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Power law and exponential decay
of inter contact times between
mobile devices
By:
Thomas Karagiannis
Jean-Yves Le Boudec
Milan Vojnovic
appeared in
MOBICOM 2007
Presented by:
Michele Albano
Human mobility patterns
High practical importance for:
informed decisions in protocol design
realistic mobility models for protocol evaluation
Previous studies provided empirical evidence:
Power Law for inter-contact times
Power Law
Empirical evidence in different traces
timescales from few minutes to half a day
Problems with power law:
if exponent <= 1, mean packet delay is infinite
experimental evidence that exponent <= 1
existing mobility models feature exponential
decay
Datasets analyzed
Dichotomy!
All traces feature:
power law up to a characteristic time
after half a day, exponential
Exp decay + daily periodicity
Return times
Each devices has a home site
where it spends most of its time
return time behaves like inter-contact time
Effects of the dichotomy
CCDF tail is low like in exponential
mean inter-contact times are finite
existing models support the dichotomy
simple random walk on 1d and 2d finite torus
random waypoint on a chain
... NOT infinite torus (only power law)
Spatial breakdown
Devices met at a few distinct sites:
how many sites cover 90% contacts, or 90%
total contact time?
Temporal breakdown
CCDFs for a random device-pair
not substantially different from total CCDF
Strong time of day nonstationarity
residual inter-contact time: day 6h, night 17h
short contacts (<1m) while two devices move
long contacts (~10h) while at job or home
Conclusions
Power law / exponential dichotomy
Low tail => No infinite packet delay
Return times ~ Inter-contact times
Contacts in few sites
Long contact in home sites
Interest for stationary infrastructure nodes