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GSGS33: Scalable Self-configuration and Self-healing in Wireless Networks
Hongwei Zhang & Anish Arora
Introduction
Sensor networks are not deployed manually
self-configuration (into interconnected clusters)
Sensor nodes and wireless links are subject to a rich class of faults
self-healing (of clusters and interconnections)
Sensor networks need to scale well in time, space, and resources
scalability in self-configuration and self-healing
Scalability via locality
An ideal goal for locality : self-healing should be a function of the size of
perturbation (in time, space, and energy) Example: problem of dining philosophers
for correctness: dining philosophers need “information”
only from philosophers at distance ≤ 2 hops
for fault-tolerance: (Nesterenko and Arora’02) if state corruptions occur within a 2-hop neighborhood,
they can be corrected within the neighborhood itself
any number of Byzantine philosophers can be tolerated as
long as they are ≥ 2 hops away
Locality via choice of model
Locality for some graph problems is hard
e.g. self-configuration and self-healing of routing tree
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Our approach to simplifying design of locality
choose a proper model for specific problems
System model
System multiple “small” nodes and one “big” node, on a plane node distribution
density: ( Rt s.t. with high probability,
there are multiple nodes in any circular area of radius Rt)
localization: relative location between nodes can be estimated
Perturbations dynamic nodes
joins, leaves (deaths), state corruptions
mobile nodes
Geography-aware self-configuration
Geographic radius of clusters is crucial for communication quality, energy dissipation, data aggregations
& applications
Problem statement Given
R: ideal cell radius (R > Rt)
Construct a set of cells , connected via a “head” node in each cell
s.t. radius of each cell is in [ R-c , R+c ] , where c = f (Rt)
each node belongs to only one cell cells and the connectivity graph over head nodes self-heal locally
Outline
Static networks Dynamic networks Mobile dynamic networks Related work Conclusions
Static networks
An ideal case:
In reality: no node may exist at some geometric centers (ILs), but, with high probability there are nodes no more than Rt away from any IL
R R3IL1
IL2
(IL = Ideal Location)
Rt
How to find the set of cell heads
Bottom-up ? hard to guarantee the
placement and size of
clusters
Top-down w.r.t. big node
use diffusing computation
but, accumulation in
deviation of head location
from IL is a problem
H0
GAP
R t
i
Organizing neighboring clusters & heads
Deviation problem is handled locally
instead of using real locations, node i
uses its and its parent’s ILs
i calculates the ILs of next band cells in
its search region < LD , RD > big node: <0o , 360o> other nodes: <-60o-a , 60o+a> , where
a Sin-
1(Rt / R)
for each IL, i ranks nodes within Rt
radius of the IL (by <D, A>), and
selects the highest ranked node as the
corresponding cluster head
IL(i)
IL(p.i)
RtLD RD
i2
-60o 60o
R3
search region
a
i2
jAD
Rt
GR
Summary: static networks
Cell structure is hexagonal cell radius:
Time taken to form the structure is (Db), where Db = the maximum distance between the big node and the small nodes
Scalability in self-configuration: local coordination: only with nodes within range
local knowledge: each node maintains info about a constant
number of nearby nodes
])32(,)32([ tt RRRR
tRR 23
Outline
Static networks Dynamic networks Mobile dynamic networks Related work Conclusions
Dynamic networks
Dynamics include: node join, leave (death), state corruption
Common vs. rare common perturbations: node density is preserved rare perturbations: node density is destroyed
Scalable self-healing is achieved via locality in: intra-cell healing inter-cell healing sanity checking of state (invariants)
Local intra-cell healing
Head shift upon head leaving (death)
local in a radius of Rt
Cell shift upon the death of all the nodes in an
area of radius Rt
local in a radius of R independent but consistent shift at
individual cells sliding of the global
head level structure
OIL
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0GR
Rt
R
IL
GR
Rt
R
H0
H0H0H0
Local inter-cell healing & sanity checking
Local inter-cell healing :
upon failure of intra-cell healing at head j, first, the parent of j tries to find a new head j’ if that fails, the children of j find new parents
Local sanity checking of state invariants :
upon detecting violation of the hexagonality property, node corrects itself after checking with its neighbors when state perturbation includes several nodes, the
perturbed region corrects itself from the outside going in, and all nodes are corrected within time proportional to size of perturbed region
Summary: dynamic networks
Cell radius for cells not adjoining any gap:
for cells adjoining a gap:
Head tree is now minimum distance tree rooted at the big node
Stabilization time from perturbed state: (Dp),
where Dp = diameter of the continuously
perturbed area
])32(,)32([ tt RRRR
])32(,)32([ ptt dRRRR
Summary: dynamic networks (contd.)
Scalability in self-healing: local fault-containment and healing local knowledge
Local healing and fault-containment enables stable cell structure
lengthened lifetime: (nc) , where nc = the
number of nodes in a cell
Outline
Static networks Dynamic networks Mobile dynamic networks Related work Conclusions
Mobile dynamic networks
H0
H0
d
d23
Outline
Static networks Dynamic networks Mobile dynamic networks Related work Conclusions
Related work
Cellular hexagon structure (Mac Donald ’79) Preconfigured & not considering self-healing
LEACH (Heinzelman et al ’00) No guarantee about the placement and size of
clusters Perturbations dealt with by globally repeating
the whole clustering process
Related work (contd.)
Logical-radius based clustering (in Banerjee ’01) non-local cluster maintenance, and no consideration of
state corruption only logical radius long links and link asymmetry are
possible multiple rounds of diffusion
Self-stabilization tree maintenance (in Arora & Gouda ’90)
not fault containing local mending (in Kutten & Peleg ’95)
local in time, not in space
Outline
Static networks Dynamic networks Mobile dynamic networks Related work Conclusions
Conclusions
GS3 is scalable self-configuration self-healing
And this is achieved by exploiting the model properties in wireless sensor networks
Density Localization
(Note: we have also designed an algorithm for “local containment of faults in general spanning trees” for dynamic networks)