1. Recognizing Exponential Inter-Contact Time in VANETs
Hongzi Zhu
Appeared at IEEE INFOCOM 2010, San Diego

2. Introduction to Vehicular Ad hoc Networks
A special case of MANET and DTN
Vehicles can talk while moving
Vehicle density accounts
Wireless communication
inter-vehicle, vehicle-roadside
Data forwarding
Store-and-forward vs. store-carry-forward
Provision of rich applications
Next-generation intelligent transportation system (ITS), e.g., driving safety, efficient traffic infrastructure management, onboard entertainment

3. Why Mobility Models?
System performance heavily depends on vehicular mobility characteristics
how often can two vehicles encounter
how long can such communications last
Inter-contact time (ICT)
studies the time elapsed between two successive contacts of the same two vehicles
No existing vehicular mobility models based on real experiments
theoretical mobility models, such as RWM, RWP and RDM, not practical for real systems
some empirical studies mainly based on human mobility, indicating that the ICT tail distribution follows a power law distribution (heavy tail)
How about in VANETs?

4. ShanghaiGrid Project
6,800 taxies and 3,600 buses equipped with GPS devices

5. Collecting Taxi GPS Trace Data
GPRS channel
GPS signals

6. Taxi GPS Trace Data Collecting vehicular trace data
(demo available at
select motion trace data from 2,100 taxies
during the whole month of February in 2007
Data description
loaded taxies send GPS reports every one minute
vacant taxies send GPS reports every 15 seconds
a GPS report: ID, the longitude and latitude coordinates of current location, timestamp, speed, heading and the status of the taxi (i.e., loaded or vacant)

7. A real contact between v1 and v2
Extracting Contacts
A contact happens when the reported locations of two taxies are within a given time window and within a given communication range at the same time
Using sliding time window to examine contacts between a pair of taxies
A real contact between v1 and v2
A GPS report from v1
A sliding time window t1
A GPS report from v2

8. Calculate Inter-Contact Time
the time elapsed between two successive contacts of the same pair of vehicles
ICT1
ICT2
ICT3

9. Impact of Sliding Time Window Size
Large time windows
false contacts: two taxies may actually be far away from reported locations
increase the weight of small values of inter-contact times in the whole distribution
Small time windows
miss real contacts: two taxies encountered but did not send reports simultaneously
increase the weight of large values of inter-contact times in the distribution

10. Tail Distribution (CCDF) of the Inter-Contact Time
Straight lines in linear-log scale indicate exponential tail distributions, i.e., P{X>t} ~e-βt
This rapid cutoff is caused by the limited duration of the trace data
Linear-log scale, time window (TW): 1s, 30s and 60s, communication range (CR): 50m and 100m

11. Establishing Model Parameters
Remove the cutoff part
seek for the divide point from which the second derivatives (decay acceleration) of the log-scaled P{X>t} are nonzero (take a small positive value in practice).
Identify the exponent constant β
perform the least square regression analysis

12. Future Work
Investigate the key factors that generate the exponential tail distributions
Establish theoretical models suit for VANETs
Investigate the ultimate end-to-end delay with regards to link failures

13. Thank you!
Q&A