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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
