Constrained Random Walks on Random Graphs: Routing Algorithms for Large Scale Wireless Sensor Networks

Presented by Guangyu Dong

Sergio D. Servetto, Cornell UniversityGuillermo Barrenechea, Ecole Polytechnique Federale de Lausanne

Outline

Contribution Motivation & Background Related Work Random Walk Approaches

For regular and static graphs For irregular and static graphs For dynamic graphs

Summary & Comments

Contribution A routing protocol for WSN that tries to do

load balancing among intermediate nodes. Making use of multiple paths that exist from

source to destination by making local packet forwarding decisions – A novel approach to implicitly maintain multipath

Current algorithm is only valid for grid-topology sensor network

Motivation Consider the routing in a large-scale WSN

with unreliability and dynamics A single node has limited capacity The unique characteristics of WSN calls for

multipath routing techniques Searching for possible routes? Route creation and destruction?

Random walk approach use an implicit way to solve these two problems

Multiple Paths Routing Advantages

Minimize critical points of failure

Achieve load-balancing Disadvantages

More energy consumption

Not Clear Performance? Security?

Ways to Do Multipath Routing Highly-resilient, energy-efficient multipath routing

Routes packet through a “primary path” while maintaining several other paths as backup.

Trajectory-based routing Each time source can randomly select a path for the packet Stateless

SPEED Each packet has an unanticipated path. Stateless Is it really a multipath routing protocol?

Random Walk Packet goes to a random direction at each node Not stateless

Random Walk Approach Decentralized algorithms

Complexity independent of the size of the network Dependence on the state of other nodes decays

with separation distance Taking advantage of a vast number of

multiple paths without explicitly listing them. Walking is constrained

Packets visit nodes on short (low delay) routes?? The number of packets that visit a node is independent

of the particular node

Assumptions and goals

Infinite lifetime via renewable energy source Goal is to preserve energy to maximize node throughput

while still alive As opposed to finite lifetime where the goal is to preserve

energy to prolong existence of the network So will it still work when some kind of power control

mechanism is used? For example, ASCENT or SPAN? The network is a grid

The approach has a big dependence on graph structure No straightforward way to extend to a random graph

Every node know its distance to source and destination

Forwarding Decision based on PDF

v

u1

u2

un

…..

p1

p2

pn

n

iip

1

1

Forwarding Decision in Grid

vu3

u4

u1

u2

p4

p1

p2

4

1

1i

ip

p3[i,j]

Notation and Terminology

N(v)={u1,…,un_v}-neighbors of v

пv={p1,…,pn_v}-pdf over neighbors of v

GN=grid of size NxN D(l)-set of nodes on lth diagonal de[i,j]-distance from node [i,j] to nearest boundary

node Expansion region: packets move across diagonals

with increase in number of nodes (decrease in pkt/node density)

Compression region: opposite of expansion

Graph GN

S

u4

u1vu3

u2

R

P3 P1

P4

P2

0 1 2 N-1…...0

1

2

N-1

...[3,2]

de[3

,2]=

2

Expansion & Compression Regions

S

R

0 1 2 N-1…...0

1

2

N-1

…...

D(0) D(1) D(2)

D(2N-2)

D(N-1)

D(N)

D(N+1)

Expansion Region Compression Region

Regular, static graphs (RSG)

Network is grid such that each interior node has 4 neighbors

Constraints:(c.1) Packet will not go backward

(c.2) For nodes on a same diagonal, they must be visited equally often

The diagonals close to source and destination only have a few nodes. Does it still make sense to do load balancing?

Sampling pdf for uniform packet distribution A packet at node [i,j] makes a binary decision

to move to [i+1,j] or [i,j+1] (c.1) with some probability p (by convention, to node closer to boundary):

)2( 1|)(|

],[

)1( 1|)(|

],[|)(|

jiD

jidP

jiD

jidjiDP

ecmp

eex

RSG Examples (N=4)

S

R

1/2 2/3 3/4

1/2

2/3

3/4

1/3

1/2

1/3

1

1/4

1/3 1/2 1/3

2/3

1 1

1/4

2/3

1/2

1

0 1 2

0

1

2

11

1/2

3

3 In the expansion stage, packet is more likely to be forwarded toward the boundary

In the compression stage, packet is more likely to be forwarded apart from the boundary

All possible paths have the same length

Simulation Results (RSG)

A Random walk based A Random walk based on flipping a fair coin.on flipping a fair coin.

A Random walk based A Random walk based on RSG algorithmon RSG algorithm

Distributed Computation of Coordinates Each node simply needs to know its own

coordinates Find coordinates using Distributed Bellman

Ford algorithm (local message exchange) Only good for a grid An initializing process necessary Introduces delay for initial packets

Irregular, static graphs (ISG) Same as RSG but delete a random set of

nodes permanently Impossible to achieve exact load balancing

Use node labels: (s,d)=(# routes to source, # routes to destination)

Can compute labels using recursion: number of routes to a node is the sum of the

numbers of routes at the two previous nodes Still a GRID!

Example of Node Labels (N=4)

1,7 1,3 0,1

1,4 2,3 2,3 2,1

4,12,21,1

7,13,11,11,1

0 1 2

0

1

2

3

3

Forwarding pdf on a best-effort basis The probability that v will

forward packet to the node (s1, d1) and (s2, d2)

Pex (s << d): Packet more likely forwarded to node with less source routes

Pcmp(s>=d): Packet more likely forwarded to node with more destination routes 21

221

121

121

2

2,

1,

2,

1,

dd

dp

dd

dp

ss

sp

ss

sp

cmp

cmp

ex

ex

ISG Examples (N=4)

1,7 1,3 0,0 0,1

1,4 2,3 2,3 2,1

4,12,20,01,1

7,13,11,11,1

0 1 2

0

1

2

3

31/2

11

1

1/22/3

1

1

1/31

1 1/2

1/2

1

1/2

1

1/2

1,20 1,10 1,4 1,1

1,10 2,6 3,3 4,1

10,16,23,31,4

20,110,14,11,1

1/2 2/3 3/4

1/22/3

3/4

1/31/2

1/3

1

1/4

1/3 1/2 1/3

2/3

1 1

1/42/3

1/2

1

0 1 2

0

1

2

11

1/2

3

3

Ideal Case

Equivalent to RSG

General Case

Simulation Results (ISG)

A Random walk based A Random walk based on flipping a fair coin.on flipping a fair coin.

A Random walk based A Random walk based on ISG algorithmon ISG algorithm

Dynamic Graphs (DG) Same as ISG but nodes turn ON/OFF

independently over When a node changes state: the one-hop

neighbors change labels and possibly trigger further label changes More than half of the N*N nodes will be affected

Packet may be routed to a dead end due to delayed propagation of labels change, which will result in packet delay or loss.

Concerns: Delays in propagating updates Sensitivity to inaccuracies in labels

Remember the first assumption?

The Overhead A large number of nodes need to keep a

state for each stream An initializing process to compute labels for

all nodes Beacon messages exchanged between

neighboring nodes: Check if neighbors are alive Exchanging labels

State change of a node will affect a large part of the network. The degree of influence depends on the distance between changing node and source/destination.

Simulation Results (DG)

A Random walk based A Random walk based on DG algorithmon DG algorithm

A Random walk based A Random walk based on flipping a fair coin.on flipping a fair coin.

More Simulation Results (DG)

Open Issues Extends to general graph?

Each node has arbitrary number of neighbors How to trade off between delay and load

balancing? The overhead to compute and maintain the labels

depends on how many nodes are in the rectangle area

Design algorithm under the same principles Pex (s < d): Packet more likely forwarded to node with

less source routes Pcmp(s>=d): Packet more likely forwarded to node with

more destination routes

Summary & Comments A decentralized random walk algorithm to do

multipath routing Highly topology dependent: algorithm is hard to

extend to generally random graph Mobility not addressed All intermediate nodes have to keep routing state

(N*N) with considerable overhead A large number of nodes will be affected when a

node switch between ON/OFF. An unrealistic energy model Inappropriate for multiple or dynamic packet streams

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

Hongwei Zhang, Anish AroraComputer Science Department

The Ohio State University3

Outline Contributions System models and goals GS-3 Algorithms

For static network For dynamic network For dynamic and mobile network

Problems Conclusion

Contributions An algorithm aiming to organize wireless

network into a ideal cellular hexagonal structure

Self-healing under perturbations The clustering criteria, Geographic radius , is

taken into consideration which many previous works didn’t

Scalability in large scale multi-hop wireless networks achieved by divide and conquer strategy

Geographic Radius Cluster

Density of wireless network increases

Cluster with fixed radius

Head Graph

Radius is limited by maximum transmit range

Related Work SPAN & ASCENT

Kind of clustering protocol (active node is cluster head)

No big node For power control purpose, other nodes will sleep What if other nodes don’t sleep? Can GS-3 be used for power control?

Many Other Clustering Algorithms Geographic radius or Logical radius Local or Global self-stabilizing Some of them are for energy saving

Cellular Structure

R

R3

IL

ILBig NodeHead NodeAssociate Node

t

t

RRAN

RRHNBN

Range

Transmit

23

23&

System Models Node Distribution Assumption:

there are multiple nodes in each circular area of radius Rt (radius tolerance)

Every node know its location Wireless Transmission Assumption:

Nodes adjust the transmission range Message transmission is always reliable

Perturbation Models Dynamics: nodes’ leaving, joins, deaths and state corruptions Mobility: nodes’ movements.

Perturbation Frequency: Joins, leaves and death are unanticipated and rare, while node

death is predictable The probability that a node moves distance d is proportional to 1/d

Goals Each cell has radius of R±c (c is a function of

Rt)?? Each node in at most one cell A node in a cell if and only if it’s connected to

the big node Number of children for each node in head

graph is bounded (≤6) Self-healing in the presence of dynamics and

mobility

Definitions

0-band1-band2-band

i=P(j )

j

j=CH(k)k

IL(j )

H0

Algorithm for Static Networks No perturbation, no Rt

gap Always H0 starts to be a

head A head search for new

heads in search region For H0, the search region

is the whole 1-band Cell heads in search

region are selected by i Nodes not selected as

head choose their best heads

i

P(i )

IL(i )

IL(P(i ))

RD’

LD RD

Will a node in k-band always have a parent from (k-1)-band?

Dynamic Network Perturbations

Joining, leaving and death of nodes State corruption Rt gap

Maintenance Mechanisms Head shift Cell shift Cell abandonment State check

Algorithm for Dynamic Network Head selection same as GS-3 S Rt gap

No head is selected Nodes become associates of neighboring cells Parent does periodical check

Node join Try to find the best head If fails, try to find a potential head from associates If still fail, retries later. If a head is announcing itself, it selects this head as its head

Node leaves or dies Intra-cell maintenance: head shift, cell shift, cell abandon Inter-cell maintenance: cell is monitored and recovered by parent

and children heads if intra-call operation fails It the parent fails then the children finds other parents

Why not Rt=R?

Cell Maintenance

A) Head Shi ft B) Cel l Shi ft C) Cel l Abandon

IL

IL’

Cell will be abandoned when distance between IL’ and IL of some neighbor is beyond [√3R-2Rt, √3R+2Rt]. (Rt gap!!)

Abandoned cell will be restored later if possible The whole head graph will slide as a whole?

Traffic load cannot be uniform Density varies across the network Central cell usually will not shift

Algorithm for Dynamic Network (cont’) Associate node always tries to find better head Head node always tries to find better parent State corruption (done by head)

Periodical sanity checking (for invariants and fixpoint) on hexagonal relation.

If checking fails, ask neighboring heads to check their state If all neighboring heads are valid, its state is corrupted,

then node becomes an associate Otherwise, cannot decide????

What if perturbations are not isolated?? Will the algorithm still converge? Need theoretical verification or validation from simulations

Problems Continuous Rt gap? (see next page picture) A connectable node is possibly not

connected to the big node. So the third goal cannot be achieved

How can we guarantee a safe leaving? What’s the transmission range of associate

node and head node? Is there difference between them?

Coutinuous Rt Gap

Mobile Dynamic Network Small node movements: leaves at old

location, joins at new location Big node movements

The closest head becomes the proxy of big node The proxy becomes the root of the head graph

What if big node moves to a null cell?

Example of Big Node Movement

Problems How to put all these complicated

mechanisms together? What if perturbations are not isolated?

Will the algorithm still converge?? Control overhead Need to be validated by simulations

Summary & Comments Algorithm tries to organize wireless network into a

ideal cellular hexagonal structure with fixed cell radius

Try to do self-healing when assuming isolated perturbations

Some of the mechanisms are not likely to work A complicated theoretical protocol without clear

analysis or validation by simulation result What kind of application can we run on this

structure? What’s the overhead to maintain this structure?

Roads of Developing Algorithm

Random Walk GS-3

1st Step Regular Static Grid Static Network without Rt gap

2nd Step Irregular Static Grid Dynamic Network

3rd Step Dynamic Grid Mobile Dynamic Network