gs 3 gs 3 : scalable self-configuration and self-healing in wireless networks hongwei zhang &...

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


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


Mobile dynamic networks

H0

H0

d

d23

Outline


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


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)

gs 3 gs 3 : scalable self-configuration and self-healing in wireless networks hongwei zhang &...

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