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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
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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.
29
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.
30
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
35
Region 1 [ 2k <= d]
dk k
36
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)
37
=
Region 3 [ d =k ]
d
38
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