Lecture - Sophia Antipolis

Using Complex Networks for Mobility Modeling

Thrasyvoulos (Akis) Spyropoulos

EURECOM www.eurecom.fr/~spyropou

Thrasyvoulos Spyropoulos / spyropoul@eurecom.fr

Eurecom, Sophia-Antipolis

Many domains

Network Design user on the phone

Thrasyvoulos Spyropoulos / spyropou@eurecom.fr

Eurecom, Sophia-Antipolis 2

Mobility Models are Required For:

 Performance evaluation



Analytical Models

• System dynamics must be tractable in order to derive characteristics of interest



Simulations

• Often used as an alternative when models are too complex (no analytical derivation)

• But still complementary to the analytical approach

 Algorithm Design



Networking solutions should be designed according to mobility characteristics



Evaluation of Cellular Networks

 Aim at providing integrated communications (i.e., voice, video, and data) between nomadic subscribers in a seamless fashion

Mobile user will generate handoffs

VLR

Mobile

Switching

Center

HLR

 Input



Arrival rate of new calls (traffic) Mobile user

Generates new call



Arrival rate of handoffs (mobility)

 Output



HLR load, probability of call rejection, mean download per file

Keeps current

User location

4 Thrasyvoulos Spyropoulos / spyropou@eurecom.fr


(Direct) Device-to-Device Communication



Data/Malware Spreading Over D2D

D

F

E

D

A

D

D

B

D

D

C



Contact Process: Due to node mobility



Q: How long until X% of nodes “infected”?



Random Waypoint (RWP) Model (1)

Random Way Point: Basics



Random Waypoint (RWP) Model (2)

1.

2.

3.

4.



A node chooses a random destination anywhere in the network field

The node moves towards that destination with a velocity chosen randomly from [0, Vmax]

After reaching the destination, the node stops for a duration defined by the “pause time” parameter.

This procedure is repeated until the simulation ends

Parameters: Pause time T, max velocity Vmax



RWP Model Shortcomings

1) RWP leads to non-uniform distribution of nodes due to bias towards the center of the area, due to non-uniform direction selection .

2) Average speed decays over time due to nodes getting ‘stuck’ at low speeds



Random (RW) Walk Model (1)

 Similar to RWP but



Nodes change their speed/direction every time slot







New direction  is chosen randomly between (0,2  ]

New speed chosen from uniform (or Gaussian) distribution

When node reaches boundary it bounces back with (   )



Random Walk (2)

Exercise: Does this resolve the 2 RWP problems?



Understanding mobility is complex



Realistic Models Quickly Get VERY complicated!



Classification of Mobility Models

 Scale





Microscopic

- accurately describes the motion of mobile individuals

Macroscopic

- considers the displacement of mobile entities (e.g., pedestrians, vehicles, animals) at a coarse grain, for example in the context of large geographic areas such as adjacent regions or cells

 Inputs



Standard Parameters: speed, direction, …







Additional Inputs: map, topology, preferred/popular locations…

Behavioral: intention, social relations, time-of-day schedule,…

Inherent Randomness: stochastic models (Markov, ODEs, Queuing)

14 Thrasyvoulos Spyropoulos / spyropou@eurecom.fr


A Macroscopic Mob. Model for Cell. Networks

 A simple handover model





 cell -> state need to find transition probabilities depend on road structure, user profile, statistics

0.8

0.2

user on the phone

0.6

0.4

0.5

0.3

0.4

0.2

0.7

0.15

0.2

Cellular Network


Markov Chain


Quick Primer on Markov Chains

P 





0.8

0.6

0.2

0.4





 (π sunny

, π rainy

)  (3/4,1/4)

Stationary Eq.

π i

= Σ j

π j p ji or π = π·P and Σ i

π i

= 1

1) Transitions probabilities can be measured

 get

P  find cell occupancy π

2) Design matrix

P  fit any desired cell occupancy (e.g. “hotspots”)

Issues: a) 1-2 potentially hard to implement b) Is the model “realistic”?

16 Eurecom, Sophia-Antipolis Thrasyvoulos Spyropoulos / spyropou@eurecom.fr

Device-to-Device Networks: Macroscopic View



Connect devices to each other

 Bluetooth, WiFi direct

 It’s all about Contacts!

 Opportunities to exchange data

Contacts are driven by our mobility in a social context!



The Contact Graph



Contact Graph Representation of Mobility

 Represent Mobility using a Social/Complex Graph







Physics, Sociology discipline study of large graphs scale-free, small-world, navigation, etc, strong tie between nodes

• social (friends)

• geographic (familiar strangers) time

Actual Graph (over time) aggregate

Conceptual Graph



Time-based Aggregation

(used by SimBet, BubbleRap)

 „Growing Time Window“ : Edges for all contacts in [0, T]

 „Sliding Time Window“ : Edges for all contacts in [TΔT, T]

Example: ETH trace, 20 nodes on one floor

ΔT = 1h

✗

ΔT = 2h

✔

ΔT = 72h

✗

!

Different networks need different time windows



20

!

Social Properties of Real Mobility Datasets

 Different origins: AP associations, Bluetooth scans and self- reported

 Gowalla dataset

 ~ 440’000 users

 ~ 16.7 Mio check-ins to ~ 1.6 Mio spots

 473 “power users” who check-in 5/7 days



It’s a “small world” after all!

 Small numbers (in parentheses) are for random graph

 Clustering is high and paths are short!



Community Structure

 Louvain community detection algorithm

 All datasets are strongly modular!  clear community structure exists



Do Random Walk Models have Social Behavior?

 „Growing Time Window“ : Edges for all contacts in [0, T]

 „Sliding Time Window“ : Edges for all contacts in [TΔT, T]



24

24

Making Mobility Models “Social”

Random Walk leads to random contact graphs:

Real Mobility leads to contact graphs like this:

3 State-of-the-art Mobility Models

 TVCM: [Hsu et al., Trans. on Networking ‘09] (location-driven, simple)

 Ghost-Simps: [Borrel et al., Trans. on Networking ‘09] (location-driven, complex)

 CMM/HCMM: [Musolesi et al, ACM Realman ‘06] (social/location-driven)

TVCM HCMM



What about Data Spreading via Contacts?

Assumption 1) Underlay Graph  Erdos-Renyi (Poisson)

Assumption 2) Contact Process  Poisson(λ ij

), Indep.

Assumption 3) Contact Rate  λ ij

= λ (homogeneous)

ET dst



1

λ ln(N)

N



26

How realistic is this?

A Poisson Graph


A Real Contact Graph

(ETH Wireless LAN trace)


Arbitrary Contact Graphs



Bounding the Transition Delay

E [ T k , k



1

C a

]

 i



C a

1



,

 ij j



C a

 max

C a





 i



C a

1



,

 ij j



C a







 min

C a

1





 i



C a



,

 ij j



C a







 What are we really saying here??

 Let a = 3  how can split the graph into a subgraph of 3 and a subgraph of N-3 node, by removing a set of edges whose weight sum is minimum ?



A 2nd Bound on Epidemic Delay

  min a





 min

C a a ( N i



C a



,

 ij j



C a







 a )

E [ D epid

]

 a

N 



1 a ( N

1

 a )

 a

 a

N 



1 a ( N

1

 a )





1

 ln N

N

 Φ – conductance: relates to “ min-cut ” of the contact graph

 It also relates to the graph “spectrum” (i.e., eigenvalues )



MERCI!



Lecture - Sophia Antipolis

Data/Malware Spreading Over D2D

Contact Process: Due to node mobility

Q: How long until X% of nodes “infected”?

Contacts are driven by our mobility in a social context!

Time-based Aggregation

Do Random Walk Models have Social Behavior?

What about Data Spreading via Contacts?

MERCI!

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Lecture - Sophia Antipolis

Data/Malware Spreading Over D2D

Contact Process: Due to node mobility

Q: How long until X% of nodes “infected”?

Contacts are driven by our mobility in a social context!

Time-based Aggregation

Do Random Walk Models have Social Behavior?

What about Data Spreading via Contacts?

MERCI!

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