Modeling and Control of Information Flow Sinem Coleri Ergen Xuanming Dong Ram Rajagopal Pravin...
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Transcript of Modeling and Control of Information Flow Sinem Coleri Ergen Xuanming Dong Ram Rajagopal Pravin...
Modeling and Control of Information Flow
Sinem Coleri Ergen
Xuanming Dong
Ram Rajagopal
Pravin Varaiya
University of California Berkeley
Outline
• Modeling of information flow– Distributed sampling in dense sensor
networks– Event detection schemes (Ephremides)
• Control of information flow– Introducing redundancy for energy efficiency– TCP/UDP performance in mobile high-speed
networks– Determining faults based on correlations
Outline
• Modeling of information flow– Distributed sampling in dense sensor
networks– Event detection schemes (Ephremides)
• Control of information flow– Introducing redundancy for energy efficiency– TCP/UDP performance in mobile high-speed
networks– Determining faults based on correlations
Distributed Sampling: System Model
Snapshot of spatially bandlimited 1-D sensor field
Goal: Reconstruct the sensor field, despite quantization and noise errors
Approach: Use dither-based sampling
1-bit dither-based sampling
f(x)+db(x)
Quantization error with ideal ADC
Reconstruction error reaches a non-zero floor level instead of
PCM-Style Samplingf(x) Dither-based Samplingf(x)+d(x)
Reconstruction error decreases as 2:
Dither-based Samplingf(x)+d(x)
Non-ideal ADC
• Circuit noise– Device noise,
conducted noise, radiated noise
• Aperture uncertainty– Not able to sample at
the exact location and time
• Comparator ambuigity– Limited ability to
resolve an input voltage in a certain amount of time quantization
errorrandom error
crosscorrelation
bottleneck
There may be no zero crossing
Guaranteeing Zero-crossing
Fact The probability of a non-crossing goes to zero exponentially in the number of nodes r in the n-th interval
Diversity Averaging
+1
0
-1
+1
0
-1
f(x)+d(x)
r1=1,r
2=16
r1=2,r2=8
f(x)+d(x)
r=r1r2
f1(x)f2(x)
averaging
• Guarantee zero crossing inside each Nyquist interval by high enough r2
• Distribute density for quantization and non-ideal ADC
Distributing Density
quantization error
random error
crosscorrelation
Mean-squareerror:
Worst case pernode energyconsumption:
distributingdensity
Fault Tolerance:
Robust to node failures
Every alternate node failing halving node density
Introduce randomness?
Future Work
• Decrease energy consumption by introducing randomness
• Accuracy-energy trade-off in– Finding a relevant function of sensor field
• Maximum, mean
– Specific tasks• Detection, classification, localization
Outline
• Modeling of information flow– Distributed sampling in dense sensor
networks– Analysis of event detection schemes
• Control of information flow– Introducing redundancy for energy efficiency– TCP/UDP performance in mobile high-speed
networks– Determining faults based on correlations
Motivation
Sensor Placement•Minimize the cost while providing high coverage and resilience
to failures
Energy Management•MAC Layer: eliminating collisions, idle listening, overhearing
•Routing Layer: balancing energy consumption•Application Layer: data compression
RELAY NODES
Relay Nodes
• High sensing coverage may bring some geometric deficiencies– Don’t limit energy provisioning to the existing sensor
nodes relay nodes
Relay nodes may decreaseenergy consumption
Previous Work
• Relay nodes to maintain connectivity– Minimum number of relay nodes to maintain
connectivity with a limited range– Formulated as a Steiner Minimum Tree with min. # of
Steiner points (SMT-MSP) problem– Only decreasing transmission range may not achieve
energy efficiency
• Relay nodes to maximize lifetime– Formulated as a mixed-integer non-linear
programming problem– Heuristic algorithms with no performance guarantee
Relay Nodes in Predetermined Locations
Sensor node
Relay node
fixed if i and j are fixed
LINEAR PROGRAMMING PROBLEM
Relay Nodes in Any Location
Sensor node
Relay node
Variable if either i or j or both are relay locations
NOT A CONVEX OPTIMIZATION PROBLEM
Relay Nodes in Any Location
Approximation constant:
Simulations
Configuration of sensor nodes in parking lot
Grid size = 20ft
Outline
• Modeling of information flow– Distributed sampling in dense sensor
networks– Event detection schemes (Ephremides)
• Control of information flow– Introducing redundancy for energy efficiency– TCP/UDP performance in mobile high-speed
networks– Determining faults based on correlations
TCP/UDP performance in mobile high-speed networks: single user
routerInternet
ContentProvider
Access Point
router
PSTN
Base Station
GSM
IEEE 802.11WLAN
System and Channel Model
Rayleigh Fading:
Threshold-based Adaptive Modulation
A0 A1 A2 A3 A4
S1 S2 S3 S4
Channel Model: Finite State Markov Chain
Semi-Markov TCP Cong. Control Model
TCP State Space:
Slow Start
cwnd
Time
Timeout
Timeout
Fast Retransmitand Recovery
AIMD (Additive Increase/Multiplicative Decrease)
Size of TCP States:
TCP Throughput Calculation
Define
Delay
Throughput:
Analytical vs ns2 simulation
Cross-Layer Design
TCP
LLC
PHY
MAC
To
Airl
ink
IPMIB
Data PlaneManagement Plane
UDP
Adaptive TCP Configuration
Rate
Doppler Spread
Rate
Doppler Spread
SNR
SNR
Future Work
• Empirically measure mobile channel using 802.11p (DSRC) to validate model
Outline
• Modeling of information flow– Distributed sampling in dense sensor
networks– Event detection schemes (Ephremides)
• Control of information flow– Introducing redundancy for energy efficiency– TCP/UDP performance in mobile high-speed
networks– Determining faults based on correlations
Determining Faults based on Correlations
• One Sensor: Failure detection based on the detection of abrupt changes
i
The output of transformation experiences an abrupt change in the case of failure. This is a classical statistical problem
Determining Faults based on Correlations
• Multiple Sensors: Failure detection based on abrupt changes in the correlation
i
j
The output of transformation experiences an abrupt change in the case of the failure of at least one node.
Future Work
• A network of nodes– Detection of faulty sensors based on the
detection of abrupt changes in correlations– Analysis of the trade-off between delay,
accuracy and density– Testing of the algorithms on the traffic data