Networking Algorithms

Mani Srivastava UCLA

[Project: Dynamic Sensor Nets (ISI-East)]

Outline

I. Dynamic location discovery

II. Topology management

III. Dynamic MAC address assignment

I. Dynamic Location Discovery

Discovery of absolute and relative location important Location-based naming and addressing, geographical routing, tracking

GPS not enough LOS-requirements, costly, large, power-hungry

Ad hoc precludes trilateration with special high power beacons also, susceptible to failure

Problem: given a network of sensor nodes where a few nodes know their location (e.g. through GPS) how do we calculate the location of the other nodes?

Known Location

Unknown Location

Ad-Hoc Localization System (AHLoS)

GOALS

Localization in a distributed fashion

Trade-offs Robustness Computation vs. communication

Ranging using Ultrasound

Integrated with routing messages Location discovery almost free

Implementation Ranging using radio-synchronized

ultrasound 3m range, noisy

Accuracy: Iterative: ~ 10 cm Collaborative: ~ 3 cm

Iterative Weighted Multilateration

Collaborative Multilateration

Iterative Multilateration

Atomic multilateration applied iteratively across the network may stall if network is sparse, % of beacons is low, terrain obstacles

Step 1

Step 2

Step 3

% Initial BeaconsTotal Nodes

% Resolved Nodes

Uniformly distributed deployment in a field 100x100. Node range = 10.

Iterative Multilateration Accuracy

00.020.040.060.08

0.10.120.140.160.18

12 13 16 18 20 21 24 26 28 31 34 36 38 40 42 44 47 49

Node Id

Err

or

Dis

tan

ce (

m)

Ranging Error Ranging + Beacon Error

50 Nodes 10% beacons 20mm white gaussian ranging error

Collaborative Multilateration

Step 1: form “Collaborative Subtrees” within their neighborhood an unknown node is collaborative if it has at least 3

participating neighbors a node is participating if it is either a beacon, or if it is

an unknown node that is also participating at each node at least one of its participating nodes are

new to the set at least one of the beacons used to determine the

position of a node should not be collinear with the other beacons used to determine the node position

Step II: obtain initial location estimate for subsequent computation use beacon locations & hop distances to obtain

approximate location bounds

Step III: perform computation Measurement Update part of Kalman Filter Centralized, at a leader elected in the subtree or, Fully Distributed

can start computing locations based on node connectivity and initial estimate

Uncertainty of estimatedlocation in first iteration

Uncertainty of estimatedlocation in second iteration

Example

Network of 30 nodes6 beacons, 24 unknowns

Ranging noise experimentally derived

0

5

10

15

20

25

30

35

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Node Id

Err

or

Dis

tan

ce

(mm

)

Centralized Distributed

Computation & Communication Expense

0

10,000,000

20,000,000

30,000,000

40,000,000

50,000,000

60,000,000

70,000,000

6 9 14 19 24

No. of Unknown Nodes

Flo

ps

Centralized Distributed

Computation Expense Results using the FLOPS command in MATLAB

0

10

20

30

40

50

60

70

80

0.01 0.1 1 10 20 30 40 50 60 70 80 90 100

Convergence Criteria

Avg error distanceNo. of transmssion / unknown nodeNo. of KF-ops / transmission (computation)

Computation vs. Communication Tradeoff

Total number of transmissions: Centralized 70 packets Distributed 416 packets

Centralized approach has additional overhead for leader election

II. Topology Management

Two phases of sensor network operation Detect event Relay information to users

Energy consumption of radio dominates that of sensors & CPU perform event detection continuously

The only energy efficient mode of the radio is the sleep mode put radio to sleep as often as possible

Existing approaches: density-energy trade-off keep enough nodes awake to handle the data forwarding (forwarding state) but for substantial energy savings we need large densities

Observation most of the time, the network is only monitoring its environment, waiting

for an event to happen (monitoring state)

Idea: put node radios to sleep and wake them up when they need to forward data low duty-cycle paging channel using a 2nd radio: trades off energy savings

for setup latency

STEM: High-level Operation

TxPow

erP

ower

Time

f1

f2Tx /RxSleep

Sleep

Rx

Pow

erP

ower

Time

f1

f2Tx /RxSleep

Initiator node

Target node

Wakeup plane

Data plane

Wakeup plane

Data plane

Detailed Operation

f1

f1

Target node

Initiator node

Train of beacon packets

TRx

B1B2 1. beacon received

2. beacon acknowledge

T

Latency – Energy Analysis

• Setup latency

• Energy savings

232

RxS

TTT

T

T

E

E Rx0

Appropriate choice of interval sizes

Mostly monitoring state: << 1 or >> 1

f1

f2

Wakeup plane

Data plane

Fraction of time in the forwarding state: 1

Forwarding state Monitoring state

Energy-Latency Trade-off

0E

E

Rx

S

T

T

= 101

• The tradeoff between energy and delay is manipulated by varying T

T E TS

• The energy savings increase as the monitoring state becomes more dominant,

= 102

= 103

= 104

TRx = 0.225 s

Topology Management in Forwarding State

• Conserve traffic forwarding capacity

• Divide network in virtual grids

• Each node in a grid is equivalent from a traffic forwarding perspective

• Keep 1 node awake in each grid at each time

GAF: Geographic Adaptive Fidelity [Ya2001]

M’ M 1.0 0 0

1.5 0.87 13.7

2.0 1.59 25.0

2.5 2.22 35.0

3.0 2.82 44.3

• GAF reduces the energy by a factor M’

• This factor is a function of the average number of nodes in a grid: M

Me

MM

1

Average num

ber of neighbors of a nodefor uniformly random

node deployment

Comparing STEM & GAF

Rx

S

T

T

STEM

GAF

Leverage latency

Leverage density

Curve of comparable energy savings

Combining STEM and GAF forJoint Energy-Latency-Density Trade-off

Rx

S

T

T

0E

E

GAF alone

STEM alone

= 200

= 100

= 60

= 30

= 10

As in GAF, 1 node is active in each grid the grid can be considered a virtual node

This virtual node runs the STEM protocol

III. Dynamic MAC Address Assignment

Wireless spectrum is broadcast medium MAC addresses are required

In wireless sensor networks, data size is small Unique MAC address present unneeded overhead

Employ spatial address reuse (similar to reuse in cellular systems) MAC address, link ids

Two aspects Dynamic assignment algorithm Address representation

40

1

1 2

2

3

5

Distributed Assignment Algorithm

0

0

1

2

0

13

2

0

1

0

0

1

2

4

1

3

1. Network is operational (nodes have valid address)

2. Listen to periodic broadcasts of neighboring nodes

3. In case of conflict, notify node (this node resends a broadcast)

4. Choose non-conflicting address and broadcast address in a periodic cycle. At this point the new node has joined the network.

Additive convergence: network remains operational during address selection

Mapping: unique ID to spatially reusable address

Algorithm also valid when unidirectional links

Encoded Address Representation

Address range 0-11 12-

1718-19 20-22 23 …

Codeword size (bits)

4 5 6 7 8 …

Encoded (bits/address) 1.7

Fixed size (bits/address) 2

Address

Frequency

Dav = 0.01 nodes/m2

0

1

2

3

0

10

110

1110 1 2 3

Fre

q. o

f oc

curr

ence

0.5

0.3

0.1

Size of the address field?

Non-uniform address frequency Huffman encoding Robust: can represent any address

Practical address selection All addresses with same codeword

size are equivalent Choose random address in that range

to reduce conflict messages

Non-uniform Network Density

X(m)

Nodes/m2

Y (m)X(m)

Average address size (bits)

Y (m)

Effect of Packet Losses ( = 10)

Address

Frequency

Pdrop

Convergence time (s)

Scalability

Address assignment Distributed algorithm with periodic localized communication

Address representation Encoded addresses depend only on distribution

Scales perfectly(neglecting edge effects)

Off-line Centralized Distributed

++ - +

Unique Fixedreusable

Encoded reusable

-- +

Rep

rese

nta

tion

Ass

ign

men

t

Average address size (bits)

=10

=5

=15

=20

Uni

que

addr

ess

Number of nodes

Simulation Results

Our schemes

SchemeAddress selection type

Av. size

(bits)

Address size

scalability

Globally unique Manufacturing

128 +

Network wide unique

Deployment 14

Centr. / Distr.

4.7

Encoded dynamic

Distributed 4.4 +

Fixed size dynamic

Dynamic Address Allocation: Summary

Spatial reuse of address

Dynamic assignment algorithm Localized: scalability Additive convergence: robustness

Encoded address representation Independent of network size: scalability Variable length addresses: robustness