AISP Workshop, May 2, 2007 1

Querying in Wireless Sensor Networks

Bhaskar Krishnamachari

Ming Hsieh Department of Electrical Engineering

USC Viterbi School of Engineering

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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

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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.

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Structural monitoring Bio-habitat monitoring

Military surveillanceDisaster 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

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Two Paradigms

• Continuous collection

• Distributed storage and querying

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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

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Fundamental Scaling Lawsfor 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.

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• 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

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

• m atomic events and qi queries for the ith event, all uniformly distributed

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

• Each transmission incurs a unit energy cost

Preliminaries

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Data-Centric Querying Approaches

• Unstructured: expanding ring searches, random walks.

• Structured: Geographic Hash Table, DIFS, DIM

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Energy Cost Scaling

• Creplication = c1

r : # of copies of an event

N : # of nodes

• Csearch(unstructured) = c2 • Csearch(structured) = c3

EVENTEVENT REPLICATIONUNSTRUCTURED QUERYSTRUCTURED QUERY

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Energy Optimization Formulation

S : total storage size

m : the total number of events

qi : the query rate for ith event

ri : the number of copies of ith event

Cs(ri) : the expected minimum search cost of ith event

Cr(ri) : the expected replication cost of ith event

Cr(r) = c1 Cs(r) = c2

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Optimization Solution

Minimizer

The Optimized Total Cost

(inactive constraint)

(active constraint)

qi : # of queries for event i

N : # of nodesS : total storage

sizem : # of events

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Optimal Total Cost

Simplified, assuming : q : # of queries per event

N : # of nodesS : total storage

sizem : # of eventsif

if

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Illustration of Energy Scaling

m : # of eventsq : # of queries

per event

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I - Storage and Energy Scalability Results

Energy Condition

The energy requirement per node is bounded

if and only if mq1/2 = O(N1/4)

Energy constraint is stricter than storage constraint

m : # of eventsq : # of queries per eventN : # of nodes

Storage ConditionA network scales efficiently with bounded storage per node

if mq1/2 = o(N3/4)

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II - Fixed Energy Budget Results

S – successful operation region

N : # of nodese: per-node energy budget

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III - Network Lifetime Scaling Results

Network Lifetime as a function of Network Size

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Summary• Only certain classes of applications can be sustained in arbitrarily

large sensor networks.

• Specifically, if mq1/2 = O(N1/4) for unstructured networks, and mq2/3 = O(N1/2) 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

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Comparison of Push-Pull Schemesfor Querying

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

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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.

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- sink/querier

- source/event node

-Hashed location where events are stored

N

N

Data Centric Storage (DCS)

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- sink/querier

- source/event node

Needles

Query path (comb)

s

N

N

Comb Needles (CN)

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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

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0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Average no of events (E)

Qu

ery

Pro

ba

bili

ty (

Q) DCS is better

CN is better

ALL-Type Query: DCS vs CN (Without Summaries)

(2 2 )CNC N Q Q E E Q

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0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Average no of events (E)

Qu

ery

Pro

ba

bili

ty (

Q)

CN is better

DCS is better

ALL-Type Query: DCS vs CN (With Summaries)

Θ ~ 39.78

2 2 4CNC N Q E N Q

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0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Average no of events (E)

Qu

ery

Pro

ba

bili

ty (

Q)

DCS is better

SCN is better

upper

lower

ANY-Type Query: DCS vs SCN

Θlower ~ 1.56

Θupper ~ 3.16

22 2

1 1SCN

N Q E NC

E E

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Random Walk QueriesFor 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.

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Random Walk QueriesFor 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.

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Simple Enhancementfor Heterogeneous Networks

• Push event greedily to high degree nodes (local maximum)

• Querier issues simple random walk

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Simulation Results

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

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Analysis on Linear Topology

dk k

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Resistance Method

• Hitting time (huv) : expected time taken by a random walk starting at u to reach.

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

• Cuv = huv + hvu , in general huv ≠ hvu but in case of symmetry huv = hvu

1 ohm resistors

Cuv = 2 m Ruv

• m : number of edges

• Ruv : effective resistance between u and v

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

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dk

Region 1

Region 2

Region 3

r(k) r(k)

k

k

d

k

d

3 Regions

2k <= d

k < d <2k

d <= k

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Region 1 [ 2k <= d]

dk k

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d-kr(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)

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=

Region 3 [ d =k ]

d

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Expected Hitting Time

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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(k2)

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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)

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Cover Time Visit Load

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Thanks