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CMPE 259 Sensor Networks
Katia Obraczka
Winter 2005
Topology Control II
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Announcements
Homework due on 02.14. Projects? Gabriel Elkaim’s talk on GPS: 02.09. Venkatesh Rajendra’s talk on MAC:
02.16.
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PEAS
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PEAS
Probing Environment, Adaptive Sleeping.
“Extra” nodes are turned off. Nodes keep minimum state.
No need for neighborhood-related state. PEAS consiers very high node density
and failures are likely to happen.
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Bi-modal operation
Probing environment. Adaptive sleeping.
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PEAS state diagram
Working
Sleeping Probing
No reply for probe
Wakes up
Hears probe reply.
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Probing
When node wakes up, enters probing mode.
Is there working node in range? Broadcasts PROBE to range Rp. Working nodes send REPLY (randomly
scheduled). Upon receiving REPLY, node goes back to
sleep.• Adjusts sleeping interval accordingly.
Else, switches to working state.
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Considerations
Probing range is application-specific. Robustness (sensing and communication)
versus energy-efficiency. Location-based probing as a way to
achieve balance between redundancy and energy efficiency.
Randomized sleeping time. Better resilience to failure. Less contention. Adaptive based on “desired probing rate”.
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More considerations…
Multiple PROBEs (and multiple REPLIES) to compensate for losses. Multiple PROBEs randomly spread over
time. Multiple working nodes in the
neighborhood. Favor “oldest” one.
Nodes with fixed transmit power. Deployment density.
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Evaluation
Simulations. Simulated failures: failure rate and
failure percentage. Metrics:
Coverage lifetime. Delivery lifetime.
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Results
With and without failures. From the paper…
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“Exposure In Wireless Ad-Hoc Sensor Networks”
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Sensor Coverage
Given: Field A N sensors
How well can the field be observed ? Closest Sensor (minimum distance) only
Worst Case Coverage: Maximal Breach Path Best Case Coverage: Maximal Support Path
Multiple Sensors: speed and path considered
Minimal Exposure Path
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Exposure - Semantics Likelihood of detection by sensors function
of time interval and distance from sensors. Minimal exposure paths indicate the worst
case scenarios in a field: Can be used as a metric for coverage
• Sensor detection coverage• Wireless (RF) transmission coverage
For RF transmission, exposure is a potential measure of quality of service along a specific path.
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Preliminaries: Sensing Model
KpsdpsS
),(),(
Sensing model Sensing model SS at an arbitrary point at an arbitrary point p p for for a sensor a sensor s s ::
where where d(s,p)d(s,p) is the Euclidean distance between is the Euclidean distance between the sensor the sensor ss and the point and the point pp, and positive , and positive constants constants and and K K are technology- and are technology- and environment-dependent parameters.environment-dependent parameters.
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Preliminaries: Intensity Model(s)
Effective sensing intensity at point Effective sensing intensity at point pp in field in field F F ::
n
iA psSpFI1
),(),(
),(),(
),(),(
min
min
psSpFI
SspsdpsdSss
C
mm
All All SensorsSensors
Closest Closest SensorSensor
KK Closest Sensors Closest SensorsK=3K=3 for Trilateration for Trilateration
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Definition: Exposure
The The ExposureExposure for an object for an object OO in the in the sensor field during the interval [sensor field during the interval [tt11,t,t22]] along along
the path the path p(t)p(t) is: is:
2
1
)()(, ,),( 21
t
t
dtdt
tdptpFItttpE
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Exposure – Coverage Problem Formulation
Given: Field A N sensors Initial and final points I and F
Problem: Find the Minimal Exposure Path PminE in
A, starting in I and ending in F.
PminE is the path in A, along which the exposure is the smallest among all paths from I to F.
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Special case – one sensor
pS =(1,-1)
s = (0,0) x
y
pD =(-1,1)
Minimal exposure path for one sensor in a Minimal exposure path for one sensor in a square field:square field:
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General Exposure Computations
Analytically intractable. Need efficient and scalable methods to
approximate exposure integrals and search for Minimal Exposure Paths.
Use a grid-based approach and Use a grid-based approach and numerical methods to approximate numerical methods to approximate Exposure integrals.Exposure integrals.
Use existing efficient graph search Use existing efficient graph search algorithms to find Minimal Exposure algorithms to find Minimal Exposure Paths.Paths.
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Minimal Exposure Path Algorithm
Use a grid to approximate path exposures. The exposure (weight) along each edge of the
grid approximated using numerical techniques. Use Dijkstra’s Single-Source Shortest Path
Algorithm on the weighted graph (grid) to find the Minimal Exposure Path.
Can also use Floyd-Warshall All-Pairs Shortest Paths Algorithm to find PminE between arbitrary start and end points.
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Generalized Grid
(a) n=2, m=1 (b) n=2, m=2 (c) n=2, m=3
Generalized Grid – 1Generalized Grid – 1stst order, 2 order, 2ndnd order, 3 order, 3rdrd order …order …More movement freedom More movement freedom more accurate more accurate resultsresults
Approximation quality improves by increasing grid divisionsApproximation quality improves by increasing grid divisionswith higher costs of storage and run-time. with higher costs of storage and run-time.
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Minimal Exposure Path Algorithm Complexity
Single Source Shortest Path (Dijkstra) Each point is visited once in the worst case. For an nxn grid with m divisions per edge:
n2(2m-1)+2nm+1 total grid points. Worst case search: O(n2m) Dominated by grid construction. 1GHz workstation with 256MB RAM requires less than
1 minute for n=32, m=8 grids.
All-Pairs Shortest Paths (Floyd-Warshall) Has a average case complexity of O(p3). Dominated by the search: O((n2m)3) Requires large data structures to store paths.
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Uniform Random Deployment
Minimal exposure path for 50 randomly deployed sensors Minimal exposure path for 50 randomly deployed sensors using the All-Sensor intensity model (using the All-Sensor intensity model (IIAA).).
8x8 m=18x8 m=1Exposure:Exposure: 0.70790.7079Length:Length: 1633.91633.9
16x16 m=216x16 m=2Exposure:Exposure: 0.69760.6976Length:Length: 1607.71607.7
32x32 m=832x32 m=8Exposure:Exposure: 0.69450.6945Length:Length: 1581.01581.0
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Exposure – Statistical Behavior
20 52 84 116 1480.05
0.1
0.15
0.2
0.25
0.3
Number of SensorsR
elat
ive
Std
. Dev
.
Exposure(d-2 Sensor Model)
Closest
All
20 52 84 116 1480.2
0.4
0.6
0.8
1.0
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2Exposure
(d-4 Sensor Model)
Number of Sensors
Rel
ativ
e S
td. D
ev.
All
Closest
Diminishing relative standard deviation in exposure for 1/d2 and 1/d4 sensor models.
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Deterministic Deployments
Minimal exposure path under the All-Sensor intensity model Minimal exposure path under the All-Sensor intensity model ((IIAA) and deterministic sensor deployment schemes. ) and deterministic sensor deployment schemes.
CrossCross SquareSquare TriangleTriangle HexagonHexagon
Exposure LevelExposure Level(compared to Square)(compared to Square) 1.5x1.5x30x~120
1.5x3x6x~20
HexagonTriangleCrossSensors
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Exposure – Research Directions
Localized implementations Performance and cost studies subject to
Wireless Protocols (MAC, routing, etc) Errors in measurements
• Locationing• Sensing• Numerical errors
Computation based on incomplete information
• Not every node will know the exact position and information about all other nodes
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Parametric probabilistic routing
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Approaches to routing Ad hoc network “on-demand” routing:
Compute path then send data. If data is small, overkill?
Flooding is expensive. Wanderer approach: pick neighbor with
some probability to forward data to. Problems?
Pure gossip: flooding+wanderer. At each node, picks one or the other with
some probability. Either almost all nodes receive packet or
almost no nodes receive it.
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Proposed approach
Parametric probability routing: Controlled flooding. Every node decides to forward packet to
neighbors using a probability function. Probability function based on: distance to
destination, distance from original source to destination, number of copies already received, etc.
2 variants:• Destination attractor.
– S-D distance and CS-D distance.• Directed transmission.
– Also uses number of hops already traversed by packet.
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Destination attractor
PRi, or retransmission probability, given by: (1+k) PRi-1 if packet is getting closer to D.
(1-k) PRi-1 if packet is getting farther from D.
PRi-1 if same or undefined.
k can be adjusted to compensate for “noise” due to losses, mobility, etc.
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Directed transmission
Nodes on shortest path from S-D should forward with high probability.
PRi = exp{k[d(S,D) – d(Ri,D) – I]}, where d(S,D) is distance between source and
destination. d(Ri,D) is distance between current node
and destination, and i is number of hops traveled so far.
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Estimating global information
Number of hops traveled so far, i, is easy. Estimating distance to D:
Each sensor includes its current estimate of distance to D.
When receiving that information from neighbor, sensor updates its information by adding 1.
Sensor chooses its d(S,D) to be the minimum of the currently received information from neighbors.
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Evaluation
Simulations. Noise is used to simulate inaccuracies. Metrics:
Load Lag. Fraction delivered. Overhead?
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Results
From paper…