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)+d b (x) 

Quantization error with ideal ADC Reconstruction error reaches a non-zero floor level instead of PCM-Style Sampling f(x) Dither-based Samplingf(x)+d(x)  Reconstruction error decreases as  2 :

Dither-based Sampling f(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 error random error cross correlation 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 f(x)+d(x) r 1 =1, r 2 =16 r 1 =2, r 2 =8 f(x)+d(x) r=r 1  r 2 f 1 (x) f 2 (x) averaging Guarantee zero crossing inside each Nyquist interval by high enough r 2 Distribute density for quantization and non-ideal ADC

Distributing Density quantization error random error cross correlation Mean-square error: Worst case per node energy consumption:   distributing density 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 decrease energy 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 router Internet Content Provider Access Point router PSTN Base Station GSM IEEE WLAN

System and Channel Model Rayleigh Fading:

Threshold-based Adaptive Modulation A0A0 A1A1 A2A2 A3A3 A4A4 S1S1 S2S2 S3S3 S4S4

Channel Model: Finite State Markov Chain

Semi-Markov TCP Cong. Control Model TCP State Space: Slow Start cwnd Time Timeout Fast Retransmit and 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 T o A i r l i n k IP MIB Data Plane Management Plane UDP Adaptive TCP Configuration Rate Doppler Spread Rate Doppler Spread SNR

Future Work Empirically measure mobile channel using p (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