1. IMT - Institutions Markets Technologies
Institute for Advanced Studies
Lucca
Human Mobility Models
for Opportunistic Networks
PhD Program in Computer Science and Engineering
XXV Cycle
Dmytro Karamshuk
dmytro.karamshuk@imtlucca.it
Supervisor: Luciano Lenzini
Co-supervisor: Marco Conti
February 2012

2. Why do we study human mobility
● modelling ad-hoc wireless networks
● modelling information propagation, disease
spreading etc.
● developing new mobile services, e.g., location
recommendation systems
● security systems in location based social networks
● transportation, urban infrastructure

3. Study of Human Mobility

4. Properties of Human Mobility
● in human mobility we study how people visit different places
● we are interested in social, spatial, and temporal characteristics of the
visits

5. Mobility Properties - Spatial
How far we travel from place to place?

6. Mobility Properties – Temporal
● returning time probability ● visits of top k-th location
How frequently we visit different places?

7. Mobility Properties - Social
● To what extend our
movements depend
on our social ties?
● How the influence of
our social ties depend
on time?
● How the places
associated with
different social
communities are
spatially distributed?
How our social ties influence the choice of the places we visit?

8. Mobility Properties – Social (another view)
● inter-contact time
i.e. time between two consecutive contacts
of two persons (mobile devices)
●
this in t e r-c o n ta c t tim e s characteristic is crucial for studying mobile social
networks, particularly opportunistic networks based on p2p communications
●
usually this is the o u tpu t o f th e m o b ilit y m o de llin g

9. Mobility Models
● models based on maps of preferred locations accounts only on the preferential
selection of the places to visit
● models based on personal agendas aim to reproduce temporal details of the
place visiting, e.g., periodical patterns

10. “Social” Mobility Models
● “social” models explore
graphs of social ties to
manage users'
movements
● in “social” models users
account on their friends'
position while selecting
next place to go
● the graph of the contacts
might be “time-varying”,
i.e., the strength of the
ties depends on a
particular day, time of
day etc.

11. Comparison of the Models
● D. Karamshuk, C. Boldrini, M. Conti, and A. Passarella. Human mobility models
for opportunistic networks. IEEE Commun. Mag, 2011

12. Conclusion on Models
● existing models concentrate on modelling spatial trajectories of
movements, not the time sequences of visits to the places
● as a result specific temporal characteristics of visits are usually
hard-coded inside the model
● models are usually too complex for analytically traceability

13. Arrival Based Mobility Framework
● defines mobility in terms of visits sequences not trajectories
● customizable for any temporal patterns of visits
● provides a framework for analytical analysis of the temporal
dependencies between visits and contacts

14. Adding Spatial Dimension to Social Graphs
● cliques (i.e., fully connected
sub-graphs) of users share
common meeting places
● cliques are overlapping and
hierarchically organized
● example: a company has
meeting rooms shared by all
employees, while each
subdivision of the company
has their own offices, shared
only by the members of the
subdivision. The subdivisions
might share common
members.
We develop an algorithm that:
● takes a social graph as input
● partitions the graph into a set of overlapping and hierarchically organized cliques
● generates arrival network by assigning each clique a separate meeting place

15. Adding Spatial Dimension to Social Graphs
The clique partitioning algorithm consists of two main parts:
● finding the cover of the maximum overlapping cliques in the input social graph (we
use BronKerbosch algorithm)
● reproducing hierarchical cliques structure by randomly splitting the cliques

16. Example
step N1 step N2
step N3 result

17. Adding Temporal Dimension
To characterise the temporal dimension of
human mobility we model time sequences of
users' arrivals to places with stochastic point
processes.
For simplicity we consider that arrival processes are:
● independent
● discrete (e.g., with the time unit equal to one day)
● the contact between persons happen if they both arrive in
the same place in the same time slot
Although, the framework could be extended to other cases.

18. Case studies
Input: Output:
● social graph ● inter-contact times distribution
● link removal probability for arrival
network generating algorithm
● arrival processes for each pair of
user and place

19. Case studies - Bernouli Processes
Input: Output:
● random graph with number of nodes ● power law distribution of inter-
n and probability of link χ contact times
●
removal probability α
● Bernoulli arrival processes with
rates where Y is a
standard normal random variable

20. Case studies – Type of Processes
Input: Output:
● similar as in the first case, but arrival ● power law distribution of inter-
processes with geometric contact times
distribution of inter-arrival times and
the same distribution of rates

21. Case studies – Rates Distribution
Input: Output:
● similar as in the first case but the ● inter-contact times distribution with
Bernoulli arrival processes with exponential shape
identical rates

22. Conclusion on the framework
● Preliminary results of the analysis show that the distribution of
rates, of arrival processes plays major role in the resulting
distribution of the inter-contact times.
● This result allows us to show how very different distributions for
the aggregate inter-contact times can be obtained starting from
simple Bernoulli arrival processes.
● This finding is also very interesting from the standpoint of a
mathematical analysis of the proposed framework, as Bernoulli
processes possesses a number of properties (e.g., single parameter,
memory-less property) that significantly simplifies the analysis.

23. Analytical Analysis – Idea N1
Idea N1:
● describe contact point process between a pair of users if we know
that the individual arrival processes are independent Bernoulli
point processes

24. Analytical Analysis – Idea N2
The idea is motivated by the paper which studies general heterogeneous
environments where each individual characteristics have the same type but different
parameters, i.e., rates.
●A. Passarella and M. Conti. Characterising aggregate inter-contact times in
heterogeneous opportunistic networks. NETWORKING 2011
Idea N2:
● derive analytically the aggregate characteristic of the contact
sequences, i.e., aggregate inter-contact times distribution

25. Analytical Analysis - Schema

26. Analytical Analysis – Contact Process
Contacts between two users in a Contacts between two users in all
single meeting place. shared meeting places.
● The single-place contact process ●The contact process between
resulting from independent Bernoulli contacts resulting from single-place
arrival processes is a Bernoulli arrival contact processes which, in their turn,
process emerge from independent Bernoulli
arrival processes is a Bernoulli
process

27. Analytical Analysis – Rates
The rate of a contact process depends on individual arrival rates as:
Therefore, we can define the distribution of the contact sequences rates by tuning
the distribution of the arrival rates.
As an example, we show how the exponential
distribution of the contact rates emerge if the
arrival rates are taken as
where Y is a standard normal random variable

28. Analytical Analysis – Inter-contact times

29. Conclusion
● The framework allows us to model the way users visit different
places and contact each other in those places
● The framework is customizable for any social environment by
taking social graph as an input parameter
● The framework is customizable for any temporal patterns of
users' visits to places by taking arrival stochastic processes as an
input parameter
● Temporal characteristics of the contact sequences can be analysed
analytically
D. Karamshuk, C. Boldrini, M. Conti, and A. Passarella. An arrival based
framework for human mobility modeling. Technical report, IIT CNR, 2011

30. Future Work
● configure the framework with realistic settings
● study socio-spatial properties of human mobility networks, i.e.,
correlation between social and spatial communities, spatial
distribution of the closely linked communities, places vs physical
locations, etc.
● study temporal properties of users' arrivals, i.e., temporal
characteristics of the arrival time sequences, synchronization
between different users' arrivals, etc.

31. Data Sources
● Users checkin in different places
with their GPS-enabled mobile
phones.
● Share their checkins via social
networks, e.g., Twitter, Facebook
● We can collect that information
through public APIs
Location based online social-networks

32. Thank you for attention!