Querying in Wireless Sensor Networks

flangeeasyMobile - Wireless

Nov 21, 2013 (3 years and 9 months ago)

68 views

AISP Workshop, May 2, 2007

1

Querying in Wireless Sensor Networks


Bhaskar Krishnamachari

Ming Hsieh Department of Electrical Engineering

USC Viterbi School of Engineering


2

Example: Interference
-
Free Channel
Allocation

Prior Work: Phase Transitions and
Complexity in Wireless Networks


Work with Ramon Bejar, Stephen Wicker, Cesar Fernandez, Bart Selman, Ashish
Goel, Sanatan Rai

3

Wireless Sensor Networks


Large scale networks of small embedded devices, each with
sensing, computation and communication capabilities.



Use of wireless networks of embedded computers “
could well dwarf
previous milestones in the information revolution



National
Research Council Report:
Embedded, Everywhere
, 2001.


4

Structural monitoring

Bio
-
habitat monitoring

Military surveillance

Disaster management

Industrial monitoring

Note: images used may be copyrighted. Used here for limited educational purposes only. Not intended for commercial or public
use
.

Home/building security


Wide Ranging Applications

5

Two Paradigms



Continuous collection



Distributed storage and querying

6

Focus of this Talk


Analysis and Design of Mechanisms for Storage
and Querying:



Fundamental Scaling Laws


Comparison of Push
-
Pull Query Mechanisms


Enhancing Random Walk
-
based Queries

7

Fundamental Scaling Laws

for Store and Query Sensor Networks

Joon Ahn and Bhaskar Krishnamachari, "Fundamental Scaling Laws for Energy
-
Efficient Storage and Querying in Wireless Sensor Networks",
ACM MobiHoc
, May
2006.

8


Race between increasing supply and demand:

-

Energy and storage

-

Application
-
specific event and query traffic




The winner of this race determines scalability.

In a Nutshell

9



N

nodes deployed in a 2D area with constant density for
some time duration T



m

atomic events and q
i
queries for the i
th

event, all
uniformly distributed



Can create r
i

replicas for event i to reduce search cost
(at the expense of increased replication cost)



Each transmission incurs a unit energy cost

Preliminaries

10

Data
-
Centric Querying Approaches




Unstructured
: expanding ring searches,
random walks.



Structured:
Geographic Hash Table, DIFS, DIM

11

Energy Cost Scaling


C
replication

=
c
1


r

: # of copies
of an event

N
: # of nodes



C
search
(
unstructured
) = c
2



C
search
(
structured
) = c
3

EVENT

EVENT REPLICATION

UNSTRUCTURED QUERY

STRUCTURED QUERY

12

Energy Optimization Formulation


S

: total storage size

m

: the total number of events

q
i

: the query rate for
i
th

event

r
i

: the number of copies of
i
th

event

C
s
(r
i
)

: the expected minimum
search cost of
i
th

event

C
r
(r
i
)

: the expected replication
cost of
i
th

event

C
r
(r) = c
1

C
s
(r) = c
2


13

Optimization Solution


Minimizer

The Optimized Total Cost

(inactive constraint)

(active constraint)

q
i

: # of queries
for event i

N
: # of nodes

S

: total storage
size

m

: # of events

14

Optimal Total Cost

Simplified, assuming :

q

: # of queries
per event

N
: # of nodes

S

: total storage
size

m

: # of events

if

if

15

Illustration of Energy Scaling

m

: # of events

q

: # of queries
per event


16

I

-

Storage and Energy Scalability
Results


Energy Condition

The energy requirement per node is bounded

if and only if mq
1/2

= O(N
1/4
)


Energy constraint is stricter than storage constraint

m

: # of events

q

: # of queries per
event

N
: # of nodes

Storage Condition

A network scales efficiently with bounded storage per node

if

mq
1/2

= o(N
3/4
)

17

II

-

Fixed Energy Budget Results

S


successful operation region

N
: # of nodes

e: per
-
node
energy budget

18

III

-

Network Lifetime Scaling Results

Network Lifetime as a function of Network Size

19

Summary


Only certain classes of applications can be sustained in arbitrarily
large sensor networks.




Specifically,
if
mq
1/2

=

O(N
1/4
)

for unstructured networks, and
mq
2/3

=
O(N
1/2
)
for structured networks:

a.
The network can operate with bounded energy and storage per
node.

b.
The network lifetime does not decrease with network size for a
given energy budget.




These results generalize in a straightforward manner to 1D and 3D
deployments.
3D deployments are inherently more scalable.



The results can be reinterpreted to understand how to tier sensor
networks into zones with localized queries





20

Comparison of Push
-
Pull Schemes

for Querying

Shyam Kapadia and Bhaskar Krishnamachari, "Comparative Analysis of Push
-
Pull Query Strategies
for Wireless Sensor Networks," DCOSS, 2006.

21

Overview


Two Hybrid Push
-
Pull Schemes:


Geographic Hash Tables/Data Centric Storage [1]


Comb
-
Needles [2]


[1] S. Shenker et al., Data
-
centric storage in sensornets, ACM CCR,
Jan 2003.


[2] X. Liu et al., Combs, needles, haystacks: balancing push and pull for
discovery in large
-
scale sensor networks, ACM SenSys '04.

22

-

sink/querier

-

source/event node

-
Hashed location where


events are stored

N
N
Data Centric Storage

(DCS)

23

-

sink/querier

-

source/event node

Needles

Query

path

(comb)

s

N
N
Comb Needles (CN)

24

Model Assumptions


Square Grid of N nodes


Sink located at left
-
bottom corner


Events (say E) valid for an epoch


Single attribute (event type)


Uniform distribution of events across nodes


Energy measured in number of unicast transmissions


Query probability Q


Aggregation


One packet summary of all events


No modeling of collisions and contention

25

0
10
20
30
40
50
60
70
80
90
100
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Average no of events (E)
Query Probability (Q)
DCS is better
CN is better
ALL
-
Type Query: DCS vs CN

(Without Summaries)

(2 2 )
CN
C N Q Q E E Q
       
26

0
10
20
30
40
50
60
70
80
90
100
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Average no of events (E)
Query Probability (Q)
CN is better
DCS is better

ALL
-
Type Query: DCS vs CN

(With Summaries)

Θ

~ 39.78

2 2 4
CN
C N Q E N Q
       
27

0
1
2
3
4
5
6
7
8
9
10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Average no of events (E)
Query Probability (Q)
DCS is better
SCN is better

upper


lower

ANY
-
Type Query: DCS vs SCN

Θ
lower

~ 1.56

Θ
upper

~
3.16

2
2 2
1 1
SCN
N Q E N
C
E E
  
   
 
28

Random Walk Queries

For Heterogeneous Networks

Marco Zuniga, Chen Avin, and Bhaskar Krishnamachari, "Using Heterogeneity to Enhance
Random Walk
-
based Queries," USC Computer Engineering Technical Report CENG
-
2006
-
8, August 2006.

29

Random Walk Queries

For Heterogeneous Networks

Marco Zuniga, Chen Avin, and Bhaskar Krishnamachari, "Using Heterogeneity to Enhance
Random Walk
-
based Queries," USC Computer Engineering Technical Report CENG
-
2006
-
8, August 2006.

30

Simple Enhancement

for Heterogeneous Networks



Push event greedily to high degree nodes (local
maximum)



Querier issues simple random walk

31

Simulation Results

A small fraction of high
-
degree cluster
-
heads (<10%)
can provide a query cost improvement between 30%
and 90%.

32

Analysis on Linear Topology

d

k

k

33

Resistance Method


Hitting time

(h
uv
) : expected time taken by a random walk starting at
u
to
reach.


Commute time
(C
uv
) : expected time taken by a random walk starting at
u
to reach
v
and come back to
u
.


C
uv

= h
uv

+ h
vu
, in general h
uv



h
vu
but in case of symmetry h
uv

=

h
vu

1 ohm
resistors

C
uv

= 2 m R
uv


m : number of edges


R
uv

: effective resistance between u and v

Chandra et al., 1989, The electrical resistance of a graph captures its commute and cover times, ACM STOC

34

d

k

Region 1

Region 2

Region 3

r(
k
)

r(
k
)

k

k

d

k

d

3 Regions

2k <= d

k < d <2k

d <= k

35

Region 1 [ 2k <= d]

d

k

k

36

d
-
k

r(
d
-
k
)

1/2

<

<

=

α

= 2k
-
d

d
-
k

r(
d
-
k
)

1/2

Region 2 [ k < d < 2k ]

α

r(
d
-
k
)

r(
d
-
k
)

r(
d
-
k
)

r(
d
-
k
)

37

=

Region 3 [ d =k ]

d

38

Expected Hitting Time

39

Result

The first local minima for the query cost is obtained
when the fraction of high
-
degree nodes is 4/5k, where
cost is reduced by a factor of
Θ
(k
2
)

40

Enhancing Random Walks

Using Power of Choice

Chen Avin and Bhaskar Krishnamachari, "The Power of Choice in Random Walks: An Empirical Study,"
9th ACM/IEEE International Symposium on Modeling, Analysis and Simulation of Wireless and Mobile
Systems, (MSWiM), Malaga, Spain, October 2006. (Best Paper Award)

41

Cover Time

Visit Load

42

Thanks