly
  bounded region around the perturbed area.
• Only local coordinations is needed in both the
  self configuration and self healing processes.

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• SYSTEM MODEL
• -- System nodes
• -- Perturbations.
• System nodes-
• The set of nodes which form the cellular
  hexagonal structure.
• (Each has a certain wireless range). Node
  Distribution assumption is that there are
  multiple nodes in each circular area of radius Rt
  (radius tolerance)
• Wireless Transmission assumption
• Nodes adjust the transmission range .

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• PERTURBATIONS
• 2 types , Dynamic and mobile.
• Dynamic consists of leaves, joins, deaths and
  state corruptions??
• Mobile consists of node movements.
• Probability Frequency Assumption
• Joins, leaves and death are unanticipated while
  node death is
• predictable.
• The probability that a node moves distance d
  is proportional to
• 1/d
• The 3 types of networks that exists are static,
  dynamic and
• Mobile

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• Self configuration and self healing
• Each cell has a unique head and rest
  associates.
• All the heads in the structure form the head
  graph.
• The associates communicate to nodes in other
  cells
• Only through the big node.
• The self healing configuration problem is to
  partition the system so that max distance b/w
  nodes in a partition are bounded.

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• An algorithm which forms the ideal Cellular
  Hexagonal
• Structure.
• Given a radius R (ideal cell radius) , the
  hexagonal structure and the head graph should be
  made which takes care of all the perturbations we
  talked about.

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• Requirements for the construction of the cells
  and the head graph
• Each cell is of radius Rc/R-c where c is a small
  bounded value with respect to R, and is a
  function of Rt
• Each node is at most one cell.
• A node is in a cell if and only if it is
  connected to the big node
• The set of cells and the head graph are
  self-healing in the presence of dynamic as well
  as mobile nodes. By self-healing, a system can
  recover from a perturbed tate to its stable state
  by itself.

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• STATIC NETWORKS
• The nodes are neither dynamic nor mobile and so
  we dont have to consider perturbations.
• Only the plane has to be divided into cellular
  hexagonal structure which meet the requirements
  a,b and c.
• The geometric center of the the cell is called
  the Ideal Location (IL)
• The concept of Rt (radius tolerance) is
  introduced. It is required to to select a head
  for a cell , when we dont find a node in the
  exact IL of the cell.
• Every associates are allowed to select their own
  heads. (Essentially it should be the best head)

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• Cell bands.
• We designate cell with the big node as the
  central cell.
• Each set of cells of equal minimum distance from
  the central cells , is called a cell band..

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• GS-3 S Algorithm.
• Always the Big node starts the computation.
• It selects the child heads and they continue
  it.
• The search area for the big node is 0..360 and
  that of the child nodes is -60º- to 60 where
  is sin-1 Rt/sqrt(3) R.
• A node j which is not a head becomes an
  associate and it selects its best head.
• Algorithm Modules
• There are 2 programs, for Big node and for
  small nodes. Underlying these are programs for
  head organisation

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• HEAD_ORG to organise heads
• HEAD_ORG _RESPOND AND ASSOCIATE_ORG_RESPOND to
  respond to head_org
• Head_org A head I gets the states of the nodes
  in the search region, selects the heads and sends
  the sets of heads to cells with in sqrt(3) R
  2Rt.
• In Head_Org_Resp a head sends its state to
  another head which is at most sqrt(3) R 2Rt.
  The associates in response to a Head_Org at a
  head at most sqrt(3) R 2Rt away.

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• Analysis
• Analysis of GS-3 S done by discussing invariant,
  fix point and self-stabilisation.
• Invariant-
• Used for checking the corectness of the
  algorithm
• Invariant, a state predicate which is always
  true in every system computation. In this case
  the invariants are I1, I2 and I3
• I1 which is connectivity, is I1.1 and I1.2
• Which states that all heads which are
  connected to the Gh are also connected to the Gp.
  Also Gh is rooted at the big node H0

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• I2 which is hexagonal structure, is I2.1, I2.2,
  I2.3 and I2.4.
• They state that each inner cell has exactly 6
  neighbours and each boundary cell has less than 6
  neighbouring cells. The distance of heads of the
  boundary cells is bounded by sqrt(3) R 2 Rt,
  sqrt(3) R 2 Rt ?????
• I2.3 says that the big node has 6 children if
  it is a inner cell and 5 children if it is
  boundary cell.
• I2.4 ??? Says that each cell is of a radius R
  Rrandom
• where R random is at most 2 Rt/sqrt(3)
  

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• I3 which is Cell Optimality says that each
  associate in an inner cell belongs to only one
  cell and chooses the best head as its head.
• FIXPOINTS
• States that either no actions is enabled or the
  enables actions does not change any systems we
  are interested in . SF F1, F2, F3 and F4.
• F1 and F2 same as that of invariant.
• F3 is almost same as Invariants except that I3 is
  for just inner cells where F3 is for all the
  cells.
• F4 is coverage , set of heads and cells cover all
  the visible nodes in a system.

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• Self stabilisation
• 2 Theorems are used which states that , from
  any states , every computation of GS3-S reaches a
  state where SI holds with in a constant amount of
  time.
• Scalability
• GS-3 S is scalable in that it requires local
  coordination among nodes with in sqrt(3) R 2Rt
  distance from one another. ???

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• DYNAMIC NETWORKS.
• Perturbations takes place in Dynamic Networks..
• Also there may be the presence of Rt- gaps ?? in
  dynamic networks.
• 3 mechanisms for node leave and death.. i.Head
  shift, ii.cell shift and iii.Cell abandonment..
• The other perturbations are taken care by self
  stabilization.

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• Head Shift
• Dynamic networks associates divided into
  candidates and non candidates. Candidates , the
  nodes which are within Rt distance from the
  IL(for heads), the rest non candidates.. If a
  head leave occurs a new head is found from the
  candidates list..
• If all the candidates leaves then cell shift
  takes care of the problem.
• Cell Shift
• Takes place when all the candidates in the list
  gets exhausted.
• IL changed to IL1 so that a new candidate list
  can be got

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• Also the head graph as well as the head level
  structure slide as a whole
• Cell Abandonment
• Incase of highly perturbed situation, when IL is
  changed to IL1 then may be the distance b/w the
  heads of the neighbouring cells will be more than
  the standard. In this case the cells is abandoned
  and cells join another cell.

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• GS-3 D Algorithm
• Head selection almost same as GS-3 S.. But the
  possibility of Rt Gap is there.
• In presence of Rt Gap no head for that cell is
  selected.
• All nodes become associates for the neighbouring
  nodes. If later a node comes in Rt region?? It is
  selected as the head .(periodic checking)
• ----------------------------------------------
• When node join takes place, it tries to find the
  best head for its head with in sqrt(3) R2Rt ???
  If not it tries to find the best associate as its
  surrogate head??..
• If fails then waits and tries after some time..
• If a head is executing Head_Org , it responds
  with Associate_Org_Respond..

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• Node leave and death dealt with with intra cell
  and inter cell maintenance.
• When head leaves then the highest ranked
  candidate becomes the head. (intra cell
  maintenance)
• In inter cell maintenance, the parent head
  monitors the child heads. When intra cell
  maintenance fails parents tries to recover it
• It the parent fails then the children finds other
  parents
• Node state corruption dealt by sanity checking..
  (Periodic)
• The hexagonal relation is checked with the
  neighbouring heads.
• If violated then if the neighbours are OK then
  it is corrupted and becomes an associate..

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• Algorithm Modules
• Modified head organization modules \
• New modules for node join
• For intra and inter cell maintenance
• For Sanity checking
• Head Organisation Module
• While Head Org, not only data of children head,
  kept, also of candidates set and neighbouring
  sets.
• No Head selected if there is a Rt Gap.
• A node selected a new head, if the new head
  which is executing the Head_Org, is better than
  the first head.
• Node Join
• Small_Node_Bootup, Head_Join_Resp and
  Asociative_Join_Resp.
• Small_Node_Bootup used by a bootup node ??? , to
  find a nearyby head or associate.

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• Head_Join_Resp and Associate_Join_Resp
  executed by head or associate in response
  to the Bootup call.
• Intra Cell Maintanence
• Head_Intra_Cell, Candidate_Intra_Cell,
  Associate_Intra_Cell and Big_Slide
• Head_Intra_Cell executed by a Head , exchanges
  heartbeats?? with the associates of its cell.
  Head becomes a Associate if resource scarce.
• Candidate_Intra_Cell Heartbeats executed
  between the head and if head fails , then a new
  candidate is selected. If head transits to
  bootup?? Then candidate also does.

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• Associate_Intra_Cell
• When Head fails then the associate changes to
  bootup
• BIG_SLIDE
• Executed by Big node. Keeps the head in its
  original coverage, and resume head role when OIL
  becomes the IL.
• Inter-cell maintenance
• Implemented by module Head_Inter_Cell
• Basically used to find the parent of the head so
  that the path to H0 is closer.

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• Sanity_Checking
• Implemented as in Static networks.
• Analysis
• Invariant
• Same as that of GS3-S , except that the
  concept of
• Tuple ltICC,ICPgtcomes into picture, the max
  number of child heads of nodes other that Big
  nodes become 5 and radius of an inner cell depend
  upon the tuple ltICC,ICPgt.
• Fixpoint
• Same as GS3-S except that F1.2 is
  strengthened and F2.4 is relaxed.

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• F1.2 In F1.2, Gh is a minimum distance
  spanning tree of Ghn rooted at H0.
• F2.4 , in F2.4 Rrandom is 2R/sqrt(3) Dp, where
  Dp is diameter of gap perturbed area adjoining
  the boundary cell.
• Self-Stabilization
• Every computation reaches a state where DI
  holds with in time O(Dc), where Dc is diameter of
  state corrupted area.
• From every state where DI holds, every
  computation reaches a state where DF holds with
  in time O(max(Dd/c1),Td)
• c1avg speed of message diffusion
• Td max difference b/w lifetime of two
  neighbouring candidates

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• MOBILE DYNAMIC NETWORKS
• Mobility can be considered as a correlated node
  join and leave. Inspite of big node movement,
  the path between H0 and other heads should be
  minimum.
• They use a proxy head. Also the impact of the
  movement affects only sqrt(3)d/2, d is the
  distance where H0 moves.
• Algorithm
• If H0 moves away from the IL then , the proxy
  node comes in to picture and it retreats from the
  position of the Head node. When H0 moves with in
  IL of any other cell later, it replaces the
  existing head and then becomes H0 again?????

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• Algo modules
• New big_move, modified big node, intra cell
  and inter cell maintenance.
• Analysis
• The same invariant and Fixedpoint as GS3-D
  except for a new predicate F5which state that the
  big node H0 chooses the best neighboring node as
  its proxy.