IMT - Institutions Markets TechnologiesInstitute for Advanced Studies

Lucca

Human Mobility Modelsfor Opportunistic Networks

PhD Program in Computer Science and EngineeringXXV Cycle

Dmytro Karamshukdmytro.karamshuk@imtlucca.it

Supervisor: Luciano LenziniCo-supervisor: Marco Conti

February 2012

Why do we study human mobilityWhy 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

Study of Human Mobility Study of Human Mobility

Properties of Human MobilityProperties of Human Mobility

● in human mobility we study in human mobility we study howhow people visitpeople visit different different placesplaces● we are interested in we are interested in socialsocial, , spatialspatial, and , and temporaltemporal characteristics of the characteristics of the visitsvisits

Mobility Properties - SpatialMobility Properties - Spatial

How far we travel from place to place?How far we travel from place to place?

Mobility Properties – TemporalMobility Properties – Temporal

● returning time probability ● visits of top k-th location

How frequently we visit different places?How frequently we visit different places?

Mobility Properties - SocialMobility Properties - Social

How our social ties influence the choice of the places we visit?How our social ties influence the choice of the places we visit?

● 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?

Mobility Properties – Social (another view)Mobility Properties – Social (another view)● inter-contact time

i.e. time between two consecutive contacts of two persons (mobile devices)

● this this inte r-c o nta c t t im e sinte r-c o nta c t t im e s characteristic is crucial for studying mobile social characteristic is crucial for studying mobile social networks, particularly opportunistic networks based on p2p communications networks, particularly opportunistic networks based on p2p communications

● usually this is the usually this is the o utput o f the m o b ility m o de llingo utput o f the m o b ility m o de lling

Mobility Models Mobility Models

● models based on models based on maps of preferred locations maps of preferred locations accounts only on the preferential accounts only on the preferential selection of the places to visitselection of the places to visit

● models based on models based on personal agendaspersonal agendas aim to reproduce temporal details of the aim to reproduce temporal details of the place visiting, e.g., periodical patterns place visiting, e.g., periodical patterns

““Social” Mobility ModelsSocial” Mobility Models

● ““social” models explore social” models explore graphs of social tiesgraphs of social ties to to manage users' manage users' movementsmovements

● in “social” models users in “social” models users account on their account on their friends' friends' positionposition while selecting while selecting next place to gonext place to go

● the graph of the contacts the graph of the contacts might be might be “time-varying”“time-varying”, , i.e., the strength of the i.e., the strength of the ties depends on a ties depends on a particular day, time of particular day, time of day etc.day etc.

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

Conclusion on ModelsConclusion 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

Arrival Based Mobility FrameworkArrival 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

Adding Spatial Dimension to Social GraphsAdding 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 We develop an algorithmalgorithm that: that:● takes a social graph as inputtakes a social graph as input● partitions the graph into a set of overlapping and hierarchically organized cliquespartitions the graph into a set of overlapping and hierarchically organized cliques● generates arrival network by assigning each clique a separate meeting placegenerates arrival network by assigning each clique a separate meeting place

Adding Spatial Dimension to Social GraphsAdding Spatial Dimension to Social GraphsThe The clique partitioningclique partitioning algorithm consists of two main parts: algorithm consists of two main parts:

● finding the cover of the finding the cover of the maximum overlapping cliquesmaximum overlapping cliques in the input social graph (we in the input social graph (we use BronKerbosch algorithm) use BronKerbosch algorithm)

● reproducing reproducing hierarchical cliqueshierarchical cliques structure by randomly splitting the cliques structure by randomly splitting the cliques

ExampleExample

step N1step N1 step N2step N2

step N3step N3 resultresult

Adding Temporal DimensionAdding Temporal Dimension

To characterise the temporal dimension of To characterise the temporal dimension of human mobility we model time sequences of human mobility we model time sequences of users' arrivals to places with stochastic point users' arrivals to places with stochastic point processes. 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.

Case studiesCase studies

Input: ● social graph

● link removal probability for arrival network generating algorithm

● arrival processes for each pair of user and place

Output:● inter-contact times distribution

Case studies - Bernouli ProcessesCase studies - Bernouli Processes

Output:● power law distribution of inter-

contact times

Input:● random graph with number of nodes n and probability of link χ

● removal probability α

● Bernoulli arrival processes with rates where Y is a standard normal random variable

Case studies – Type of ProcessesCase studies – Type of Processes

Input:● similar as in the first case, but arrival

processes with geometric distribution of inter-arrival times and the same distribution of rates

Output:● power law distribution of inter-

contact times

Case studies – Rates DistributionCase studies – Rates Distribution

Input:● similar as in the first case but the

Bernoulli arrival processes with identical rates

Output:● inter-contact times distribution with

exponential shape

Conclusion on the frameworkConclusion 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.

Analytical Analysis – Idea N1Analytical Analysis – Idea N1

Idea N1:Idea N1:● describe contact point process between a pair of users if we know describe contact point process between a pair of users if we know

that the individual arrival processes are independent Bernoulli that the individual arrival processes are independent Bernoulli point processespoint processes

Analytical Analysis – Idea N2Analytical Analysis – Idea N2

● A. Passarella and M. Conti. Characterising aggregate inter-contact times in heterogeneous opportunistic networks. NETWORKING 2011

Idea N2:Idea N2:● derive analytically the aggregate characteristic of the contact derive analytically the aggregate characteristic of the contact

sequences, i.e., aggregate inter-contact times distribution sequences, i.e., aggregate inter-contact times distribution

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.

Analytical Analysis - SchemaAnalytical Analysis - Schema

Analytical Analysis – Contact ProcessAnalytical Analysis – Contact ProcessContacts between two users in a

single meeting place.Contacts between two users in all

shared meeting places.

● The single-place contact process The single-place contact process resulting from independent Bernoulli resulting from independent Bernoulli arrival processes is a Bernoulli arrival arrival processes is a Bernoulli arrival processprocess

● The contact process between The contact process between contacts resulting from single-place contacts resulting from single-place contact processes which, in their turn, contact processes which, in their turn, emerge from independent Bernoulli emerge from independent Bernoulli arrival processes is a Bernoulli arrival processes is a Bernoulli processprocess

Analytical Analysis – RatesAnalytical Analysis – Rates

The rate of a contact process depends on individual arrival rates as: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 Therefore, we can define the distribution of the contact sequences rates by tuning the distribution of the arrival rates.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

Analytical Analysis – Inter-contact timesAnalytical Analysis – Inter-contact times

ConclusionConclusion

● 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 D. Karamshuk, C. Boldrini, M. Conti, and A. Passarella. An arrival based framework for human mobility modeling. Technical report, IIT CNR, 2011framework for human mobility modeling. Technical report, IIT CNR, 2011

Future WorkFuture 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.

Data SourcesData Sources

Location based online social-networksLocation based online social-networks

● 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

Thank you for attention!