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