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