constrained random walks on random graphs: routing algorithms for large scale wireless sensor...
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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