Timothy, Mario, Debra, Shiro, Henry, Jan

Investigating the Wireless Wire

One-week NECSI course on Complex Systems,

June 2003

An example for a ‚smart dust‘ particle:

SR

The problem:

allow communication where there is no net / satellite

technically spoken:

Percolation problem with active elements, as opposed to (classical) passive conductors

The model:• matrix of 15 x 30 cells

• radius of transmission: 2 neighbours

• (transmit if recieve 2 messages / tick)

• refractory time

• probability to fire:

Pfire = 1- α(#messages received - redundancy)

for #messages received > redundancy

• starting with 3 messages

• limited lifetime

Questions:

1. Is the system robust (chaotic propagation)?

2. Increases lifetime of the system as α increases?

3. What role plays the density of particles?

1)Robustness

(http://www2.kke.co.jp/mas.e/MASCommunity1.html)

1) high α / short refractory

or

2) low density

may cause chaotic propagation.

Results:

1) Robustness, continued

Analogy to reentrant waves on heart tissue

(Smith & Cohen 1984, actual research)

2) Increasing α:

(graph of Tim)

Results: lifetime of system can be doubled

0

10

20

30

40

50

60

0 5 10 15 20 25

Message Number

#Su

cces

sfu

l o

ut

of

50_

0

0.1

0.15

0.2

0.3

3) Varying the density

(Graph of Tim)

Results: perfect coverage is not optimal

120

125

130

135

140

145

150

0 2 4 6 8 10

Message Number

#S

uccessfu

l ou

t o

f150_

1

0.9

0.8

Conclusion:

• robust connection doable

• lifetime of system can be doubled!

Possible applications:

after earthquakes, battlefield,

but also: cellphone towers in neighbourhood